 CoCalc Shared Fileswww / cgi-bin / old_logs / logfile_magma-to_2004-10-11.txt
Author: William A. Stein

************** MAGMA *****************
Host 134.58.253.114 (134.58.253.114)
Time: Wed Sep  8 07:49:06 2004

Input: RR<T>:=PolynomialRing(GF(2));

F<u>:=ext<GF(2) | T^87+T^13+1>;
R<x>:=PolynomialRing(F);

//repeat
f:=x^5+Random(F)*x^3+Random(F)*x^2+Random(F)*x+Random(F);
C:=HyperellipticCurve(f,x^2+x+1);
J:=Jacobian(C);
o:=#J;
order:=Numerator(o/2);
//until IsPrime(order);

Output: Magma V2.11-6     Wed Sep  8 2004 07:48:57 on sha      [Seed = 1846664862]
-------------------------------------

Total time: 7.070 seconds, Total memory usage: 7.09MB

************** MAGMA *****************
Host 134.58.253.114 (134.58.253.114)
Time: Wed Sep  8 07:49:30 2004

Input: RR<T>:=PolynomialRing(GF(2));

F<u>:=ext<GF(2) | T^87+T^13+1>;
R<x>:=PolynomialRing(F);

//repeat
f:=x^5+Random(F)*x^3+Random(F)*x^2+Random(F)*x+Random(F);
C:=HyperellipticCurve(f,x^2+x+1);
J:=Jacobian(C);
o:=#J;
order:=Numerator(o/2);
//until IsPrime(order);
order;

Output: Magma V2.11-6     Wed Sep  8 2004 07:49:23 on sha      [Seed = 1696257535]
-------------------------------------

11972621413014815917488946133041115984685406683095373

Total time: 6.980 seconds, Total memory usage: 7.19MB

************** MAGMA *****************
Host 128.250.6.243 (128.250.6.243)
Time: Wed Sep  8 12:41:19 2004

Input: TatePairing(2,3,4);

Output: Magma V2.11-6     Wed Sep  8 2004 12:41:19 on sha      [Seed = 41710926]
-------------------------------------

>> TatePairing(2,3,4);;
^
User error: Identifier 'TatePairing' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 128.250.6.243 (128.250.6.243)
Time: Wed Sep  8 12:41:30 2004

Input: ?tata

Output: Magma V2.11-6     Wed Sep  8 2004 12:41:30 on sha      [Seed = 108556639]
-------------------------------------

No references for word "tata"

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 128.250.6.243 (128.250.6.243)
Time: Wed Sep  8 12:41:37 2004

Input: ?tate

Output: Magma V2.11-6     Wed Sep  8 2004 12:41:36 on sha      [Seed = 175406377]
-------------------------------------

===============================================================================
PATH: /magma/ring-field-algebra/function-field/Divisors/divisor-class-group/\
TateLichtenbaumPairing
KIND: Intrinsic
===============================================================================
TateLichtenbaumPairing(D1, D2, m) : DivFunElt, DivFunElt, RngIntElt -> RngElt

The Tate--Lichtenbaum pairing Cl_0[m] x Cl_0/mCl_0 -> k.
===============================================================================

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 128.250.6.243 (128.250.6.243)
Time: Wed Sep  8 12:42:50 2004

Input: ?tate

Output: Magma V2.11-6     Wed Sep  8 2004 12:42:49 on sha      [Seed = 275671034]
-------------------------------------

===============================================================================
PATH: /magma/ring-field-algebra/function-field/Divisors/divisor-class-group/\
TateLichtenbaumPairing
KIND: Intrinsic
===============================================================================
TateLichtenbaumPairing(D1, D2, m) : DivFunElt, DivFunElt, RngIntElt -> RngElt

The Tate--Lichtenbaum pairing Cl_0[m] x Cl_0/mCl_0 -> k.
===============================================================================

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 24.125.49.176 (24.125.49.176)
Time: Wed Sep  8 12:51:52 2004

Input: <math display='block'>
<semantics>
<mrow>
<mfrac>
<mrow>
<mn>20</mn>
</mrow>
<mrow>
<mn>1.1</mn>
</mrow>
</mfrac>
<mo>+</mo><mfrac>
<mrow>
<mn>22</mn>
</mrow>
<mrow>
<msup>
<mrow>
<mo stretchy='false'>(</mo><mn>1.1</mn><mo stretchy='false'>)</mo>
</mrow>
<mn>2</mn>
</msup>

</mrow>
</mfrac>
<mo>+</mo><mfrac>
<mrow>
<mn>24</mn>
</mrow>
<mrow>
<msup>
<mrow>
<mo stretchy='false'>(</mo><mn>1.1</mn><mo stretchy='false'>)</mo>
</mrow>
<mn>3</mn>
</msup>

</mrow>
</mfrac>
<mo>+</mo><mfrac>
<mrow>
<mn>26</mn>
</mrow>
<mrow>
<msup>
<mrow>
<mo stretchy='false'>(</mo><mn>1.1</mn><mo stretchy='false'>)</mo>
</mrow>
<mn>4</mn>
</msup>

</mrow>
</mfrac>
<mo>+</mo><mfrac>
<mrow>
<mn>28</mn>
</mrow>
<mrow>
<msup>
<mrow>
<mo stretchy='false'>(</mo><mn>1.1</mn><mo stretchy='false'>)</mo>
</mrow>
<mn>5</mn>
</msup>

</mrow>
</mfrac>
<mo>=</mo>
</mrow>
<annotation encoding='MathType-MTEF'>
</annotation>
</semantics>
[/itex]

Output: Magma V2.11-6     Wed Sep  8 2004 12:51:51 on sha      [Seed = 3668222750]
-------------------------------------

>> <math display='block'>
^

>>       <mrow>
^

>>             <mrow>
^

>>                <mn>20</mn>
^

>>             </mrow>
^

>>                <mn>1.1</mn>
^

>>             </mrow>
^

>>          </mfrac>
^

>>          <mo>+</mo><mfrac>
^

>>                <mn>22</mn>
^

>>             </mrow>
^

>>                <msup>
^

>>                      <mo stretchy='false'>(</mo><mn>1.1</mn><mo stretchy='f
^

>>                   </mrow>
^

>>                   <mn>2</mn>
^

>>                </msup>
^

>>             </mrow>
^

>>          </mfrac>
^

>>          <mo>+</mo><mfrac>
^

>>                <mn>24</mn>
^

>>             </mrow>
^

>>                <msup>
^

>>                      <mo stretchy='false'>(</mo><mn>1.1</mn><mo stretchy='f
^

>>                   </mrow>
^

>>                   <mn>3</mn>
^

>>                </msup>
^

>>             </mrow>
^

>>          </mfrac>
^

>>          <mo>+</mo><mfrac>
^

>>                <mn>26</mn>
^

>>             </mrow>
^

>>                <msup>
^

>>                      <mo stretchy='false'>(</mo><mn>1.1</mn><mo stretchy='f
^

>>                   </mrow>
^

>>                   <mn>4</mn>
^

>>                </msup>
^

>>             </mrow>
^

>>          </mfrac>
^

>>          <mo>+</mo><mfrac>
^

>>                <mn>28</mn>
^

>>             </mrow>
^

>>                <msup>
^

>>                      <mo stretchy='false'>(</mo><mn>1.1</mn><mo stretchy='f
^

>>                   </mrow>
^

>>                   <mn>5</mn>
^

>>                </msup>
^

>>             </mrow>
^

>>          </mfrac>
^

>>          <mo>=</mo>
^

>>       </mrow>
^

>>       <annotation encoding='MathType-MTEF'>
^

>>          [email protected]@[email protected]@+=faaafaart1ev1aaat0uyJj1BTfMBaerbuLwBLnharmWu51
^

>>       </annotation>
^

>>    </semantics>
^

>> [/itex]
^

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 194.42.0.254 (194.42.0.254)
Time: Wed Sep  8 15:17:10 2004

Input: SetVerbose("Code",true);

print(MinimumDistance(QRCode(GF(2),161)));

Output: Magma V2.11-6     Wed Sep  8 2004 15:17:10 on sha      [Seed = 4119588390]
-------------------------------------

Linear Code over GF(2) of length 161 with 114 generators. Is cyclic
Lower Bound: 1, Upper Bound: 48
BCHBound gives the lower bound = 4
Cyclic codes require enumeration of only  one generator matrix (rank 114)
Time Taken: 0.00
Starting search for low weight codewords... (reset timings)
Enumerating using 1 generator at a time:
New codeword identified of weight 23, time 0.00
New codeword identified of weight 22, time 0.00
New codeword identified of weight 21, time 0.00
New codeword identified of weight 20, time 0.00
New codeword identified of weight 4, time 0.00
Completed: lower =  3, upper =  4. Elapsed: 0.00s
Enumerating using 2 generators at a time:
Completed: lower =  5, upper =  4. Elapsed: 0.00s
Final Results: lower = 5, upper = 4, Total time: 0.00
4

Total time: 0.199 seconds, Total memory usage: 3.66MB

************** MAGMA *****************
Host 194.42.0.254 (194.42.0.254)
Time: Wed Sep  8 15:17:58 2004

Input: SetVerbose("Code",true);
print("gf2 n151 QR");
print(MinimumDistance(QRCode(GF(2),151)));
save"QRcodes.var";
print("gf2 n161 QR");
print(MinimumDistance(QRCode(GF(2),161)));
save"QRcodes.var";
print("gf2 n167 QR");
print(MinimumDistance(QRCode(GF(2),167)));
save"QRcodes.var";
print("gf2 n191 QR");
print(MinimumDistance(QRCode(GF(2),191)));

Output: WARNING: MAGMA command contains unsafe command 'save', so it will not be executed.

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:19:48 2004

Input: ModularSymbols(980948945);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-6     Wed Sep  8 2004 17:19:48 on sha      [Seed = 3166866087]
-------------------------------------

Current total memory usage: 3.6MB, failed memory request: 17961.6MB
System Error: User memory limit has been reached

Total time: 0.199 seconds, Total memory usage: 3.76MB

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:19:55 2004

Input: ModularSymbols(980948);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-6     Wed Sep  8 2004 17:19:53 on sha      [Seed = 3100020398]
-------------------------------------

Current total memory usage: 62.1MB, failed memory request: 61.9MB
System Error: User memory limit has been reached

Total time: 1.669 seconds, Total memory usage: 65.09MB

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:20:35 2004

Input: while true
x := 2;
end while;

Output: Magma V2.11-6     Wed Sep  8 2004 17:20:35 on sha      [Seed = 2999747710]
-------------------------------------

>>    x := 2;
^

>> end while;;
^

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:22:00 2004

Input: while true do
x := 2;
end while;

Output: Magma V2.11-6     Wed Sep  8 2004 17:21:54 on sha      [Seed = 2281287962]
-------------------------------------

Errors: /bin/sh: line 1: 12008 Killed                  /usr/local/bin/magma

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:22:07 2004

Input: while true do
x := 2;
end while;

Output: Magma V2.11-6     Wed Sep  8 2004 17:20:40 on sha      [Seed = 2414983496]
-------------------------------------

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:22:57 2004

Input: while true do
x := 2;
end while;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep  8 2004 17:22:36 on sha      [Seed = 2682365676]
-------------------------------------

Errors: /bin/sh: line 1: 12016 Killed                  /usr/local/bin/magma

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:23:22 2004

Input: while true do
x := 2;
end while;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep  8 2004 17:23:01 on sha      [Seed = 2548674253]
-------------------------------------

Errors: /bin/sh: line 1: 12024 Killed                  nice /usr/local/bin/magma

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:23:38 2004

Input: while true do
x := 2;
end while;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep  8 2004 17:23:16 on sha      [Seed = 1612601674]
-------------------------------------

Errors: /bin/sh: line 1: 12046 Killed                  nice -n 19 /usr/local/bin/magma

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:39:30 2004

Input: 2+2

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep  8 2004 17:39:30 on sha      [Seed = 1896827921]
-------------------------------------

4

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:39:33 2004

Input: 2+2

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep  8 2004 17:39:32 on sha      [Seed = 2130788889]
-------------------------------------

4

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 140.247.241.194 (140.247.241.194)
Time: Wed Sep  8 17:39:57 2004

Input: 2+2

Output: Magma V2.11-6     Wed Sep  8 2004 17:39:56 on sha      [Seed = 4169581990]
-------------------------------------

4

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Fri Sep 10 15:09:49 2004

Input: G:=GongruenceSubgroup(12);
Generators(G);

Output: Magma V2.11-6     Fri Sep 10 2004 15:09:49 on sha      [Seed = 1633803204]
-------------------------------------

>> G:=GongruenceSubgroup(12);
^
User error: Identifier 'GongruenceSubgroup' has not been declared or assigned

>> Generators(G);;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Fri Sep 10 15:10:18 2004

Input: G:=CongruenceSubgroup(12);
Generators(G);

Output: Magma V2.11-6     Fri Sep 10 2004 15:10:02 on sha      [Seed = 1718016820]
-------------------------------------

[
[ 23 -12]
[ 48 -25],

[  83  -48]
[ 396 -229],

[ 143  -84]
[ 492 -289],

[  59  -36]
[ 336 -205],

[ 215 -132]
[ 588 -361],

[ 227 -144]
[ 588 -373],

[ 131  -84]
[ 432 -277],

[ 155 -108]
[ 432 -301],

[ 203 -144]
[ 492 -349],

[  47  -36]
[ 252 -193],

[ 167 -132]
[ 396 -313],

[  59  -48]
[ 252 -205],

[ 131 -108]
[ 336 -277],

[ 35 -12]
[108 -37],

[ 227  -84]
[1008 -373],

[  95  -36]
[ 636 -241],

[ 347 -132]
[1296 -493],

[ 371 -144]
[1332 -517],

[ 263 -108]
[ 996 -409],

[ 347 -144]
[1188 -493],

[  83  -36]
[ 528 -229],

[ 299 -132]
[1008 -445],

[ 107  -48]
[ 564 -253],

[ 239 -108]
[ 852 -385],

[ 131  -72]
[ 504 -277],

[ 109  -60]
[ 456 -251],

[ 107  -60]
[ 708 -397],

[ 277 -156]
[ 744 -419],

[ 275 -156]
[ 996 -565],

[ 455 -264]
[1284 -745],

[ 371 -216]
[ 888 -517],

[ 527 -312]
[1380 -817],

[ 311 -192]
[1440 -889],

[ 563 -348]
[1380 -853],

[ 347 -216]
[ 792 -493],

[ 325 -204]
[ 744 -467],

[ 539 -348]
[1284 -829],

[  37  -24]
[ 276 -179],

[  35  -24]
[ 264 -181],

[ 191 -132]
[ 696 -481],

[ 563 -396]
[1008 -709],

[ 167 -120]
[ 636 -457],

[  599  -432]
[ 1632 -1177],

[  83  -60]
[ 516 -373],

[ 215 -156]
[ 696 -505],

[ 263 -192]
[1152 -841],

[ 803 -588]
[1296 -949],

[ 587 -432]
[ 996 -733],

[ 179 -132]
[ 636 -469],

[ 311 -240]
[1152 -889],

[ 635 -492]
[1008 -781],

[  551  -432]
[ 1440 -1129],

[ 143 -120]
[ 516 -433],

[ 311 -264]
[ 708 -601],

[  83  -72]
[ 264 -229],

[ 479 -132]
[2268 -625],

[ 515 -144]
[2364 -661],

[ 491 -144]
[2172 -637],

[ 431 -132]
[1884 -577],

[ 347 -108]
[1584 -493],

[ 169  -60]
[ 876 -311],

[ 433 -156]
[1596 -575],

[ 431 -156]
[1992 -721],

[ 587 -216]
[1992 -733],

[  503  -192]
[ 2832 -1081],

[ 563 -216]
[1848 -709],

[  887  -348]
[ 3000 -1177],

[  61  -24]
[ 516 -203],

[  59  -24]
[ 504 -205],

[ 1031  -432]
[ 3840 -1609],

[ 371 -156]
[1572 -661],

[ 1019  -432]
[ 2748 -1165],

[ 311 -132]
[1416 -601],

[  551  -240]
[ 2592 -1129],

[ 263 -120]
[1212 -553],

[ 575 -264]
[1884 -865],

[  61  -36]
[ 588 -347],

[ 1103  -684]
[ 4104 -2545],

[  647  -408]
[ 2856 -1801],

[  443  -312]
[ 2472 -1741],

[  647  -456]
[ 2964 -2089],

[  323  -252]
[ 1524 -1189],

[  875  -684]
[ 2964 -2317],

[ 109  -96]
[ 612 -539],

[ 121 -108]
[ 456 -407],

[ 455 -108]
[2532 -601],

[ 589 -156]
[2760 -731],

[ 527 -156]
[2760 -817],

[ 1451  -432]
[ 5364 -1597],

[ 443 -132]
[2460 -733],

[  97  -36]
[1032 -383],

[  601  -336]
[ 3132 -1751],

[  901  -504]
[ 3924 -2195],

[ 1883  -432]
[ 8844 -2029],

[ 133  -36]
[1548 -419],

[-1  0]
[12 -1],

[169 -36]
[108 -23]
]

Total time: 15.589 seconds, Total memory usage: 79.63MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Fri Sep 10 15:10:33 2004

Input: G:=CongruenceSubgroup(12);
Generators(G);

Output: Magma V2.11-6     Fri Sep 10 2004 15:10:14 on sha      [Seed = 421110871]
-------------------------------------

[
[ 23 -12]
[ 48 -25],

[  83  -48]
[ 396 -229],

[ 143  -84]
[ 492 -289],

[  59  -36]
[ 336 -205],

[ 215 -132]
[ 588 -361],

[ 227 -144]
[ 588 -373],

[ 131  -84]
[ 432 -277],

[ 155 -108]
[ 432 -301],

[ 203 -144]
[ 492 -349],

[  47  -36]
[ 252 -193],

[ 167 -132]
[ 396 -313],

[  59  -48]
[ 252 -205],

[ 131 -108]
[ 336 -277],

[ 35 -12]
[108 -37],

[ 227  -84]
[1008 -373],

[  95  -36]
[ 636 -241],

[ 347 -132]
[1296 -493],

[ 371 -144]
[1332 -517],

[ 263 -108]
[ 996 -409],

[ 347 -144]
[1188 -493],

[  83  -36]
[ 528 -229],

[ 299 -132]
[1008 -445],

[ 107  -48]
[ 564 -253],

[ 239 -108]
[ 852 -385],

[ 131  -72]
[ 504 -277],

[ 109  -60]
[ 456 -251],

[ 107  -60]
[ 708 -397],

[ 277 -156]
[ 744 -419],

[ 275 -156]
[ 996 -565],

[ 455 -264]
[1284 -745],

[ 371 -216]
[ 888 -517],

[ 527 -312]
[1380 -817],

[ 311 -192]
[1440 -889],

[ 563 -348]
[1380 -853],

[ 347 -216]
[ 792 -493],

[ 325 -204]
[ 744 -467],

[ 539 -348]
[1284 -829],

[  37  -24]
[ 276 -179],

[  35  -24]
[ 264 -181],

[ 191 -132]
[ 696 -481],

[ 563 -396]
[1008 -709],

[ 167 -120]
[ 636 -457],

[  599  -432]
[ 1632 -1177],

[  83  -60]
[ 516 -373],

[ 215 -156]
[ 696 -505],

[ 263 -192]
[1152 -841],

[ 803 -588]
[1296 -949],

[ 587 -432]
[ 996 -733],

[ 179 -132]
[ 636 -469],

[ 311 -240]
[1152 -889],

[ 635 -492]
[1008 -781],

[  551  -432]
[ 1440 -1129],

[ 143 -120]
[ 516 -433],

[ 311 -264]
[ 708 -601],

[  83  -72]
[ 264 -229],

[ 479 -132]
[2268 -625],

[ 515 -144]
[2364 -661],

[ 491 -144]
[2172 -637],

[ 431 -132]
[1884 -577],

[ 347 -108]
[1584 -493],

[ 169  -60]
[ 876 -311],

[ 433 -156]
[1596 -575],

[ 431 -156]
[1992 -721],

[ 587 -216]
[1992 -733],

[  503  -192]
[ 2832 -1081],

[ 563 -216]
[1848 -709],

[  887  -348]
[ 3000 -1177],

[  61  -24]
[ 516 -203],

[  59  -24]
[ 504 -205],

[ 1031  -432]
[ 3840 -1609],

[ 371 -156]
[1572 -661],

[ 1019  -432]
[ 2748 -1165],

[ 311 -132]
[1416 -601],

[  551  -240]
[ 2592 -1129],

[ 263 -120]
[1212 -553],

[ 575 -264]
[1884 -865],

[  61  -36]
[ 588 -347],

[ 1103  -684]
[ 4104 -2545],

[  647  -408]
[ 2856 -1801],

[  443  -312]
[ 2472 -1741],

[  647  -456]
[ 2964 -2089],

[  323  -252]
[ 1524 -1189],

[  875  -684]
[ 2964 -2317],

[ 109  -96]
[ 612 -539],

[ 121 -108]
[ 456 -407],

[ 455 -108]
[2532 -601],

[ 589 -156]
[2760 -731],

[ 527 -156]
[2760 -817],

[ 1451  -432]
[ 5364 -1597],

[ 443 -132]
[2460 -733],

[  97  -36]
[1032 -383],

[  601  -336]
[ 3132 -1751],

[  901  -504]
[ 3924 -2195],

[ 1883  -432]
[ 8844 -2029],

[ 133  -36]
[1548 -419],

[-1  0]
[12 -1],

[169 -36]
[108 -23]
]

Total time: 15.580 seconds, Total memory usage: 79.63MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Fri Sep 10 15:10:48 2004

Input: G:=CongruenceSubgroup(12);
Generators(G);

Output: Magma V2.11-6     Fri Sep 10 2004 15:10:25 on sha      [Seed = 488480868]
-------------------------------------

[
[ 23 -12]
[ 48 -25],

[  83  -48]
[ 396 -229],

[ 143  -84]
[ 492 -289],

[  59  -36]
[ 336 -205],

[ 215 -132]
[ 588 -361],

[ 227 -144]
[ 588 -373],

[ 131  -84]
[ 432 -277],

[ 155 -108]
[ 432 -301],

[ 203 -144]
[ 492 -349],

[  47  -36]
[ 252 -193],

[ 167 -132]
[ 396 -313],

[  59  -48]
[ 252 -205],

[ 131 -108]
[ 336 -277],

[ 35 -12]
[108 -37],

[ 227  -84]
[1008 -373],

[  95  -36]
[ 636 -241],

[ 347 -132]
[1296 -493],

[ 371 -144]
[1332 -517],

[ 263 -108]
[ 996 -409],

[ 347 -144]
[1188 -493],

[  83  -36]
[ 528 -229],

[ 299 -132]
[1008 -445],

[ 107  -48]
[ 564 -253],

[ 239 -108]
[ 852 -385],

[ 131  -72]
[ 504 -277],

[ 109  -60]
[ 456 -251],

[ 107  -60]
[ 708 -397],

[ 277 -156]
[ 744 -419],

[ 275 -156]
[ 996 -565],

[ 455 -264]
[1284 -745],

[ 371 -216]
[ 888 -517],

[ 527 -312]
[1380 -817],

[ 311 -192]
[1440 -889],

[ 563 -348]
[1380 -853],

[ 347 -216]
[ 792 -493],

[ 325 -204]
[ 744 -467],

[ 539 -348]
[1284 -829],

[  37  -24]
[ 276 -179],

[  35  -24]
[ 264 -181],

[ 191 -132]
[ 696 -481],

[ 563 -396]
[1008 -709],

[ 167 -120]
[ 636 -457],

[  599  -432]
[ 1632 -1177],

[  83  -60]
[ 516 -373],

[ 215 -156]
[ 696 -505],

[ 263 -192]
[1152 -841],

[ 803 -588]
[1296 -949],

[ 587 -432]
[ 996 -733],

[ 179 -132]
[ 636 -469],

[ 311 -240]
[1152 -889],

[ 635 -492]
[1008 -781],

[  551  -432]
[ 1440 -1129],

[ 143 -120]
[ 516 -433],

[ 311 -264]
[ 708 -601],

[  83  -72]
[ 264 -229],

[ 479 -132]
[2268 -625],

[ 515 -144]
[2364 -661],

[ 491 -144]
[2172 -637],

[ 431 -132]
[1884 -577],

[ 347 -108]
[1584 -493],

[ 169  -60]
[ 876 -311],

[ 433 -156]
[1596 -575],

[ 431 -156]
[1992 -721],

[ 587 -216]
[1992 -733],

[  503  -192]
[ 2832 -1081],

[ 563 -216]
[1848 -709],

[  887  -348]
[ 3000 -1177],

[  61  -24]
[ 516 -203],

[  59  -24]
[ 504 -205],

[ 1031  -432]
[ 3840 -1609],

[ 371 -156]
[1572 -661],

[ 1019  -432]
[ 2748 -1165],

[ 311 -132]
[1416 -601],

[  551  -240]
[ 2592 -1129],

[ 263 -120]
[1212 -553],

[ 575 -264]
[1884 -865],

[  61  -36]
[ 588 -347],

[ 1103  -684]
[ 4104 -2545],

[  647  -408]
[ 2856 -1801],

[  443  -312]
[ 2472 -1741],

[  647  -456]
[ 2964 -2089],

[  323  -252]
[ 1524 -1189],

[  875  -684]
[ 2964 -2317],

[ 109  -96]
[ 612 -539],

[ 121 -108]
[ 456 -407],

[ 455 -108]
[2532 -601],

[ 589 -156]
[2760 -731],

[ 527 -156]
[2760 -817],

[ 1451  -432]
[ 5364 -1597],

[ 443 -132]
[2460 -733],

[  97  -36]
[1032 -383],

[  601  -336]
[ 3132 -1751],

[  901  -504]
[ 3924 -2195],

[ 1883  -432]
[ 8844 -2029],

[ 133  -36]
[1548 -419],

[-1  0]
[12 -1],

[169 -36]
[108 -23]
]

Total time: 15.580 seconds, Total memory usage: 79.63MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Fri Sep 10 15:11:08 2004

Input: G:=CongruenceSubgroup(6);
Generators(G);

Output: Magma V2.11-6     Fri Sep 10 2004 15:11:07 on sha      [Seed = 370584325]
-------------------------------------

[
[ 11  -6]
[ 24 -13],

[ 17  -6]
[ 54 -19],

[ 29 -18]
[108 -67],

[ 19 -12]
[ 84 -53],

[ 17 -12]
[ 78 -55],

[ 41 -30]
[108 -79],

[ 23 -18]
[ 78 -61],

[-1  0]
[ 6 -1],

[ 31 -12]
[168 -65],

[ 29 -12]
[162 -67],

[  71  -30]
[ 258 -109],

[  37  -30]
[ 132 -107],

[ 7 -6]
[ 6 -5]
]

Total time: 0.490 seconds, Total memory usage: 5.01MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Fri Sep 10 15:11:34 2004

Input: G:=CongruenceSubgroup(0,6);
Generators(G);

Output: Magma V2.11-6     Fri Sep 10 2004 15:11:34 on sha      [Seed = 185316917]
-------------------------------------

[
[1 1]
[0 1],

[ 1 -1]
[ 6 -5],

[ 5 -3]
[12 -7]
]

Total time: 0.190 seconds, Total memory usage: 3.76MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Fri Sep 10 15:11:49 2004

Input: G:=CongruenceSubgroup(1,6);
Generators(G);

Output: Magma V2.11-6     Fri Sep 10 2004 15:11:49 on sha      [Seed = 50576942]
-------------------------------------

[
[1 1]
[0 1],

[ 1 -1]
[ 6 -5],

[ 5 -3]
[12 -7]
]

Total time: 0.200 seconds, Total memory usage: 3.86MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Fri Sep 10 15:12:03 2004

Input: G:=CongruenceSubgroup(6);
Generators(G);

Output: Magma V2.11-6     Fri Sep 10 2004 15:12:03 on sha      [Seed = 943228387]
-------------------------------------

[
[ 11  -6]
[ 24 -13],

[ 17  -6]
[ 54 -19],

[ 29 -18]
[108 -67],

[ 19 -12]
[ 84 -53],

[ 17 -12]
[ 78 -55],

[ 41 -30]
[108 -79],

[ 23 -18]
[ 78 -61],

[-1  0]
[ 6 -1],

[ 31 -12]
[168 -65],

[ 29 -12]
[162 -67],

[  71  -30]
[ 258 -109],

[  37  -30]
[ 132 -107],

[ 7 -6]
[ 6 -5]
]

Total time: 0.490 seconds, Total memory usage: 5.01MB

************** MAGMA *****************
Host 200.104.149.67 (200.104.149.67)
Time: Fri Sep 10 16:34:10 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Fri Sep 10 2004 16:34:10 on sha      [Seed = 1330381271]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.210 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 216.51.235.246 (216.51.235.246)
Time: Sat Sep 11 01:36:59 2004

Input: x/3-3x/4=1/12

Output: Magma V2.11-6     Sat Sep 11 2004 01:36:30 on modular  [Seed = 3587578458]
-------------------------------------

>> x/3-3x/4=1/12;
^

Total time: 0.300 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 216.51.235.246 (216.51.235.246)
Time: Sat Sep 11 01:37:02 2004

Input: x/3-3x/4=1/12

Output: Magma V2.11-6     Sat Sep 11 2004 01:36:59 on modular  [Seed = 3654948418]
-------------------------------------

>> x/3-3x/4=1/12;
^

Total time: 0.230 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 216.51.235.246 (216.51.235.246)
Time: Sat Sep 11 01:37:02 2004

Input: x/3-3x/4=1/12

Output: Magma V2.11-6     Sat Sep 11 2004 01:36:59 on modular  [Seed = 3705606983]
-------------------------------------

>> x/3-3x/4=1/12;
^

Total time: 0.230 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 216.51.235.246 (216.51.235.246)
Time: Sat Sep 11 01:37:50 2004

Input: x/3-3x/4=1/12

Output: Magma V2.11-6     Sat Sep 11 2004 01:37:27 on modular  [Seed = 2897175250]
-------------------------------------

>> x/3-3x/4=1/12;
^

Total time: 0.270 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 216.51.235.246 (216.51.235.246)
Time: Sat Sep 11 01:37:50 2004

Input: x/3-3x/4=1/12

Output: Magma V2.11-6     Sat Sep 11 2004 01:37:29 on modular  [Seed = 2964553422]
-------------------------------------

>> x/3-3x/4=1/12;
^

Total time: 0.270 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 216.51.235.246 (216.51.235.246)
Time: Sat Sep 11 01:37:50 2004

Input: x/3-3x/4=1/12

Output: Magma V2.11-6     Sat Sep 11 2004 01:37:29 on modular  [Seed = 2997976268]
-------------------------------------

>> x/3-3x/4=1/12;
^

Total time: 0.300 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 217.250.186.117 (217.250.186.117)
Time: Sat Sep 11 10:12:07 2004

Input: A:=Matrix(Integers(),8,8,[2,0,1,1,1,0,0,1,0,2,-1,1,0,1,-1,0,1,-1,2,0,1,0,1,1,1,1,0,2,0,1,-1,1,1,0,1,0,2,0,1,1,0,1,0,1,0,2,-1,1,
0,-1,1,-1,1,-1,2,0,1,0,1,1,1,1,0,2]);
B:=Matrix(Integers(),8,8,[2,0,1,1,0,1,1,0,0,2,-1,1,-1,0,0,1,1,-1,2,0,1,1,1,0,1,1,0,2,-1,1,0,1,0,-1,1,-1,2,0,1,0,1,0,1,1,0,2,0,
1,1,0,1,0,1,0,2,0,0,1,0,1,0,1,0,2]);
L1:=LatticeWithGram(A);
L2:=LatticeWithGram(B);
IsIsomorphic(L1,L2);

Output: Magma V2.11-6     Sat Sep 11 2004 10:12:02 on modular  [Seed = 3031888483]
-------------------------------------

true
[ 0  0 -1  0 -1  0  1  1]
[-1  0  1  0  0  0 -1  0]
[ 1  0 -1  0 -1  0  1  0]
[-1  0  0  0  0 -1 -1  1]
[ 1  0 -1  0  0  1  1 -1]
[ 1  0 -1 -1 -1  0  0  1]
[ 0 -1 -1  1  0  1  1 -1]
[ 0  0  0 -1  0  0 -1  0]

Total time: 0.280 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Sat Sep 11 11:02:45 2004

Input: G:=CongruenceGroup(6);
Generators(G);

Output: Magma V2.11-6     Sat Sep 11 2004 11:02:13 on modular  [Seed = 2677919098]
-------------------------------------

>> G:=CongruenceGroup(6);
^
Runtime error in 'CongruenceGroup': Bad argument types
Argument types given: RngIntElt

>> Generators(G);;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 0.430 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Sat Sep 11 11:03:40 2004

Input: G:=CongruenceSubgroup(6);
Generators(G);

Output: Magma V2.11-6     Sat Sep 11 2004 11:03:28 on modular  [Seed = 1717843137]
-------------------------------------

[
[ 11  -6]
[ 24 -13],

[ 17  -6]
[ 54 -19],

[ 29 -18]
[108 -67],

[ 19 -12]
[ 84 -53],

[ 17 -12]
[ 78 -55],

[ 41 -30]
[108 -79],

[ 23 -18]
[ 78 -61],

[-1  0]
[ 6 -1],

[ 31 -12]
[168 -65],

[ 29 -12]
[162 -67],

[  71  -30]
[ 258 -109],

[  37  -30]
[ 132 -107],

[ 7 -6]
[ 6 -5]
]

Total time: 0.560 seconds, Total memory usage: 5.01MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Sat Sep 11 12:19:16 2004

Input: NumberOfSmallGroups(72);

Output: Magma V2.11-6     Sat Sep 11 2004 12:18:40 on modular  [Seed = 454655771]
-------------------------------------

50

Total time: 0.360 seconds, Total memory usage: 3.76MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Sat Sep 11 12:19:57 2004

Input: NumberOfSmallGroups(72,1);

Output: Magma V2.11-6     Sat Sep 11 2004 12:19:42 on modular  [Seed = 3806365211]
-------------------------------------

>> NumberOfSmallGroups(72,1);;
^
Runtime error in 'NumberOfSmallGroups': Bad argument types
Argument types given: RngIntElt, RngIntElt

Total time: 0.210 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Sat Sep 11 12:20:54 2004

Input: SmallGroups(72,1);

Output: Magma V2.11-6     Sat Sep 11 2004 12:20:46 on modular  [Seed = 3991898452]
-------------------------------------

>> SmallGroups(72,1);;
^
Runtime error in 'SmallGroups': Bad argument types
Argument types given: RngIntElt, RngIntElt

Total time: 0.230 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 169.226.140.70 (169.226.140.70)
Time: Sat Sep 11 12:21:15 2004

Input: SmallGroup(72,1);

Output: Magma V2.11-6     Sat Sep 11 2004 12:21:06 on modular  [Seed = 3907685497]
-------------------------------------

GrpPC of order 72 = 2^3 * 3^2
PC-Relations:
$.1^2 =$.2,
$.2^2 =$.3,
$.3^2 = Id($),
$.4^3 =$.5^2,
$.5^3 = Id($),
$.4^$.1 = $.4^2 *$.5,
$.5^$.1 = $.5^2 Total time: 0.240 seconds, Total memory usage: 3.76MB ************** MAGMA ***************** Host 68.163.241.150 (68.163.241.150) Time: Sun Sep 12 00:12:01 2004 Input: -0.02y+0.12(6000-y)=0.11y Output: Magma V2.11-6 Sun Sep 12 2004 00:11:58 on modular [Seed = 3132634968] ------------------------------------- >> -0.02y+0.12(6000-y)=0.11y; ^ User error: bad syntax Total time: 0.270 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 80.104.0.185 (80.104.0.185) Time: Sun Sep 12 08:14:42 2004 Input: 2x2 Output: Magma V2.11-6 Sun Sep 12 2004 08:14:42 on modular [Seed = 2425744465] ------------------------------------- 2 Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 80.142.110.23 (80.142.110.23) Time: Sun Sep 12 13:12:36 2004 Input: ifactor(775139191012273984388703707055959000141260608208859938488201038230553380806865010064853296771374) Output: Magma V2.11-6 Sun Sep 12 2004 13:12:33 on modular [Seed = 3991416600] ------------------------------------- >> ifactor(7751391910122739843887037070559590001412606082088599384882010382305 ^ User error: Identifier 'ifactor' has not been declared or assigned Total time: 0.220 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 80.142.110.23 (80.142.110.23) Time: Sun Sep 12 13:12:50 2004 Input: ifactor(775139191012273984388703707055959000141260608208859938488201038230553380806865010064853296771374); Output: Magma V2.11-6 Sun Sep 12 2004 13:12:50 on modular [Seed = 3620869426] ------------------------------------- >> ifactor(7751391910122739843887037070559590001412606082088599384882010382305 ^ User error: Identifier 'ifactor' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 80.142.110.23 (80.142.110.23) Time: Sun Sep 12 13:13:38 2004 Input: factor(775139191012273984388703707055959000141260608208859938488201038230553380806865010064853296771374); Output: Magma V2.11-6 Sun Sep 12 2004 13:13:37 on modular [Seed = 3755613545] ------------------------------------- >> factor(77513919101227398438870370705595900014126060820885993848820103823055 ^ User error: Identifier 'factor' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 80.142.110.23 (80.142.110.23) Time: Sun Sep 12 13:16:06 2004 Input: Factorization(775139191012273984388703707055959000141260608208859938488201038230553380806865010064853296771374); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Sun Sep 12 2004 13:15:45 on modular [Seed = 3672055788] ------------------------------------- Errors: /bin/sh: line 1: 13997 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 24.185.209.9 (24.185.209.9) Time: Sun Sep 12 20:30:42 2004 Input: 3578! Output: Magma V2.11-6 Sun Sep 12 2004 20:30:40 on modular [Seed = 774604128] ------------------------------------- >> 3578!; ^ User error: bad syntax Total time: 0.230 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 129.78.64.100 (129.78.64.100) Time: Mon Sep 13 00:29:39 2004 Input: 1; Output: Magma V2.11-6 Mon Sep 13 2004 00:29:36 on modular [Seed = 4042560470] ------------------------------------- 1 Total time: 0.230 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Mon Sep 13 13:45:26 2004 Input: R<x>:=PolynomialRing(RationalField()); K<a>:=NumberField(x^5+7*x^4+3x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.11-6 Mon Sep 13 2004 13:45:25 on modular [Seed = 825601185] ------------------------------------- >> K<a>:=NumberField(x^5+7*x^4+3x^2-x+1); ^ User error: Invalid hexadecimal integer >> OK:=MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned >> I:=2*OK; ^ User error: Identifier 'OK' has not been declared or assigned >> Factorization(I);; ^ User error: Identifier 'I' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Mon Sep 13 13:45:41 2004 Input: R<x>:=PolynomialRing(RationalField()); K<a>:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=2*OK; Factorization(I); Output: Magma V2.11-6 Mon Sep 13 2004 13:45:40 on modular [Seed = 1010344413] ------------------------------------- [ <Principal Prime Ideal of OK Generator: [2, 0, 0, 0, 0], 1> ] Total time: 0.190 seconds, Total memory usage: 3.56MB ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Mon Sep 13 13:46:11 2004 Input: R<x>:=PolynomialRing(RationalField()); K<a>:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=5*OK; Factorization(I); Output: Magma V2.11-6 Mon Sep 13 2004 13:46:11 on modular [Seed = 994027261] ------------------------------------- [ <Prime Ideal of OK Two element generators: [5, 0, 0, 0, 0] [2, 1, 0, 0, 0], 1>, <Prime Ideal of OK Two element generators: [5, 0, 0, 0, 0] [3, 1, 0, 0, 0], 2>, <Prime Ideal of OK Two element generators: [5, 0, 0, 0, 0] [2, 4, 1, 0, 0], 1> ] Total time: 0.180 seconds, Total memory usage: 3.56MB ************** MAGMA ***************** Host 130.113.105.244 (130.113.105.244) Time: Mon Sep 13 13:46:40 2004 Input: R<x>:=PolynomialRing(RationalField()); K<a>:=NumberField(x^5+7*x^4+3*x^2-x+1); OK:=MaximalOrder(K); I:=10*OK; Factorization(I); Output: Magma V2.11-6 Mon Sep 13 2004 13:46:39 on modular [Seed = 302554] ------------------------------------- [ <Principal Prime Ideal of OK Generator: [2, 0, 0, 0, 0], 1>, <Prime Ideal of OK Two element generators: [5, 0, 0, 0, 0] [2, 1, 0, 0, 0], 1>, <Prime Ideal of OK Two element generators: [5, 0, 0, 0, 0] [3, 1, 0, 0, 0], 2>, <Prime Ideal of OK Two element generators: [5, 0, 0, 0, 0] [2, 4, 1, 0, 0], 1> ] Total time: 0.190 seconds, Total memory usage: 3.56MB ************** MAGMA ***************** Host 38.112.109.12 (38.112.109.12) Time: Mon Sep 13 14:08:04 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Mon Sep 13 2004 14:08:03 on modular [Seed = 1533016189] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:46:51 2004 Input: (r1+b)*sin w3 = x2-x3+(r1+a)*(x1-x2+r1*sin w1)/(r1+a) Output: Magma V2.11-6 Mon Sep 13 2004 14:46:51 on modular [Seed = 2644064162] ------------------------------------- >> (r1+b)*sin w3 = x2-x3+(r1+a)*(x1-x2+r1*sin w1)/(r1+a); ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:47:14 2004 Input: (r1+b)*sin(w3) = x2-x3+(r1+a)*(x1-x2+r1*sin(w1))/(r1+a) Output: Magma V2.11-6 Mon Sep 13 2004 14:47:13 on modular [Seed = 2594058380] ------------------------------------- >> (r1+b)*sin(w3) = x2-x3+(r1+a)*(x1-x2+r1*sin(w1))/(r1+a); ^ User error: Identifier 'x2' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:48:10 2004 Input: Solve((r1+b)*sin(w3) = x2-x3+(r1+a)*(x1-x2+r1*sin(w1))/(r1+a)) Output: Magma V2.11-6 Mon Sep 13 2004 14:48:10 on modular [Seed = 3890433449] ------------------------------------- >> Solve((r1+b)*sin(w3) = x2-x3+(r1+a)*(x1-x2+r1*sin(w1))/(r1+a)); ^ User error: Identifier 'x2' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:04 2004 Input: (a + b) * sin(c) = d - e + (a + f) * (g - y + h * s(c))/(a + f) Output: Magma V2.11-6 Mon Sep 13 2004 14:54:04 on modular [Seed = 724534976] ------------------------------------- >> (a + b) * sin(c) = d - e + (a + f) * (g - y + h * s(c))/(a + f); ^ User error: Identifier 'd' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 66.63.133.99 (66.63.133.99) Time: Mon Sep 13 23:53:32 2004 Input: E := EllipticCurve([0,6800,0,11559996,0]); r,Lvalue:=AnalyticRank(E); r,Lvalue; Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]; Output: Magma V2.11-6 Mon Sep 13 2004 23:53:29 on modular [Seed = 1161981777] ------------------------------------- 1 13.89000000000000000031 4.028207459926197680881 Total time: 0.220 seconds, Total memory usage: 7.91MB ************** MAGMA ***************** Host 66.63.133.99 (66.63.133.99) Time: Mon Sep 13 23:55:35 2004 Input: E := EllipticCurve([0,-1,0,-3853337,-2910113895]); r,Lvalue:=AnalyticRank(E); r,Lvalue; Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]; Output: Magma V2.11-6 Mon Sep 13 2004 23:55:33 on modular [Seed = 1549498052] ------------------------------------- 1 13.89000000000000000031 4.028207459926197680881 Total time: 0.220 seconds, Total memory usage: 7.91MB ************** MAGMA ***************** Host 141.84.69.18 (141.84.69.18) Time: Tue Sep 14 03:55:27 2004 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=7917157863480469; s:=7917157863480469; FindGroupOrder2(p,s); Output: Magma V2.11-6 Tue Sep 14 2004 03:55:20 on modular [Seed = 842387703] ------------------------------------- FindGroupOrder2( p: 7917157863480469, s: 7917157863480469 ) >> K := GF(p); ^ Runtime error in 'GF': Argument 1 (7917157863480469) is not a prime power Total time: 0.240 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 141.84.69.18 (141.84.69.18) Time: Tue Sep 14 03:55:52 2004 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=23917104973173909566916321016011885041962486321502513; s:=7917157863480469; FindGroupOrder2(p,s); Output: Magma V2.11-6 Tue Sep 14 2004 03:55:47 on modular [Seed = 252242464] ------------------------------------- [ <2, 4>, <3, 1>, <29, 1>, <31, 2>, <41, 1>, <53, 1>, <107, 1>, <21589, 1>, <62773, 1>, <140419, 1>, <229781, 1>, <238729, 1>, <2286601, 1>, <3221525051, 1> ] Total time: 2.629 seconds, Total memory usage: 5.59MB ************** MAGMA ***************** Host 141.84.69.18 (141.84.69.18) Time: Tue Sep 14 04:02:40 2004 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=23917104973173909566916321016011885041962486321502513; s:=7917157863480469; FindGroupOrder2(p,s); Output: Magma V2.11-6 Tue Sep 14 2004 04:02:36 on modular [Seed = 517296] ------------------------------------- [ <2, 4>, <3, 1>, <29, 1>, <31, 2>, <41, 1>, <53, 1>, <107, 1>, <21589, 1>, <62773, 1>, <140419, 1>, <229781, 1>, <238729, 1>, <2286601, 1>, <3221525051, 1> ] Total time: 2.609 seconds, Total memory usage: 5.58MB ************** MAGMA ***************** Host 141.84.69.18 (141.84.69.18) Time: Tue Sep 14 04:05:24 2004 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=23917104973173909566916321016011885041962486321502513; s:=7917157863480469; FindGroupOrder2(p,s); Output: Magma V2.11-6 Tue Sep 14 2004 04:05:19 on modular [Seed = 404750091] ------------------------------------- [ <2, 4>, <3, 1>, <29, 1>, <31, 2>, <41, 1>, <53, 1>, <107, 1>, <21589, 1>, <62773, 1>, <140419, 1>, <229781, 1>, <238729, 1>, <2286601, 1>, <3221525051, 1> ] Total time: 2.660 seconds, Total memory usage: 5.58MB ************** MAGMA ***************** Host 134.60.67.219 (134.60.67.219) Time: Tue Sep 14 08:54:43 2004 Input: *&[1,2]; *&[]; Output: Magma V2.11-6 Tue Sep 14 2004 08:54:38 on modular [Seed = 1280042866] ------------------------------------- >> *&[1,2]; ^ User error: bad syntax >> *&[];; ^ User error: bad syntax Total time: 0.270 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.60.67.219 (134.60.67.219) Time: Tue Sep 14 08:55:01 2004 Input: &*[1,2]; &*[]; Output: Magma V2.11-6 Tue Sep 14 2004 08:55:01 on modular [Seed = 3014924455] ------------------------------------- 2 &*( S: [] ) In file "/usr/local/magma/package/LieThry/GrpCox.m", line 3006, column 16: >> W := Universe( S ); ^ Runtime error in 'Universe': Illegal null sequence Total time: 0.220 seconds, Total memory usage: 3.86MB ************** MAGMA ***************** Host 134.60.67.219 (134.60.67.219) Time: Tue Sep 14 08:55:45 2004 Input: M2:= MatrixRing(Integers(), 2); Z1:=[ M2!1, M2!1]; Z2:=[ M2!1, M2![2,1,1,2] ]; ok, T:= IsIsometric(Z1, Z2); ok; [ T * Z1[i] * Transpose(T) eq Z2[i]: i in [1..#Z1]]; ok, T:= IsIsometric( LatticeWithGram(Z1), [Z1], LatticeWithGram(Z2), [Z2]); ok; [ T * Z1[i] * Transpose(T) eq Z2[i]: i in [1..#Z1]]; Output: Magma V2.11-6 Tue Sep 14 2004 08:55:44 on modular [Seed = 3065060823] ------------------------------------- true [ true, false ] true [ true, false ] Total time: 0.200 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.130.164.48 (134.130.164.48) Time: Tue Sep 14 10:49:25 2004 Input: S<i>:=QuadraticField(-1); RingOfIntegers(S); I:=MatrixRing(Integers(),2) ! [0,1,-1,0]; E:=MatrixRing(Integers(),8) ! 1; II:=TensorProduct(E,I); EHUT3:=Matrix(RingOfIntegers(),16,16,[ 2, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-1, 1,-1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,-1, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2,-1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 1,-1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-1, 1, 0, 1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,-1, 2, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1,-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2,-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 1,-1, 1,-1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 2]); Ai1gross:=AutomorphismGroup([EHUT3,II*EHUT3]); Ai1:=Ai1gross; print "Auto-Gruppen berechnet."; L1:=LatticeWithGram(EHUT3); Output: Magma V2.11-6 Tue Sep 14 2004 10:49:22 on modular [Seed = 2846878824] ------------------------------------- Maximal Equation Order of S Auto-Gruppen berechnet. Total time: 0.320 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 134.130.164.48 (134.130.164.48) Time: Tue Sep 14 10:49:46 2004 Input: S<i>:=QuadraticField(-1); RingOfIntegers(S); I:=MatrixRing(Integers(),2) ! [0,1,-1,0]; E:=MatrixRing(Integers(),8) ! 1; II:=TensorProduct(E,I); EHUT3:=Matrix(RingOfIntegers(),16,16,[ 2, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-1, 1,-1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,-1, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2,-1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 1,-1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-1, 1, 0, 1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,-1, 2, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1,-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2,-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 1,-1, 1,-1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 2]); Ai1gross:=AutomorphismGroup([EHUT3,II*EHUT3]); Ai1:=Ai1gross; print "Auto-Gruppen berechnet."; L1:=LatticeWithGram(EHUT3); ShortVectors(L1,10,10); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.11-6 Tue Sep 14 2004 10:49:44 on modular [Seed = 2476070825] ------------------------------------- Maximal Equation Order of S Auto-Gruppen berechnet. Current total memory usage: 82.9MB, failed memory request: 61.6MB System Error: User memory limit has been reached Total time: 1.350 seconds, Total memory usage: 86.97MB ************** MAGMA ***************** Host 66.32.184.114 (66.32.184.114) Time: Tue Sep 14 17:47:30 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Tue Sep 14 2004 17:47:30 on modular [Seed = 4142977341] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 66.67.3.24 (66.67.3.24) Time: Tue Sep 14 19:03:00 2004 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=23917104973173909566916321016011885041962486321502513; s:=7917157863480469; FindGroupOrder2(p,s); Output: Magma V2.11-6 Tue Sep 14 2004 19:02:56 on modular [Seed = 1734434559] ------------------------------------- [ <2, 4>, <3, 1>, <29, 1>, <31, 2>, <41, 1>, <53, 1>, <107, 1>, <21589, 1>, <62773, 1>, <140419, 1>, <229781, 1>, <238729, 1>, <2286601, 1>, <3221525051, 1> ] Total time: 2.759 seconds, Total memory usage: 5.58MB ************** MAGMA ***************** Host 66.67.3.24 (66.67.3.24) Time: Tue Sep 14 19:03:24 2004 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=2391710497317390956691632101612121313131011885041962486321502513; s:=7917157863480469; FindGroupOrder2(p,s); Output: Magma V2.11-6 Tue Sep 14 2004 19:03:24 on modular [Seed = 1599694555] ------------------------------------- FindGroupOrder2( p: 239171049731739095669163210161212131313101188504196248632150..., s: 7917157863480469 ) >> K := GF(p); ^ Runtime error in 'GF': Argument 1 (23917104973173909566916321016121213131310118\ 85041962486321502513) is not a prime power Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 66.67.3.24 (66.67.3.24) Time: Tue Sep 14 19:03:42 2004 Input: FindGroupOrder2 := function (p, s) K := GF(p); v := K ! (4*s); u := K ! (s^2-5); x := u^3; b := 4*x*v; a := (v-u)^3*(3*u+v); A := a/b-2; x := x/v^3; b := x^3 + A*x^2 + x; E := EllipticCurve([0,b*A,0,b^2,0]); return FactoredOrder(E); end function; p:=23917104973173909566916321016011885041962486321502513; s:=7917157863480469; FindGroupOrder2(p,s); Output: Magma V2.11-6 Tue Sep 14 2004 19:03:39 on modular [Seed = 1414688167] ------------------------------------- [ <2, 4>, <3, 1>, <29, 1>, <31, 2>, <41, 1>, <53, 1>, <107, 1>, <21589, 1>, <62773, 1>, <140419, 1>, <229781, 1>, <238729, 1>, <2286601, 1>, <3221525051, 1> ] Total time: 2.669 seconds, Total memory usage: 5.58MB ************** MAGMA ***************** Host 66.63.132.20 (66.63.132.20) Time: Wed Sep 15 01:50:46 2004 Input: E := EllipticCurve([0,-1,0,-3853337,-2910113895]); r,Lvalue:=AnalyticRank(E); r,Lvalue; Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup)^2; Output: Magma V2.11-6 Wed Sep 15 2004 01:50:44 on modular [Seed = 1111808842] ------------------------------------- 1 13.89000000000000000031 >> Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#Tors ^ Runtime error in '#': Bad argument types Argument types given: Intrinsic Total time: 0.280 seconds, Total memory usage: 7.91MB ************** MAGMA ***************** Host 66.63.132.20 (66.63.132.20) Time: Wed Sep 15 01:52:03 2004 Input: E := EllipticCurve([0,-1,0,-3853337,-2910113895]); r,Lvalue:=AnalyticRank(E); r,Lvalue; Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; Output: Magma V2.11-6 Wed Sep 15 2004 01:52:03 on modular [Seed = 3099468039] ------------------------------------- 1 13.89000000000000000031 64.45131935881916289410 Total time: 0.230 seconds, Total memory usage: 7.91MB ************** MAGMA ***************** Host 66.63.132.20 (66.63.132.20) Time: Wed Sep 15 01:52:54 2004 Input: E := EllipticCurve([0,-1,0,-3853337,-2910113895]); r,AnalyticRank(E);/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; Output: Magma V2.11-6 Wed Sep 15 2004 01:52:54 on modular [Seed = 3031575870] ------------------------------------- >> r,AnalyticRank(E);/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrime ^ User error: Identifier 'r' has not been declared or assigned >> r,AnalyticRank(E);/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrime ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 66.63.132.20 (66.63.132.20) Time: Wed Sep 15 01:53:29 2004 Input: E := EllipticCurve([0,-1,0,-3853337,-2910113895]); r,Lvalue;r,Lvalue=AnalyticRank(E); Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; Output: Magma V2.11-6 Wed Sep 15 2004 01:53:29 on modular [Seed = 2913678408] ------------------------------------- >> r,Lvalue;r,Lvalue=AnalyticRank(E); ^ User error: Identifier 'r' has not been declared or assigned >> r,Lvalue;r,Lvalue=AnalyticRank(E); ^ User error: Identifier 'r' has not been declared or assigned >> Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#Tors ^ User error: Identifier 'Lvalue' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 66.63.132.20 (66.63.132.20) Time: Wed Sep 15 01:54:11 2004 Input: E := EllipticCurve([0,-1,0,-3853337,-2910113895]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; Output: Magma V2.11-6 Wed Sep 15 2004 01:54:11 on modular [Seed = 2778938778] ------------------------------------- 1 64.45131935881916289410 Total time: 0.210 seconds, Total memory usage: 7.91MB ************** MAGMA ***************** Host 66.63.132.20 (66.63.132.20) Time: Wed Sep 15 01:54:25 2004 Input: E := EllipticCurve([0,-1,0,-3853337,-2910113895]);r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; Output: Magma V2.11-6 Wed Sep 15 2004 01:54:25 on modular [Seed = 2712091020] ------------------------------------- 1 64.45131935881916289410 Total time: 0.220 seconds, Total memory usage: 7.91MB ************** MAGMA ***************** Host 66.63.132.20 (66.63.132.20) Time: Wed Sep 15 02:08:09 2004 Input: E := EllipticCurve([0, -2, 0, -3, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -4, 0, 0, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -6, 0, 5, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -8, 0, 12, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -10, 0, 21, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -12, 0, 32, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -14, 0, 45, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -16, 0, 60, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -18, 0, 77, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -20, 0, 96, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -22, 0, 117, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; E := EllipticCurve([0, -24, 0, 140, 0]); r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p in BadPrimes(E)]*(#TorsionSubgroup(E))^2; Output: Magma V2.11-6 Wed Sep 15 2004 02:08:08 on modular [Seed = 3773201812] ------------------------------------- 0 1.000029449904763315993584 >> E := EllipticCurve([0, -4, 0, 0, 0]); ^ Runtime error in 'EllipticCurve': Curve is singular 0 1.000029449904763315993584 0 0.99999159706442125556 0 1.00018562171883295894032 0 0.99995372381138473939 0 1.99995609990175417897 0 1.00039836495953203261526 1 0.88644508068722756977 0 1.00035674946902807761622 0 1.99928277796760529903 0 0.99999980943016291605 1 1.42298780590710821820 Total time: 0.290 seconds, Total memory usage: 7.91MB ************** MAGMA ***************** Host 193.13.42.18 (193.13.42.18) Time: Wed Sep 15 04:51:00 2004 Input: 5*34 Output: Magma V2.11-6 Wed Sep 15 2004 04:50:59 on modular [Seed = 1886991171] ------------------------------------- 170 Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 81.210.32.20 (81.210.32.20) Time: Wed Sep 15 06:19:07 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Wed Sep 15 2004 06:19:07 on modular [Seed = 2998658281] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 81.210.32.20 (81.210.32.20) Time: Wed Sep 15 06:19:24 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Wed Sep 15 2004 06:19:24 on modular [Seed = 3082740187] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 06:53:03 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Wed Sep 15 2004 06:53:02 on modular [Seed = 959473525] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 06:55:19 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: Magma V2.11-6 Wed Sep 15 2004 06:55:19 on modular [Seed = 3368130077] ------------------------------------- >> E:=ExtraSpecialGroup(2,3); ^ User error: bad syntax >> A:=AutomorphismGroup(E); ^ User error: Identifier 'E' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 06:57:10 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" E:=ExtraSpecialGroup(2,3: Type:= "+"); A:=AutomorphismGroup(E); Output: Magma V2.11-6 Wed Sep 15 2004 06:57:10 on modular [Seed = 3520639125] ------------------------------------- >> E:=ExtraSpecialGroup(2,3: Type:= ^ User error: bad syntax >> "+"); ^ User error: bad syntax >> A:=AutomorphismGroup(E); ^ User error: Identifier 'E' has not been declared or assigned Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 06:57:44 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" AutomorphismGroup(ExtraSpecialGroup(2,3)); Output: Magma V2.11-6 Wed Sep 15 2004 06:57:44 on modular [Seed = 3671309232] ------------------------------------- >> AutomorphismGroup(ExtraSpecialGroup(2,3)); ^ User error: bad syntax Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 06:59:48 2004 Input: E:=ExtraSpecialGroup(2,3); Output: Magma V2.11-6 Wed Sep 15 2004 06:59:47 on modular [Seed = 3790110720] ------------------------------------- Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:00:38 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:00:16 on modular [Seed = 3923806315] ------------------------------------- Errors: /bin/sh: line 1: 939 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:00:52 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:00:25 on modular [Seed = 3974466919] ------------------------------------- Errors: /bin/sh: line 1: 942 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:01:27 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:00:58 on modular [Seed = 4143945566] ------------------------------------- Errors: /bin/sh: line 1: 948 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:01:55 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:01:12 on modular [Seed = 4176582978] ------------------------------------- Errors: /bin/sh: line 1: 954 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:02:06 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:01:23 on modular [Seed = 2206917570] ------------------------------------- Errors: /bin/sh: line 1: 961 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:02:06 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:01:10 on modular [Seed = 4126970945] ------------------------------------- Errors: /bin/sh: line 1: 951 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:02:08 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:01:12 on modular [Seed = 4294352453] ------------------------------------- Errors: /bin/sh: line 1: 957 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:03:58 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:36 on modular [Seed = 2407985024] ------------------------------------- Errors: /bin/sh: line 1: 973 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:27 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:38 on modular [Seed = 2459693726] ------------------------------------- Errors: /bin/sh: line 1: 976 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:36 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:44 on modular [Seed = 2442719623] ------------------------------------- Errors: /bin/sh: line 1: 979 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:38 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:45 on modular [Seed = 2610101132] ------------------------------------- Errors: /bin/sh: line 1: 985 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:39 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:46 on modular [Seed = 2643787145] ------------------------------------- Errors: /bin/sh: line 1: 991 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:39 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:47 on modular [Seed = 2813249458] ------------------------------------- Errors: /bin/sh: line 1: 997 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:42 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:45 on modular [Seed = 2493379715] ------------------------------------- Errors: /bin/sh: line 1: 982 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:42 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:45 on modular [Seed = 2660761225] ------------------------------------- Errors: /bin/sh: line 1: 988 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:42 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:02:46 on modular [Seed = 2695479476] ------------------------------------- Errors: /bin/sh: line 1: 994 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:48 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:03:08 on modular [Seed = 3015365533] ------------------------------------- Errors: /bin/sh: line 1: 1009 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:04:49 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 15 2004 07:03:04 on modular [Seed = 2896546950] ------------------------------------- Errors: /bin/sh: line 1: 1006 Killed nice -n 19 /usr/local/bin/magma ************** MAGMA ***************** Host 212.202.8.22 (212.202.8.22) Time: Wed Sep 15 19:40:35 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Wed Sep 15 2004 19:40:35 on modular [Seed = 151034550] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 202.154.65.186 (202.154.65.186) Time: Wed Sep 15 22:03:58 2004 Input: /p 70 exp(Pi*sqrt(-1)) Output: Magma V2.11-6 Wed Sep 15 2004 22:03:58 on modular [Seed = 1364780176] ------------------------------------- >> /p 70 ^ User error: bad syntax >> exp(Pi*sqrt(-1)); ^ User error: Identifier 'sqrt' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:27:45 2004 Input: 100001100001100001100001100001100001 / 7 Output: Magma V2.11-6 Thu Sep 16 2004 10:27:45 on modular [Seed = 1599585513] ------------------------------------- 100001100001100001100001100001100001/7 Total time: 0.200 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:28:31 2004 Input: 100001100001100001100001100001100001 / 7; Output: Magma V2.11-6 Thu Sep 16 2004 10:28:31 on modular [Seed = 1179558942] ------------------------------------- 100001100001100001100001100001100001/7 Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:28:42 2004 Input: 140 / 7 Output: Magma V2.11-6 Thu Sep 16 2004 10:28:42 on modular [Seed = 1095344908] ------------------------------------- 20 Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:28:57 2004 Input: 144614461446144614461446 Output: Magma V2.11-6 Thu Sep 16 2004 10:28:56 on modular [Seed = 1279569459] ------------------------------------- 144614461446144614461446 Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:29:01 2004 Input: 144614461446144614461446 / 7 Output: Magma V2.11-6 Thu Sep 16 2004 10:29:01 on modular [Seed = 2004849933] ------------------------------------- 20659208778020659208778 Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:29:15 2004 Input: 144461444614446144461444614446 / 7 Output: Magma V2.11-6 Thu Sep 16 2004 10:29:15 on modular [Seed = 2121702418] ------------------------------------- 20637349230635163494492087778 Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:29:30 2004 Input: 144144144144144144 / 7 Output: Magma V2.11-6 Thu Sep 16 2004 10:29:30 on modular [Seed = 2037488484] ------------------------------------- 20592020592020592 Total time: 0.180 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:29:49 2004 Input: 123456 / 7 Output: Magma V2.11-6 Thu Sep 16 2004 10:29:48 on modular [Seed = 1684833903] ------------------------------------- 123456/7 Total time: 0.200 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:29:57 2004 Input: 123456123456123456123456123456123456 / 7 Output: Magma V2.11-6 Thu Sep 16 2004 10:29:57 on modular [Seed = 1869057373] ------------------------------------- 123456123456123456123456123456123456/7 Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.147.78.53 (134.147.78.53) Time: Thu Sep 16 12:07:22 2004 Input: p = 5; q = 7; n = p*q; Output: Magma V2.11-6 Thu Sep 16 2004 12:07:22 on modular [Seed = 1449045306] ------------------------------------- >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'p' has not been declared or assigned >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'q' has not been declared or assigned >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'p' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.147.78.53 (134.147.78.53) Time: Thu Sep 16 12:08:11 2004 Input: Q = Rationalfield(); p = 5; q = 7; n = p*q; Output: Magma V2.11-6 Thu Sep 16 2004 12:08:10 on modular [Seed = 1549051744] ------------------------------------- >> Q = Rationalfield(); ^ User error: Identifier 'Rationalfield' has not been declared or assigned >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'p' has not been declared or assigned >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'q' has not been declared or assigned >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'p' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.147.78.53 (134.147.78.53) Time: Thu Sep 16 12:08:17 2004 Input: Q = RationalField(); p = 5; q = 7; n = p*q; Output: Magma V2.11-6 Thu Sep 16 2004 12:08:16 on modular [Seed = 1498522239] ------------------------------------- >> Q = RationalField(); ^ User error: Identifier 'Q' has not been declared or assigned >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'p' has not been declared or assigned >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'q' has not been declared or assigned >> p = 5; q = 7; n = p*q;; ^ User error: Identifier 'p' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.147.78.53 (134.147.78.53) Time: Thu Sep 16 12:08:54 2004 Input: Q := RationalField(); p := 5; q := 7; n := p*q; Output: Magma V2.11-6 Thu Sep 16 2004 12:08:53 on modular [Seed = 1129035904] ------------------------------------- Total time: 0.200 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.147.78.53 (134.147.78.53) Time: Thu Sep 16 12:09:04 2004 Input: Q := RationalField(); p := 5; q := 7; n := p*q; print n; Output: Magma V2.11-6 Thu Sep 16 2004 12:09:04 on modular [Seed = 1279571898] ------------------------------------- 35 Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.147.78.53 (134.147.78.53) Time: Thu Sep 16 12:09:51 2004 Input: Q := RationalField(); p := 5; q := 7; n := p*q; r := 0; rand(9); Output: Magma V2.11-6 Thu Sep 16 2004 12:09:51 on modular [Seed = 1229042384] ------------------------------------- >> rand(9);; ^ User error: Identifier 'rand' has not been declared or assigned Total time: 0.200 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 134.147.78.53 (134.147.78.53) Time: Thu Sep 16 12:09:57 2004 Input: Q := RationalField(); p := 5; q := 7; n := p*q; r := 0; Rand(9); Output: Magma V2.11-6 Thu Sep 16 2004 12:09:57 on modular [Seed = 1920633329] ------------------------------------- >> Rand(9);; ^ User error: Identifier 'Rand' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:35:51 2004 Input: M:=ModularSymbols(6,5); C:=CuspidalSubspace(M); f:=qExpansionBasis(C,100); f; Output: Magma V2.11-6 Thu Sep 16 2004 14:35:51 on modular [Seed = 2290095318] ------------------------------------- [] Total time: 0.220 seconds, Total memory usage: 4.62MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:44:41 2004 Input: G := DirichletGroup(5, RationalField()); M:=ModularSymbols(5,6); C:=CuspidalSubspace(M); f:=qExpansionBasis(C,100); f; Output: Magma V2.11-6 Thu Sep 16 2004 14:44:41 on modular [Seed = 3182765053] ------------------------------------- [ q + 2*q^2 - 4*q^3 - 28*q^4 + 25*q^5 - 8*q^6 + 192*q^7 - 120*q^8 - 227*q^9 + 50*q^10 - 148*q^11 + 112*q^12 + 286*q^13 + 384*q^14 - 100*q^15 + 656*q^16 - 1678*q^17 - 454*q^18 + 1060*q^19 - 700*q^20 - 768*q^21 - 296*q^22 + 2976*q^23 + 480*q^24 + 625*q^25 + 572*q^26 + 1880*q^27 - 5376*q^28 - 3410*q^29 - 200*q^30 - 2448*q^31 + 5152*q^32 + 592*q^33 - 3356*q^34 + 4800*q^35 + 6356*q^36 + 182*q^37 + 2120*q^38 - 1144*q^39 - 3000*q^40 - 9398*q^41 - 1536*q^42 - 1244*q^43 + 4144*q^44 - 5675*q^45 + 5952*q^46 - 12088*q^47 - 2624*q^48 + 20057*q^49 + 1250*q^50 + 6712*q^51 - 8008*q^52 + 23846*q^53 + 3760*q^54 - 3700*q^55 - 23040*q^56 - 4240*q^57 - 6820*q^58 - 20020*q^59 + 2800*q^60 + 32302*q^61 - 4896*q^62 - 43584*q^63 - 10688*q^64 + 7150*q^65 + 1184*q^66 + 60972*q^67 + 46984*q^68 - 11904*q^69 + 9600*q^70 - 32648*q^71 + 27240*q^72 - 38774*q^73 + 364*q^74 - 2500*q^75 - 29680*q^76 - 28416*q^77 - 2288*q^78 - 33360*q^79 + 16400*q^80 + 47641*q^81 - 18796*q^82 + 16716*q^83 + 21504*q^84 - 41950*q^85 - 2488*q^86 + 13640*q^87 + 17760*q^88 + 101370*q^89 - 11350*q^90 + 54912*q^91 - 83328*q^92 + 9792*q^93 - 24176*q^94 + 26500*q^95 - 20608*q^96 - 119038*q^97 + 40114*q^98 + 33596*q^99 + O(q^100) ] Total time: 0.310 seconds, Total memory usage: 5.14MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:45:10 2004 Input: G := DirichletGroup(5, RationalField()); G; M:=ModularSymbols(5,6); C:=CuspidalSubspace(M); f:=qExpansionBasis(C,100); f; Output: Magma V2.11-6 Thu Sep 16 2004 14:45:10 on modular [Seed = 2964860639] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field [ q + 2*q^2 - 4*q^3 - 28*q^4 + 25*q^5 - 8*q^6 + 192*q^7 - 120*q^8 - 227*q^9 + 50*q^10 - 148*q^11 + 112*q^12 + 286*q^13 + 384*q^14 - 100*q^15 + 656*q^16 - 1678*q^17 - 454*q^18 + 1060*q^19 - 700*q^20 - 768*q^21 - 296*q^22 + 2976*q^23 + 480*q^24 + 625*q^25 + 572*q^26 + 1880*q^27 - 5376*q^28 - 3410*q^29 - 200*q^30 - 2448*q^31 + 5152*q^32 + 592*q^33 - 3356*q^34 + 4800*q^35 + 6356*q^36 + 182*q^37 + 2120*q^38 - 1144*q^39 - 3000*q^40 - 9398*q^41 - 1536*q^42 - 1244*q^43 + 4144*q^44 - 5675*q^45 + 5952*q^46 - 12088*q^47 - 2624*q^48 + 20057*q^49 + 1250*q^50 + 6712*q^51 - 8008*q^52 + 23846*q^53 + 3760*q^54 - 3700*q^55 - 23040*q^56 - 4240*q^57 - 6820*q^58 - 20020*q^59 + 2800*q^60 + 32302*q^61 - 4896*q^62 - 43584*q^63 - 10688*q^64 + 7150*q^65 + 1184*q^66 + 60972*q^67 + 46984*q^68 - 11904*q^69 + 9600*q^70 - 32648*q^71 + 27240*q^72 - 38774*q^73 + 364*q^74 - 2500*q^75 - 29680*q^76 - 28416*q^77 - 2288*q^78 - 33360*q^79 + 16400*q^80 + 47641*q^81 - 18796*q^82 + 16716*q^83 + 21504*q^84 - 41950*q^85 - 2488*q^86 + 13640*q^87 + 17760*q^88 + 101370*q^89 - 11350*q^90 + 54912*q^91 - 83328*q^92 + 9792*q^93 - 24176*q^94 + 26500*q^95 - 20608*q^96 - 119038*q^97 + 40114*q^98 + 33596*q^99 + O(q^100) ] Total time: 0.300 seconds, Total memory usage: 5.14MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:45:18 2004 Input: G := DirichletGroup(5, RationalField()); G; M:=ModularSymbols(5,6); C:=CuspidalSubspace(M); f:=qExpansionBasis(C,10); f; Output: Magma V2.11-6 Thu Sep 16 2004 14:45:18 on modular [Seed = 3082758608] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field [ q + 2*q^2 - 4*q^3 - 28*q^4 + 25*q^5 - 8*q^6 + 192*q^7 - 120*q^8 - 227*q^9 + O(q^10) ] Total time: 0.280 seconds, Total memory usage: 4.84MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:45:53 2004 Input: G := DirichletGroup(5, RationalField()); G; chars := Elements(G); M:=ModularSymbols(chars,6); M; C:=CuspidalSubspace(M); f:=qExpansionBasis(C,10); f; Output: Magma V2.11-6 Thu Sep 16 2004 14:45:53 on modular [Seed = 2862757010] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field Full modular symbols space of level 5, weight 6, and dimension 10 over Rational Field (multi-character) Space must be associated to a newform (constructed using NewformDecomposition). >> f;; ^ User error: Identifier 'f' has not been declared or assigned Total time: 0.240 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:46:13 2004 Input: G := DirichletGroup(5, RationalField()); G; chars := Elements(G); M:=ModularSymbols(chars,6); M; C:=CuspidalSubspace(M); qExpansionBasis(C,10); f; Output: Magma V2.11-6 Thu Sep 16 2004 14:46:13 on modular [Seed = 2712223629] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field Full modular symbols space of level 5, weight 6, and dimension 10 over Rational Field (multi-character) Space must be associated to a newform (constructed using NewformDecomposition). >> f;; ^ User error: Identifier 'f' has not been declared or assigned Total time: 0.240 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:46:31 2004 Input: G := DirichletGroup(5, RationalField()); G; chars := Elements(G); M:=ModularSymbols(chars,6); M; Cuspforms(M); qExpansionBasis(C,10); f; Output: Magma V2.11-6 Thu Sep 16 2004 14:46:30 on modular [Seed = 2762750587] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field Full modular symbols space of level 5, weight 6, and dimension 10 over Rational Field (multi-character) >> Cuspforms(M); ^ User error: Identifier 'Cuspforms' has not been declared or assigned >> qExpansionBasis(C,10); ^ User error: Identifier 'C' has not been declared or assigned >> f;; ^ User error: Identifier 'f' has not been declared or assigned Total time: 0.220 seconds, Total memory usage: 4.06MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:47:16 2004 Input: G := DirichletGroup(5, RationalField()); G; chars := Elements(G); M:=ModularSymbols(chars,6); M; C:=CuspidalSubspace(M); Dimension(C); Output: Magma V2.11-6 Thu Sep 16 2004 14:47:15 on modular [Seed = 1565901750] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field Full modular symbols space of level 5, weight 6, and dimension 10 over Rational Field (multi-character) 6 Total time: 0.240 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:47:28 2004 Input: G := DirichletGroup(2, RationalField()); G; chars := Elements(G); M:=ModularSymbols(chars,6); M; C:=CuspidalSubspace(M); Dimension(C); Output: Magma V2.11-6 Thu Sep 16 2004 14:47:28 on modular [Seed = 1432210381] ------------------------------------- Group of Dirichlet characters of modulus 2 over Rational Field Full modular symbols space of level 2, weight 6, and dimension 2 over Rational Field (multi-character) 0 Total time: 0.220 seconds, Total memory usage: 4.16MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:47:42 2004 Input: G := DirichletGroup(5, RationalField()); G; chars := Elements(G); M:=ModularSymbols(chars,6); M; C:=CuspidalSubspace(M); Dimension(C); Output: Magma V2.11-6 Thu Sep 16 2004 14:47:41 on modular [Seed = 1245893855] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field Full modular symbols space of level 5, weight 6, and dimension 10 over Rational Field (multi-character) 6 Total time: 0.230 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:47:57 2004 Input: G := DirichletGroup(5, RationalField()); G; Order(G); chars := Elements(G); M:=ModularSymbols(chars,6); M; C:=CuspidalSubspace(M); Dimension(C); Output: Magma V2.11-6 Thu Sep 16 2004 14:47:57 on modular [Seed = 1330106826] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field 2 Full modular symbols space of level 5, weight 6, and dimension 10 over Rational Field (multi-character) 6 Total time: 0.230 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:51:22 2004 Input: G := DirichletGroup(5, RationalField()); G; G.1 Order(G); chars := Elements(G); M:=ModularSymbols(chars,6); M; C:=CuspidalSubspace(M); Dimension(C); Output: Magma V2.11-6 Thu Sep 16 2004 14:51:22 on modular [Seed = 184789753] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field >> Order(G); ^ User error: bad syntax Full modular symbols space of level 5, weight 6, and dimension 10 over Rational Field (multi-character) 6 Total time: 0.230 seconds, Total memory usage: 4.53MB ************** MAGMA ***************** Host 129.186.52.128 (129.186.52.128) Time: Thu Sep 16 14:51:29 2004 Input: G := DirichletGroup(5, RationalField()); G; G.1; Order(G); chars := Elements(G); M:=ModularSymbols(chars,6); M; C:=CuspidalSubspace(M); Dimension(C); Output: Magma V2.11-6 Thu Sep 16 2004 14:51:28 on modular [Seed = 565736] ------------------------------------- Group of Dirichlet characters of modulus 5 over Rational Field$.1
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)
6

Total time: 0.230 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:51:51 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);
Dimension(C);

Output: Magma V2.11-6     Thu Sep 16 2004 14:51:51 on modular  [Seed = 84780186]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)
6

Total time: 0.220 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:51:57 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.2);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);
Dimension(C);

Output: Magma V2.11-6     Thu Sep 16 2004 14:51:57 on modular  [Seed = 976395183]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field

>> Order(G.2);
^
Runtime error in '.': Argument 2 can be at most 1
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)
6

Total time: 0.230 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:52:11 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);
Dimension(C);

Output: Magma V2.11-6     Thu Sep 16 2004 14:52:10 on modular  [Seed = 809013682]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)
6

Total time: 0.230 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:53:16 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);
Dimension(C);
Basis(C,10);

Output: Magma V2.11-6     Thu Sep 16 2004 14:53:16 on modular  [Seed = 926914419]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)
6

>> Basis(C,10);
^
Runtime error in 'Basis': Bad argument types
Argument types given: ModSym, RngIntElt

Total time: 0.230 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:53:29 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);
Dimension(C);
Basis(C);

Output: Magma V2.11-6     Thu Sep 16 2004 14:53:29 on modular  [Seed = 791121758]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)
6
[
(-7875*X^4 - 13070*X^3*Y - 8131*X^2*Y^2 - 11236/5*X*Y^3 - 1164/5*Y^4)*{-3/7,
-2/5} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(-5075*X^4 - 8370*X^3*Y - 5175*X^2*Y^2 - 7108/5*X*Y^3 - 732/5*Y^4)*{-3/7,
-2/5} + (-3*X^2*Y^2 + 8/5*X*Y^3)*{0, oo},
(2275*X^4 + 3810*X^3*Y + 2391*X^2*Y^2 + 3332/5*X*Y^3 + 348/5*Y^4)*{-3/7,
-2/5} + (-4*X^3*Y - 3*X^2*Y^2 - 12/5*X*Y^3)*{0, oo},
(-7100*X^4 - 11790*X^3*Y - 7339*X^2*Y^2 - 10148/5*X*Y^3 - 1052/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (64*X^3*Y - 7*X^2*Y^2 + 68/5*X*Y^3)*{0, oo},
(-8500*X^4 - 14070*X^3*Y - 8731*X^2*Y^2 - 12036/5*X*Y^3 - 1244/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(5075*X^4 + 8370*X^3*Y + 5175*X^2*Y^2 + 7108/5*X*Y^3 + 732/5*Y^4)*{-3/7,
-2/5} + (4*X^3*Y - 3*X^2*Y^2 + 12/5*X*Y^3)*{0, oo}
]

Total time: 0.250 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:53:52 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);
Decompose(C);
Basis(C);

Output: Magma V2.11-6     Thu Sep 16 2004 14:53:51 on modular  [Seed = 606897219]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)

>> Decompose(C);
^
User error: Identifier 'Decompose' has not been declared or assigned
[
(-7875*X^4 - 13070*X^3*Y - 8131*X^2*Y^2 - 11236/5*X*Y^3 - 1164/5*Y^4)*{-3/7,
-2/5} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(-5075*X^4 - 8370*X^3*Y - 5175*X^2*Y^2 - 7108/5*X*Y^3 - 732/5*Y^4)*{-3/7,
-2/5} + (-3*X^2*Y^2 + 8/5*X*Y^3)*{0, oo},
(2275*X^4 + 3810*X^3*Y + 2391*X^2*Y^2 + 3332/5*X*Y^3 + 348/5*Y^4)*{-3/7,
-2/5} + (-4*X^3*Y - 3*X^2*Y^2 - 12/5*X*Y^3)*{0, oo},
(-7100*X^4 - 11790*X^3*Y - 7339*X^2*Y^2 - 10148/5*X*Y^3 - 1052/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (64*X^3*Y - 7*X^2*Y^2 + 68/5*X*Y^3)*{0, oo},
(-8500*X^4 - 14070*X^3*Y - 8731*X^2*Y^2 - 12036/5*X*Y^3 - 1244/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(5075*X^4 + 8370*X^3*Y + 5175*X^2*Y^2 + 7108/5*X*Y^3 + 732/5*Y^4)*{-3/7,
-2/5} + (4*X^3*Y - 3*X^2*Y^2 + 12/5*X*Y^3)*{0, oo}
]

Total time: 0.260 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:57:47 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);
Decompose(C);
Basis(C);
f:=C.1;
qExpansion(f);

Output: Magma V2.11-6     Thu Sep 16 2004 14:57:47 on modular  [Seed = 3604903333]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)

>> Decompose(C);
^
User error: Identifier 'Decompose' has not been declared or assigned
[
(-7875*X^4 - 13070*X^3*Y - 8131*X^2*Y^2 - 11236/5*X*Y^3 - 1164/5*Y^4)*{-3/7,
-2/5} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(-5075*X^4 - 8370*X^3*Y - 5175*X^2*Y^2 - 7108/5*X*Y^3 - 732/5*Y^4)*{-3/7,
-2/5} + (-3*X^2*Y^2 + 8/5*X*Y^3)*{0, oo},
(2275*X^4 + 3810*X^3*Y + 2391*X^2*Y^2 + 3332/5*X*Y^3 + 348/5*Y^4)*{-3/7,
-2/5} + (-4*X^3*Y - 3*X^2*Y^2 - 12/5*X*Y^3)*{0, oo},
(-7100*X^4 - 11790*X^3*Y - 7339*X^2*Y^2 - 10148/5*X*Y^3 - 1052/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (64*X^3*Y - 7*X^2*Y^2 + 68/5*X*Y^3)*{0, oo},
(-8500*X^4 - 14070*X^3*Y - 8731*X^2*Y^2 - 12036/5*X*Y^3 - 1244/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(5075*X^4 + 8370*X^3*Y + 5175*X^2*Y^2 + 7108/5*X*Y^3 + 732/5*Y^4)*{-3/7,
-2/5} + (4*X^3*Y - 3*X^2*Y^2 + 12/5*X*Y^3)*{0, oo}
]

>> qExpansion(f);
^
Runtime error in 'qExpansion': Bad argument types
Argument types given: ModSymElt

Total time: 0.250 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:58:20 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);
Decompose(C);
Basis(C);
f:=C.1;
f;

Output: Magma V2.11-6     Thu Sep 16 2004 14:58:20 on modular  [Seed = 3418581215]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)

>> Decompose(C);
^
User error: Identifier 'Decompose' has not been declared or assigned
[
(-7875*X^4 - 13070*X^3*Y - 8131*X^2*Y^2 - 11236/5*X*Y^3 - 1164/5*Y^4)*{-3/7,
-2/5} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(-5075*X^4 - 8370*X^3*Y - 5175*X^2*Y^2 - 7108/5*X*Y^3 - 732/5*Y^4)*{-3/7,
-2/5} + (-3*X^2*Y^2 + 8/5*X*Y^3)*{0, oo},
(2275*X^4 + 3810*X^3*Y + 2391*X^2*Y^2 + 3332/5*X*Y^3 + 348/5*Y^4)*{-3/7,
-2/5} + (-4*X^3*Y - 3*X^2*Y^2 - 12/5*X*Y^3)*{0, oo},
(-7100*X^4 - 11790*X^3*Y - 7339*X^2*Y^2 - 10148/5*X*Y^3 - 1052/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (64*X^3*Y - 7*X^2*Y^2 + 68/5*X*Y^3)*{0, oo},
(-8500*X^4 - 14070*X^3*Y - 8731*X^2*Y^2 - 12036/5*X*Y^3 - 1244/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(5075*X^4 + 8370*X^3*Y + 5175*X^2*Y^2 + 7108/5*X*Y^3 + 732/5*Y^4)*{-3/7,
-2/5} + (4*X^3*Y - 3*X^2*Y^2 + 12/5*X*Y^3)*{0, oo}
]
(-7875*X^4 - 13070*X^3*Y - 8131*X^2*Y^2 - 11236/5*X*Y^3 - 1164/5*Y^4)*{-3/7,
-2/5} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo}

Total time: 0.250 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:58:46 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;

C:=CuspidalSubspace(M);

f:=C.1;
f;

Output: Magma V2.11-6     Thu Sep 16 2004 14:58:45 on modular  [Seed = 3234358270]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)
(-7875*X^4 - 13070*X^3*Y - 8131*X^2*Y^2 - 11236/5*X*Y^3 - 1164/5*Y^4)*{-3/7,
-2/5} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo}

Total time: 0.250 seconds, Total memory usage: 4.53MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 14:59:46 2004

Input: G := DirichletGroup(5, RationalField());
G;
Order(G.1);
Order(G);
chars := Elements(G);
M:=ModularSymbols(chars,6);
M;
C:=CuspidalSubspace(M);

Basis(NewSubspace(C));

Output: Magma V2.11-6     Thu Sep 16 2004 14:59:46 on modular  [Seed = 4176501506]
-------------------------------------

Group of Dirichlet characters of modulus 5 over Rational Field
2
2
Full modular symbols space of level 5, weight 6, and dimension 10 over Rational
Field (multi-character)
[
(-7875*X^4 - 13070*X^3*Y - 8131*X^2*Y^2 - 11236/5*X*Y^3 - 1164/5*Y^4)*{-3/7,
-2/5} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(-5075*X^4 - 8370*X^3*Y - 5175*X^2*Y^2 - 7108/5*X*Y^3 - 732/5*Y^4)*{-3/7,
-2/5} + (-3*X^2*Y^2 + 8/5*X*Y^3)*{0, oo},
(2275*X^4 + 3810*X^3*Y + 2391*X^2*Y^2 + 3332/5*X*Y^3 + 348/5*Y^4)*{-3/7,
-2/5} + (-4*X^3*Y - 3*X^2*Y^2 - 12/5*X*Y^3)*{0, oo},
(-7100*X^4 - 11790*X^3*Y - 7339*X^2*Y^2 - 10148/5*X*Y^3 - 1052/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (64*X^3*Y - 7*X^2*Y^2 + 68/5*X*Y^3)*{0, oo},
(-8500*X^4 - 14070*X^3*Y - 8731*X^2*Y^2 - 12036/5*X*Y^3 - 1244/5*Y^4)*{-3/7,
-2/5} + X^4*{-1/2, 0} + (-7*X^2*Y^2 - 4/5*X*Y^3)*{0, oo},
(5075*X^4 + 8370*X^3*Y + 5175*X^2*Y^2 + 7108/5*X*Y^3 + 732/5*Y^4)*{-3/7,
-2/5} + (4*X^3*Y - 3*X^2*Y^2 + 12/5*X*Y^3)*{0, oo}
]

Total time: 0.290 seconds, Total memory usage: 4.63MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 15:01:12 2004

Input: C := CuspForms(Gamma1(5),6);
C;

Output: Magma V2.11-6     Thu Sep 16 2004 15:01:12 on modular  [Seed = 4260716125]
-------------------------------------

Space of modular forms on Gamma_1(5) of weight 6 and dimension 3 over Integer
Ring.

Total time: 0.200 seconds, Total memory usage: 3.66MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 15:01:27 2004

Input: C := CuspForms(Gamma1(5),6);
C;
Dimension(C);

Output: Magma V2.11-6     Thu Sep 16 2004 15:01:27 on modular  [Seed = 4076490925]
-------------------------------------

Space of modular forms on Gamma_1(5) of weight 6 and dimension 3 over Integer
Ring.
3

Total time: 0.200 seconds, Total memory usage: 3.66MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 15:01:37 2004

Input: C := CuspForms(Gamma1(5),6);
C;
Dimension(C);
Basis(C);

Output: Magma V2.11-6     Thu Sep 16 2004 15:01:37 on modular  [Seed = 4160705982]
-------------------------------------

Space of modular forms on Gamma_1(5) of weight 6 and dimension 3 over Integer
Ring.
3
[
q - 12*q^4 - 45*q^5 + 132*q^6 + O(q^8),
q^2 - 24*q^4 + 95*q^5 - 210*q^6 + 306*q^7 + O(q^8),
q^3 - 8*q^4 + 30*q^5 - 70*q^6 + 105*q^7 + O(q^8)
]

Total time: 0.310 seconds, Total memory usage: 5.19MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 15:02:50 2004

Input: C := CuspForms(Gamma1(5),6);
C;
Precision(C,30);
Dimension(C);
Basis(C);

Output: Magma V2.11-6     Thu Sep 16 2004 15:02:49 on modular  [Seed = 3840689893]
-------------------------------------

Space of modular forms on Gamma_1(5) of weight 6 and dimension 3 over Integer
Ring.

>> Precision(C,30);
^
Runtime error in 'Precision': Bad argument types
Argument types given: ModFrm, RngIntElt
3
[
q - 12*q^4 - 45*q^5 + 132*q^6 + O(q^8),
q^2 - 24*q^4 + 95*q^5 - 210*q^6 + 306*q^7 + O(q^8),
q^3 - 8*q^4 + 30*q^5 - 70*q^6 + 105*q^7 + O(q^8)
]

Total time: 0.310 seconds, Total memory usage: 5.19MB

************** MAGMA *****************
Host 129.186.52.128 (129.186.52.128)
Time: Thu Sep 16 15:03:01 2004

Input: C := CuspForms(Gamma1(5),6);
C;
SetPrecision(C,30);
Dimension(C);
Basis(C);

Output: Magma V2.11-6     Thu Sep 16 2004 15:03:00 on modular  [Seed = 2576432037]
-------------------------------------

Space of modular forms on Gamma_1(5) of weight 6 and dimension 3 over Integer
Ring.
3
[
q - 12*q^4 - 45*q^5 + 132*q^6 - 153*q^9 - 220*q^10 + 252*q^11 + 396*q^14 +
660*q^15 - 1264*q^16 - 220*q^19 + 540*q^20 - 1188*q^21 + 2640*q^24 +
925*q^25 + 792*q^26 - 6930*q^29 + O(q^30),
q^2 - 24*q^4 + 95*q^5 - 210*q^6 + 306*q^7 - 220*q^8 - 111*q^9 + 495*q^10 -
600*q^11 + 96*q^12 + 465*q^13 - 18*q^14 - 1410*q^15 + 2880*q^16 - 2309*q^17
- 375*q^18 + 1920*q^19 - 1740*q^20 + 630*q^21 - 948*q^22 + 3730*q^23 -
3240*q^24 + 450*q^25 - 330*q^26 + 3360*q^27 - 8280*q^28 + 5280*q^29 +
O(q^30),
q^3 - 8*q^4 + 30*q^5 - 70*q^6 + 105*q^7 - 80*q^8 - 37*q^9 + 180*q^10 -
200*q^11 + 20*q^12 + 161*q^13 - 6*q^14 - 515*q^15 + 960*q^16 - 735*q^17 -
74*q^18 + 640*q^19 - 560*q^20 + 210*q^21 - 400*q^22 + 1121*q^23 - 1080*q^24
+ 300*q^25 - 110*q^26 + 1210*q^27 - 2796*q^28 + 1760*q^29 + O(q^30)
]

Total time: 0.310 seconds, Total memory usage: 5.19MB

************** MAGMA *****************
Host 217.255.64.110 (217.255.64.110)
Time: Thu Sep 16 16:11:46 2004

Input: 5+3

Output: Magma V2.11-6     Thu Sep 16 2004 16:11:46 on modular  [Seed = 2576427840]
-------------------------------------

8

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 217.255.64.110 (217.255.64.110)
Time: Thu Sep 16 16:12:04 2004

Input: lim 3^n

Output: Magma V2.11-6     Thu Sep 16 2004 16:12:04 on modular  [Seed = 2626956883]
-------------------------------------

>> lim 3^n;
^

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 137.99.17.159 (137.99.17.159)
Time: Thu Sep 16 18:02:35 2004

Input: Mod(3,4)

Output: Magma V2.11-6     Thu Sep 16 2004 18:02:35 on modular  [Seed = 2543639473]
-------------------------------------

>> Mod(3,4);
^
Runtime error in procedure call: Attempting to call something that is not
callable

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 202.246.252.129 (202.246.252.129)
Time: Thu Sep 16 23:48:53 2004

Input: 100000!

Output: Magma V2.11-6     Thu Sep 16 2004 23:48:53 on modular  [Seed = 740766679]
-------------------------------------

>> 100000!;
^

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 202.246.252.129 (202.246.252.129)
Time: Thu Sep 16 23:49:06 2004

Input: 100000!;

Output: Magma V2.11-6     Thu Sep 16 2004 23:49:06 on modular  [Seed = 3738550578]
-------------------------------------

>> 100000!;;
^

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Fri Sep 17 02:22:47 2004

Input: 111112111112111112111112111112111112 / 7

Output: Magma V2.11-6     Fri Sep 17 2004 02:22:47 on modular  [Seed = 2609928269]
-------------------------------------

111112111112111112111112111112111112/7

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Fri Sep 17 02:23:11 2004

Input: 1111121111121111121111121111121111113 / 7

Output: Magma V2.11-6     Fri Sep 17 2004 02:23:10 on modular  [Seed = 1735173321]
-------------------------------------

1111121111121111121111121111121111113/7

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Fri Sep 17 02:23:30 2004

Input: 1111121111121111121111121111121111114 / 7

Output: Magma V2.11-6     Fri Sep 17 2004 02:23:30 on modular  [Seed = 1818734574]
-------------------------------------

1111121111121111121111121111121111114/7

Total time: 0.200 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Fri Sep 17 02:23:36 2004

Input: 1111121111121111121111121111121111115 / 7

Output: Magma V2.11-6     Fri Sep 17 2004 02:23:36 on modular  [Seed = 1903866617]
-------------------------------------

1111121111121111121111121111121111115/7

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Fri Sep 17 02:23:40 2004

Input: 1111121111121111121111121111121111116 / 7

Output: Magma V2.11-6     Fri Sep 17 2004 02:23:40 on modular  [Seed = 1987950074]
-------------------------------------

158731587303015874444445873017301588

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Fri Sep 17 02:26:01 2004

Input: 111112111112111112111112111112111112 / 7

Output: Magma V2.11-6     Fri Sep 17 2004 02:26:01 on modular  [Seed = 1146062429]
-------------------------------------

111112111112111112111112111112111112/7

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Fri Sep 17 02:26:06 2004

Input: 111112111112111112111112111112111116 / 7

Output: Magma V2.11-6     Fri Sep 17 2004 02:26:06 on modular  [Seed = 1229097815]
-------------------------------------

111112111112111112111112111112111116/7

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Fri Sep 17 02:26:16 2004

Input: 111112111112111112111112111112111113 / 7

Output: Magma V2.11-6     Fri Sep 17 2004 02:26:16 on modular  [Seed = 1313180838]
-------------------------------------

15873158730301587444444587301730159

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 212.56.75.172 (212.56.75.172)
Time: Fri Sep 17 06:45:14 2004

Input: p:=3518005926601707472344309601987042658861560810593957361511478230105755939320279041;
A:=1365811763678898698181874217447040796041508547734446123826372513985529239175518442;
x:=1161405927501381213550560845440289090362279668240004844643403967810212462302188039;
K := GF(p);
A := K!A;
x := K!x;
b := x^3 + A*x^2 + x;
E := EllipticCurve([0,b*A,0,b^2,0]);
time FactoredOrder(E);

Output: Magma V2.11-6     Fri Sep 17 2004 06:45:13 on modular  [Seed = 1381618439]
-------------------------------------

>>     K := GF(p);
^
Runtime error in 'GF': Argument 1 (35180059266017074723443096019870426588615608\
10593957361511478230105755939320279041) is not a prime power

>>     A := K!A;
^
User error: Identifier 'K' has not been declared or assigned

>>     x := K!x;
^
User error: Identifier 'K' has not been declared or assigned

>>     time FactoredOrder(E);
^
Runtime error in 'FactoredOrder': Algorithm does not work for this ring

Total time: 0.200 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 144.51.64.179 (144.51.64.179)
Time: Fri Sep 17 10:06:52 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Fri Sep 17 2004 10:06:52 on modular  [Seed = 2813069748]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.59.175.120 (208.59.175.120)
Time: Fri Sep 17 11:30:05 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Fri Sep 17 2004 11:30:05 on modular  [Seed = 672659]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.59.175.120 (208.59.175.120)
Time: Fri Sep 17 11:30:33 2004

Input: 2+2;

Output: Magma V2.11-6     Fri Sep 17 2004 11:30:33 on modular  [Seed = 303583333]
-------------------------------------

4

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 66.63.132.139 (66.63.132.139)
Time: Fri Sep 17 11:52:47 2004

Input: E := EllipticCurve([0, -2, 0, -3, 0]);
r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p
E := EllipticCurve([0, -4, 0, 0, 0]);
r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p
E := EllipticCurve([0, -6, 0, 5, 0]);
r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p
E := EllipticCurve([0, -8, 0, 12, 0]);
r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p
E := EllipticCurve([0, -10, 0, 21, 0]);
r,Lvalue:=AnalyticRank(E);r,Lvalue/RealPeriod(E)/2.0/&*[TamagawaNumber(E,p) : p

Output: Magma V2.11-6     Fri Sep 17 2004 11:52:46 on modular  [Seed = 2643973283]
-------------------------------------

0 1.000029449904763315993584

>> E := EllipticCurve([0, -4, 0, 0, 0]);
^
Runtime error in 'EllipticCurve': Curve is singular
0 1.000029449904763315993584
0 0.99999159706442125556
0 1.00018562171883295894032
0 0.99995372381138473939

Total time: 0.230 seconds, Total memory usage: 7.91MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:00:24 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,0,0,
-10748538,-13564409372]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:00:24 on modular  [Seed = 2745826040]
-------------------------------------

[ <2, 11>, <31, 1>, <419, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:01:10 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,0,0,
-41721799,-103737357815]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:01:09 on modular  [Seed = 2879517325]
-------------------------------------

[ <2, 17>, <7, 5>, <43, 7> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:01:43 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-90651038,332205857413]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:01:43 on modular  [Seed = 2930046890]
-------------------------------------

[ <2, 4>, <5, 7>, <11, 2>, <59, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:02:22 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,0,
-152124005,722128101459]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:02:22 on modular  [Seed = 2426063229]
-------------------------------------

[ <2, 12>, <3, 1>, <13, 4>, <41, 3> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:03:00 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,0,
-28761644,-59360635872]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:02:59 on modular  [Seed = 2610020907]
-------------------------------------

[ <2, 8>, <3, 3>, <7, 8>, <11, 3> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:03:34 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-57266795,-166802451946]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:03:34 on modular  [Seed = 2660550411]
-------------------------------------

[ <2, 10>, <11, 2>, <17, 9> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:04:11 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-221534375,-1269186118945]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:04:10 on modular  [Seed = 2257379071]
-------------------------------------

[ <2, 16>, <3, 10>, <7, 9>, <29, 4> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:04:51 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-62263598,189122621438]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:04:51 on modular  [Seed = 2307117513]
-------------------------------------

[ <3, 16>, <11, 10>, <23, 2> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:05:28 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,0,1,
-8846298,-9973354697]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:05:28 on modular  [Seed = 2357646503]
-------------------------------------

[ <3, 8>, <5, 4>, <41, 9> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:06:04 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,0,
-2358088,-1391333392]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:06:04 on modular  [Seed = 1987849848]
-------------------------------------

[ <2, 22>, <11, 8>, <13, 3> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:38:41 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,0,
-78497089,-267713882657]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:38:40 on modular  [Seed = 757550463]
-------------------------------------

[ <2, 15>, <467, 1> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:39:15 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,0,
-226761592,16537796026324]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:39:15 on modular  [Seed = 370964007]
-------------------------------------

[ <2, 16>, <7, 1>, <47, 1>, <3853, 1>, <11813, 1>, <119634437803901, 1> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:39:32 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,0,
-1226761592,16537796026324]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:39:32 on modular  [Seed = 454130493]
-------------------------------------

[ <2, 22>, <11, 2>, <13, 10> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:40:07 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-530909526,-4708460055251]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:40:07 on modular  [Seed = 50946822]
-------------------------------------

[ <2, 4>, <3, 20>, <11, 2>, <37, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:40:49 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,0,
-181974412,944790939840]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:40:49 on modular  [Seed = 68052183]
-------------------------------------

[ <2, 8>, <41, 3>, <89, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:41:23 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-603291645,-5703318196155]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:41:23 on modular  [Seed = 151218616]
-------------------------------------

[ <2, 30>, <3, 7>, <5, 1>, <17, 2>, <19, 4> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:42:00 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-57911100,-169610897989]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:41:59 on modular  [Seed = 4076376679]
-------------------------------------

[ <3, 9>, <5, 3>, <7, 11>, <13, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:42:44 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,0,
-2589844801,50728419550751]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:42:44 on modular  [Seed = 4110325650]
-------------------------------------

[ <2, 23>, <3, 7>, <151, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:43:37 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-1020418251,-12546075035323]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:43:37 on modular  [Seed = 4244021191]
-------------------------------------

[ <2, 12>, <3, 9>, <11, 14>, <13, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:44:15 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-697923401,-7096579558711]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:44:15 on modular  [Seed = 3790308092]
-------------------------------------

[ <2, 8>, <3, 15>, <37, 2>, <43, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:44:49 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-113379806,464707239021]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:44:49 on modular  [Seed = 3637689147]
-------------------------------------

[ <2, 12>, <3, 3>, <11, 14>, <13, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:45:29 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-113241321,463855087053]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:45:29 on modular  [Seed = 3721903638]
-------------------------------------

[ <2, 13>, <3, 12>, <11, 9>, <13, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:46:15 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,1,0,
-753897173,7967079728808]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:46:15 on modular  [Seed = 3318720080]
-------------------------------------

[ <3, 2>, <5, 3>, <11, 4>, <13, 7> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:46:53 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,0,1,
-16934420,26821356306]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:46:52 on modular  [Seed = 3468995760]
-------------------------------------

[ <2, 16>, <79, 1>, <179, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:47:26 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,1,
-14661192,-21607376324]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:47:26 on modular  [Seed = 2965033708]
-------------------------------------

[ <3, 9>, <7, 8>, <61, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 13:48:06 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-196062931,1056723815733]))));

Output: Magma V2.11-6     Fri Sep 17 2004 13:48:06 on modular  [Seed = 3049248657]
-------------------------------------

[ <2, 11>, <13, 9>, <79, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 15:46:12 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-11250387,-14522750766]))));

Output: Magma V2.11-6     Fri Sep 17 2004 15:46:12 on modular  [Seed = 2745818578]
-------------------------------------

[ <2, 12>, <3, 9>, <5, 14>, <43, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 15:46:53 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-108369279,-424190475715]))));

Output: Magma V2.11-6     Fri Sep 17 2004 15:46:52 on modular  [Seed = 2930036982]
-------------------------------------

[ <2, 4>, <3, 3>, <5, 2>, <911, 1>, <376919928022446989, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 15:47:13 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-108369279,-434190475715]))));

Output: Magma V2.11-6     Fri Sep 17 2004 15:47:13 on modular  [Seed = 2510285729]
-------------------------------------

[ <2, 4>, <3, 13>, <5, 2>, <11, 1>, <31, 2> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 15:47:57 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-6867000464,219029251851123]))));

Output: Magma V2.11-6     Fri Sep 17 2004 15:47:57 on modular  [Seed = 2476338571]
-------------------------------------

[ <2, 14>, <3, 18>, <41, 7> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Fri Sep 17 15:48:46 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,0,1,
-115975872,-480898690802]))));

Output: Magma V2.11-6     Fri Sep 17 2004 15:48:45 on modular  [Seed = 2610029939]
-------------------------------------

[ <2, 9>, <3, 15>, <71, 7> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'129.94.'
************** MAGMA *****************
Host 129.94.6.30 (129.94.6.30)
Time: Sat Sep 18 03:59:27 2004

Input: 37249588852282552285743302297396100822355179407163315972232664422849771058311

Output: Magma V2.11-6     Sat Sep 18 2004 03:59:26 on modular  [Seed = 2274176039]
-------------------------------------

37249588852282552285743302297396100822355179407163315972232664422849771058311

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.185.'
************** MAGMA *****************
Host 66.185.84.202 (66.185.84.202)
Time: Sat Sep 18 04:19:36 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Sat Sep 18 2004 04:19:36 on modular  [Seed = 607029949]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

'211.28.'
************** MAGMA *****************
Host 211.28.121.5 (211.28.121.5)
Time: Sat Sep 18 08:07:03 2004

Input: 13724958885228255228574330229739610082235517940716331597223266442284977105831

Output: Magma V2.11-6     Sat Sep 18 2004 08:07:03 on modular  [Seed = 3840508161]
-------------------------------------

13724958885228255228574330229739610082235517940716331597223266442284977105831

Total time: 0.190 seconds, Total memory usage: 3.51MB

'144.137'
************** MAGMA *****************
Host 144.137.23.49 (144.137.23.49)
Time: Sat Sep 18 08:07:46 2004

Input: 37249588852282552285743302297396100822355179407163315972232664422849771058311

Output: Magma V2.11-6     Sat Sep 18 2004 08:07:46 on modular  [Seed = 4176846056]
-------------------------------------

37249588852282552285743302297396100822355179407163315972232664422849771058311

Total time: 0.190 seconds, Total memory usage: 3.51MB

'144.137'
************** MAGMA *****************
Host 144.137.23.49 (144.137.23.49)
Time: Sat Sep 18 08:14:37 2004

Input: 37249588852282552285743302297396100822355179407163315972232664422849771058311 mod 26

Output: Magma V2.11-6     Sat Sep 18 2004 08:14:36 on modular  [Seed = 251816102]
-------------------------------------

9

Total time: 0.180 seconds, Total memory usage: 3.51MB

'144.137'
************** MAGMA *****************
Host 144.137.23.49 (144.137.23.49)
Time: Sat Sep 18 08:15:06 2004

Input: 37249588852282552285743302 mod 26

Output: Magma V2.11-6     Sat Sep 18 2004 08:15:05 on modular  [Seed = 168259014]
-------------------------------------

8

Total time: 0.190 seconds, Total memory usage: 3.51MB

'144.137'
************** MAGMA *****************
Host 144.137.23.49 (144.137.23.49)
Time: Sat Sep 18 08:15:13 2004

Input: 372495888 mod 26

Output: Magma V2.11-6     Sat Sep 18 2004 08:15:13 on modular  [Seed = 304051654]
-------------------------------------

24

Total time: 0.190 seconds, Total memory usage: 3.51MB

'144.137'
************** MAGMA *****************
Host 144.137.23.49 (144.137.23.49)
Time: Sat Sep 18 08:16:29 2004

Input: 37249588852282552285743302297396100822355179407163315972232664422849771058311 mod 26

Output: Magma V2.11-6     Sat Sep 18 2004 08:16:29 on modular  [Seed = 420773633]
-------------------------------------

9

Total time: 0.190 seconds, Total memory usage: 3.51MB

'193.77.'
************** MAGMA *****************
Host 193.77.140.241 (193.77.140.241)
Time: Sat Sep 18 11:35:15 2004

Input: Input: Q := RationalField();
p := 5; q := 7; n := p*q;
r := 0;

Output: WARNING: MAGMA command contains unsafe command 'put', so it will not be executed.
'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:38:19 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,1,0,
-6231948258,-189360689955177]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:38:19 on modular  [Seed = 1009901967]
-------------------------------------

[ <3, 1>, <5, 7>, <7, 7>, <61, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:39:07 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-1206819613,16136887555156]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:39:07 on modular  [Seed = 826076370]
-------------------------------------

[ <5, 5>, <7, 7>, <11, 1>, <17, 3> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:39:49 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,1,0,
-127121156096,-17445209248916956]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:39:48 on modular  [Seed = 909896234]
-------------------------------------

[ <2, 2>, <13, 3>, <41, 10> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:40:25 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,0,0,
-1982849926,-33984821509948]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:40:25 on modular  [Seed = 1262917498]
-------------------------------------

[ <2, 5>, <3, 7>, <7, 6>, <151, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:41:02 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,0,1,
-3904770297,-93916353965924]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:41:02 on modular  [Seed = 1078828054]
-------------------------------------

[ <2, 34>, <3, 2>, <7, 1>, <31, 9> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:41:37 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,1,1,
-9277384542,343939115427227]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:41:37 on modular  [Seed = 1481999569]
-------------------------------------

[ <2, 10>, <11, 8>, <13, 10> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:42:15 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,1,
-1106997597,-14176470901579]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:42:15 on modular  [Seed = 1565557234]
-------------------------------------

[ <3, 12>, <7, 6>, <67, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:42:50 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,0,
-12412]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:42:50 on modular  [Seed = 1381994128]
-------------------------------------

>> Factorization(Numerator(Discriminant(EllipticCurve([0,-1,0,
^
Runtime error in 'EllipticCurve': Sequence length must be two or five

Total time: 0.180 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:43:08 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,0,
-1241281736,16833563535740]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:43:07 on modular  [Seed = 1465551748]
-------------------------------------

[ <2, 10>, <5, 12>, <31, 9> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:43:44 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-1112169042,14275913072724]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:43:44 on modular  [Seed = 1835053669]
-------------------------------------

[ <2, 28>, <3, 9>, <11, 9>, <17, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:44:18 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-223732895,-1275017552377]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:44:17 on modular  [Seed = 1701362252]
-------------------------------------

[ <2, 30>, <3, 9>, <11, 9>, <17, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:44:23 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-223732895,-1275017552377]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:44:23 on modular  [Seed = 2054661461]
-------------------------------------

[ <2, 30>, <3, 9>, <11, 9>, <17, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 16:47:11 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-1425212268,20709813340880]))));

Output: Magma V2.11-6     Sat Sep 18 2004 16:47:11 on modular  [Seed = 2138218680]
-------------------------------------

[ <2, 12>, <3, 9>, <11, 8>, <13, 7> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 17:13:45 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-4021030111,98141816596054]))));

Output: Magma V2.11-6     Sat Sep 18 2004 17:13:45 on modular  [Seed = 2946649006]
-------------------------------------

[ <2, 8>, <7, 13>, <17, 8> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 17:14:49 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-2648687160,-52467952043059]))));

Output: Magma V2.11-6     Sat Sep 18 2004 17:14:49 on modular  [Seed = 2812953574]
-------------------------------------

[ <2, 4>, <3, 5>, <7, 10>, <11, 4> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 17:15:28 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-23838184440,1416634705162593]))));

Output: Magma V2.11-6     Sat Sep 18 2004 17:15:27 on modular  [Seed = 3165739227]
-------------------------------------

[ <2, 4>, <3, 11>, <7, 10>, <11, 4> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 17:16:01 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-311630151,2137094698970]))));

Output: Magma V2.11-6     Sat Sep 18 2004 17:16:01 on modular  [Seed = 2981909800]
-------------------------------------

[ <2, 8>, <3, 30>, <7, 9>, <17, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Sat Sep 18 17:16:48 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,1,0,
-12220604136,519975492562527]))));

Output: Magma V2.11-6     Sat Sep 18 2004 17:16:48 on modular  [Seed = 3065729662]
-------------------------------------

[ <3, 1>, <19, 9>, <53, 1> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'80.164.'
************** MAGMA *****************
Host 80.164.88.73 (80.164.88.73)
Time: Sat Sep 18 23:56:39 2004

Input: (2x-4)+(5x-19)

Output: Magma V2.11-6     Sat Sep 18 2004 23:56:39 on modular  [Seed = 2190393594]
-------------------------------------

>> (2x-4)+(5x-19);
^

Total time: 0.190 seconds, Total memory usage: 3.51MB

'80.164.'
************** MAGMA *****************
Host 80.164.88.73 (80.164.88.73)
Time: Sat Sep 18 23:56:59 2004

Input: (2*x-4)+(5*x-19)

Output: Magma V2.11-6     Sat Sep 18 2004 23:56:59 on modular  [Seed = 2543572243]
-------------------------------------

>> (2*x-4)+(5*x-19);
^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.254 (66.63.132.254)
Time: Sun Sep 19 00:35:26 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-60076619,-176354810358]);
E;
f := P!Reverse([13697,-1424,25026,1424,13697]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: Magma V2.11-6 Sun Sep 19 2004 00:35:22 on modular [Seed = 757162153] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 60076619*x - 176354810358 over Rational Field 13697*x^4 - 1424*x^3 + 25026*x^2 + 1424*x + 13697 4 Point [ 1, 4, 20, 10 ] was singular mod 101 and ignored at the #1 lift Point [ 1, 39, 86, 65 ] was singular mod 101 and ignored at the #1 lift Point [ 1, 64, 35, 65 ] was singular mod 101 and ignored at the #1 lift Point [ 1, 92, 52, 72 ] was singular mod 101 and ignored at the #3 lift [] Scheme over Rational Field defined by 2*r1^2 + 4*r1*r3 + 2*r1*r4 - 2*r2^2 + 2*r2*r3 - 43*r3^2 - 74*r3*r4 + 45*r4^2, 4*r1*r2 + 2*r1*r3 - 4*r1*r4 - 2*r2*r4 + 38*r3^2 - 90*r3*r4 - 36*r4^2 >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: Sch[FldRat]

Total time: 3.140 seconds, Total memory usage: 9.15MB

'141.84.'
************** MAGMA *****************
Host 141.84.69.18 (141.84.69.18)
Time: Sun Sep 19 12:51:06 2004

Input: FindGroupOrder2 := function (p, s)
K := GF(p);
v := K ! (4*s);
u := K ! (s^2-5);
x := u^3;
b := 4*x*v;
a := (v-u)^3*(3*u+v);
A := a/b-2;
x := x/v^3;
b := x^3 + A*x^2 + x;
E := EllipticCurve([0,b*A,0,b^2,0]);
return FactoredOrder(E);
end function;

for i:=5, 100 do
print(FindGroupOrder2(52068472442119144511578580563, i));
endfor;

Output: Magma V2.11-6     Sun Sep 19 2004 12:51:05 on modular  [Seed = 757191925]
-------------------------------------

>> for i:=5, 100 do
^

>>   print(FindGroupOrder2(52068472442119144511578580563, i));
^
User error: Identifier 'i' has not been declared or assigned

>> endfor;
^
User error: Identifier 'endfor' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'141.84.'
************** MAGMA *****************
Host 141.84.69.18 (141.84.69.18)
Time: Sun Sep 19 12:51:14 2004

Input: FindGroupOrder2 := function (p, s)
K := GF(p);
v := K ! (4*s);
u := K ! (s^2-5);
x := u^3;
b := 4*x*v;
a := (v-u)^3*(3*u+v);
A := a/b-2;
x := x/v^3;
b := x^3 + A*x^2 + x;
E := EllipticCurve([0,b*A,0,b^2,0]);
return FactoredOrder(E);
end function;

for i:=5 to 100 do
print(FindGroupOrder2(52068472442119144511578580563, i));
endfor;

Output: Magma V2.11-6     Sun Sep 19 2004 12:51:14 on modular  [Seed = 809289747]
-------------------------------------

User error: syntax error at end of input

Total time: 0.180 seconds, Total memory usage: 3.51MB

'141.84.'
************** MAGMA *****************
Host 141.84.69.18 (141.84.69.18)
Time: Sun Sep 19 12:52:16 2004

Input: FindGroupOrder2 := function (p, s)
K := GF(p);
v := K ! (4*s);
u := K ! (s^2-5);
x := u^3;
b := 4*x*v;
a := (v-u)^3*(3*u+v);
A := a/b-2;
x := x/v^3;
b := x^3 + A*x^2 + x;
E := EllipticCurve([0,b*A,0,b^2,0]);
return FactoredOrder(E);
end function;

for i:=5 to 100 do
print(FindGroupOrder2(52068472442119144511578580563, i));
end for;

Output: Magma V2.11-6     Sun Sep 19 2004 12:52:16 on modular  [Seed = 926666582]
-------------------------------------

FindGroupOrder2(
p: 52068472442119144511578580563,
s: 5
)
>>    E := EllipticCurve([0,b*A,0,b^2,0]);
^
Runtime error in 'EllipticCurve': Curve is singular

Total time: 0.190 seconds, Total memory usage: 3.51MB

'141.84.'
************** MAGMA *****************
Host 141.84.69.18 (141.84.69.18)
Time: Sun Sep 19 12:52:46 2004

Input: FindGroupOrder2 := function (p, s)
K := GF(p);
v := K ! (4*s);
u := K ! (s^2-5);
x := u^3;
b := 4*x*v;
a := (v-u)^3*(3*u+v);
A := a/b-2;
x := x/v^3;
b := x^3 + A*x^2 + x;
E := EllipticCurve([0,b*A,0,b^2,0]);
return FactoredOrder(E);
end function;

for i:=7 to 100 do
print(FindGroupOrder2(52068472442119144511578580563, i));
end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Sun Sep 19 2004 12:52:25 on modular  [Seed = 976667218]
-------------------------------------

[ <2, 4>, <3, 2>, <59, 1>, <2319593, 1>, <2642095695684730973, 1> ]
[ <2, 2>, <3, 2>, <7, 1>, <71, 1>, <59069, 1>, <49267023929131497563, 1> ]
[ <2, 4>, <3, 2>, <324017563, 1>, <1115947576524982363, 1> ]
[ <2, 5>, <3, 2>, <11, 1>, <4290784843, 1>, <3830477591267753, 1> ]
[ <2, 2>, <3, 1>, <149, 1>, <433, 1>, <67254202306006181317921, 1> ]
[ <2, 2>, <3, 2>, <2777, 1>, <33569, 1>, <15515224075103423687, 1> ]
[ <2, 3>, <3, 2>, <173, 1>, <23567, 1>, <177374806783259308159, 1> ]
[ <2, 4>, <3, 5>, <5, 1>, <73, 1>, <701, 1>, <1129, 1>, <46360035105330971, 1> ]
[ <2, 2>, <3, 2>, <17, 1>, <106276111, 1>, <800548707853977073, 1> ]
[ <2, 4>, <3, 1>, <47, 1>, <137, 1>, <373, 1>, <451654500887954154239, 1> ]
[ <2, 5>, <3, 1>, <7, 1>, <59, 1>, <95111, 1>, <13807746470005060213, 1> ]
[ <2, 7>, <3, 1>, <37, 1>, <149, 1>, <5867557, 1>, <4191778277008061, 1> ]
[ <2, 3>, <3, 3>, <173, 1>, <2341, 1>, <595214590838826559661, 1> ]
[ <2, 4>, <3, 1>, <5, 1>, <7, 1>, <47, 1>, <115454827, 1>, <5711571294552547, 1>
]
[ <2, 3>, <3, 1>, <5, 2>, <7, 1>, <383, 1>, <857, 1>, <4147679, 1>,
<9106276074671, 1> ]
[ <2, 3>, <3, 2>, <5, 1>, <7, 1>, <20662092238936086441996659, 1> ]
[ <2, 3>, <3, 2>, <5, 1>, <23, 1>, <127, 1>, <205487, 1>, <2903699, 1>,
<82986000109, 1> ]
[ <2, 4>, <3, 2>, <5, 1>, <7, 1>, <739, 1>, <15094649473, 1>, <926140400501, 1>
]
[ <2, 2>, <3, 2>, <7, 1>, <17, 1>, <1301, 1>, <9629, 1>, <9679, 1>, <19219, 1>,
<5215616069, 1> ]
[ <2, 5>, <3, 2>, <7, 1>, <998917, 1>, <25855616931807236989, 1> ]
[ <2, 3>, <3, 2>, <13, 2>, <151, 1>, <1060108003, 1>, <26731822904513, 1> ]
[ <2, 3>, <3, 2>, <5, 1>, <144634645672552438449230539, 1> ]
[ <2, 2>, <3, 1>, <13, 1>, <419, 1>, <796592504163128556319201, 1> ]
[ <2, 4>, <3, 3>, <41, 1>, <2237, 1>, <10565309407, 1>, <124382427707, 1> ]
[ <2, 3>, <3, 1>, <151517, 1>, <45773183, 1>, <312817555947307, 1> ]
[ <2, 4>, <3, 2>, <7, 1>, <13, 1>, <17, 1>, <71, 1>, <98459, 1>,
<33435533844299399, 1> ]
[ <2, 5>, <3, 2>, <59, 1>, <1283, 1>, <156139, 1>, <1274723, 1>, <11999867909,
1> ]
[ <2, 2>, <3, 3>, <41, 1>, <4547, 1>, <2586081874273471781849, 1> ]
[ <2, 3>, <3, 1>, <166219, 1>, <13052176255953353074019, 1> ]
[ <2, 3>, <3, 6>, <5, 3>, <281, 1>, <2447, 1>, <38351, 1>, <293453, 1>,
<9229789, 1> ]
[ <2, 4>, <3, 2>, <7, 2>, <83, 1>, <139, 1>, <195479, 1>, <3272075102878229, 1>
]
[ <2, 2>, <3, 8>, <5, 1>, <17, 2>, <23, 1>, <59696535096457491493, 1> ]
[ <2, 4>, <3, 2>, <5, 1>, <59032305047, 1>, <1225046570326177, 1> ]
[ <2, 2>, <3, 3>, <3797, 1>, <12953, 1>, <9802573754275474937, 1> ]
[ <2, 3>, <3, 2>, <1619, 1>, <683401777, 1>, <653611053069451, 1> ]
[ <2, 2>, <3, 2>, <1446346456725536565435187439, 1> ]
[ <2, 2>, <3, 1>, <5, 2>, <7, 1>, <17, 1>, <23, 1>, <101, 1>, <12248881, 1>,
<51257921947153, 1> ]
[ <2, 3>, <3, 1>, <5, 1>, <7, 4>, <67, 1>, <2697283700309339260607, 1> ]
[ <2, 4>, <3, 4>, <7, 1>, <89, 1>, <197, 1>, <327352424934192469093, 1> ]
[ <2, 2>, <3, 2>, <311, 1>, <941, 1>, <4942222841287177592537, 1> ]
[ <2, 7>, <3, 1>, <7, 2>, <13, 1>, <23, 1>, <617, 1>, <30347, 1>,
<494282705690569, 1> ]
[ <2, 4>, <3, 1>, <17, 2>, <31, 1>, <41, 1>, <79, 1>, <1113527, 1>,
<33570851954039, 1> ]
[ <2, 3>, <3, 3>, <5, 1>, <48211548557517806059739281, 1> ]
[ <2, 3>, <3, 2>, <103, 1>, <487, 1>, <101939878093, 1>, <141426907337, 1> ]
[ <2, 2>, <3, 5>, <19609, 1>, <13970723603, 1>, <195539375873, 1> ]
[ <2, 10>, <3, 1>, <399023, 1>, <118569221, 1>, <358247962733, 1> ]
[ <2, 4>, <3, 1>, <7, 1>, <17, 1>, <19, 2>, <89, 1>, <2944679, 1>,
<96349944816901, 1> ]
[ <2, 2>, <3, 1>, <179, 1>, <48193, 1>, <502986811545409709657, 1> ]
[ <2, 2>, <3, 1>, <33331, 1>, <357503, 1>, <166539851, 1>, <2186489443, 1> ]
[ <2, 14>, <3, 1>, <37, 1>, <2912668307, 1>, <9829714145233, 1> ]
[ <2, 4>, <3, 1>, <113, 1>, <9599644624284496401794497, 1> ]
[ <2, 4>, <3, 1>, <1084759842544151226795668981, 1> ]
[ <2, 6>, <3, 2>, <13, 1>, <19, 1>, <89, 1>, <251, 1>, <443, 1>, <87697433, 1>,
<421697537, 1> ]
[ <2, 2>, <3, 4>, <11, 1>, <29, 1>, <41, 1>, <21391, 1>, <574412919110233367, 1>
]
[ <2, 3>, <3, 1>, <47, 1>, <71, 1>, <277, 1>, <197927, 1>, <743849, 1>,
<15941816057, 1> ]
[ <2, 3>, <3, 2>, <17, 1>, <113, 1>, <443, 1>, <4517, 1>, <188131344258396373,
1> ]
[ <2, 2>, <3, 3>, <13, 2>, <449, 1>, <55721, 1>, <19595353, 1>, <5818968983, 1>
]
[ <2, 4>, <3, 1>, <1084759842544144253924955389, 1> ]
[ <2, 3>, <3, 2>, <19, 1>, <54165029951, 1>, <702699673490999, 1> ]

Errors: /bin/sh: line 1: 24603 Killed                  nice -n 19 /usr/local/bin/magma

'141.84.'
************** MAGMA *****************
Host 141.84.69.18 (141.84.69.18)
Time: Sun Sep 19 12:54:12 2004

Input: FindGroupOrder2 := function (p, s)
K := GF(p);
v := K ! (4*s);
u := K ! (s^2-5);
x := u^3;
b := 4*x*v;
a := (v-u)^3*(3*u+v);
A := a/b-2;
x := x/v^3;
b := x^3 + A*x^2 + x;
E := EllipticCurve([0,b*A,0,b^2,0]);
return FactoredOrder(E);
end function;

for i:=7 to 30 do
print(i,":",FindGroupOrder2(52068472442119144511578580563, i));
end for;

Output: Magma V2.11-6     Sun Sep 19 2004 12:54:12 on modular  [Seed = 370863747]
-------------------------------------

>>   print(i,":",FindGroupOrder2(52068472442119144511578580563, i));
^
Runtime error: No constructor provided for this type of object

Total time: 0.660 seconds, Total memory usage: 5.58MB

'141.84.'
************** MAGMA *****************
Host 141.84.69.18 (141.84.69.18)
Time: Sun Sep 19 12:55:21 2004

Input: FindGroupOrder2 := function (p, s)
K := GF(p);
v := K ! (4*s);
u := K ! (s^2-5);
x := u^3;
b := 4*x*v;
a := (v-u)^3*(3*u+v);
A := a/b-2;
x := x/v^3;
b := x^3 + A*x^2 + x;
E := EllipticCurve([0,b*A,0,b^2,0]);
return FactoredOrder(E);
end function;

for i:=7 to 30 do
print i,":",FindGroupOrder2(52068472442119144511578580563, i);
end for;

Output: Magma V2.11-6     Sun Sep 19 2004 12:55:11 on modular  [Seed = 487712211]
-------------------------------------

7 : [ <2, 4>, <3, 2>, <59, 1>, <2319593, 1>, <2642095695684730973, 1> ]
8 : [ <2, 2>, <3, 2>, <7, 1>, <71, 1>, <59069, 1>, <49267023929131497563, 1> ]
9 : [ <2, 4>, <3, 2>, <324017563, 1>, <1115947576524982363, 1> ]
10 : [ <2, 5>, <3, 2>, <11, 1>, <4290784843, 1>, <3830477591267753, 1> ]
11 : [ <2, 2>, <3, 1>, <149, 1>, <433, 1>, <67254202306006181317921, 1> ]
12 : [ <2, 2>, <3, 2>, <2777, 1>, <33569, 1>, <15515224075103423687, 1> ]
13 : [ <2, 3>, <3, 2>, <173, 1>, <23567, 1>, <177374806783259308159, 1> ]
14 : [ <2, 4>, <3, 5>, <5, 1>, <73, 1>, <701, 1>, <1129, 1>, <46360035105330971,
1> ]
15 : [ <2, 2>, <3, 2>, <17, 1>, <106276111, 1>, <800548707853977073, 1> ]
16 : [ <2, 4>, <3, 1>, <47, 1>, <137, 1>, <373, 1>, <451654500887954154239, 1> ]
17 : [ <2, 5>, <3, 1>, <7, 1>, <59, 1>, <95111, 1>, <13807746470005060213, 1> ]
18 : [ <2, 7>, <3, 1>, <37, 1>, <149, 1>, <5867557, 1>, <4191778277008061, 1> ]
19 : [ <2, 3>, <3, 3>, <173, 1>, <2341, 1>, <595214590838826559661, 1> ]
20 : [ <2, 4>, <3, 1>, <5, 1>, <7, 1>, <47, 1>, <115454827, 1>,
<5711571294552547, 1> ]
21 : [ <2, 3>, <3, 1>, <5, 2>, <7, 1>, <383, 1>, <857, 1>, <4147679, 1>,
<9106276074671, 1> ]
22 : [ <2, 3>, <3, 2>, <5, 1>, <7, 1>, <20662092238936086441996659, 1> ]
23 : [ <2, 3>, <3, 2>, <5, 1>, <23, 1>, <127, 1>, <205487, 1>, <2903699, 1>,
<82986000109, 1> ]
24 : [ <2, 4>, <3, 2>, <5, 1>, <7, 1>, <739, 1>, <15094649473, 1>,
<926140400501, 1> ]
25 : [ <2, 2>, <3, 2>, <7, 1>, <17, 1>, <1301, 1>, <9629, 1>, <9679, 1>, <19219,
1>, <5215616069, 1> ]
26 : [ <2, 5>, <3, 2>, <7, 1>, <998917, 1>, <25855616931807236989, 1> ]
27 : [ <2, 3>, <3, 2>, <13, 2>, <151, 1>, <1060108003, 1>, <26731822904513, 1> ]
28 : [ <2, 3>, <3, 2>, <5, 1>, <144634645672552438449230539, 1> ]
29 : [ <2, 2>, <3, 1>, <13, 1>, <419, 1>, <796592504163128556319201, 1> ]
30 : [ <2, 4>, <3, 3>, <41, 1>, <2237, 1>, <10565309407, 1>, <124382427707, 1> ]

Total time: 9.390 seconds, Total memory usage: 5.58MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 22:47:50 2004

Input: P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(31991),7,"grev-lex");
I:= ideal<P | c6*c5*c4*c3*c2*c1*c0-1,
(((((c5+c6)*c4+c6*c5)*c3+c6*c5*c4)*c2+c6*c5*c4*c3)*c1+c6*c5*c4*c3*c2)*c0+c6*c5*c
4*c3*c2*c1,
((((c4+c6)*c3+c6*c5)*c2+c6*c5*c4)*c1+c6*c5*c4*c3)*c0+c5*c4*c3*c2*c1+c6*c5*c4*c3*
c2,
(((c3+c6)*c2+c6*c5)*c1+c6*c5*c4)*c0+c4*c3*c2*c1+c5*c4*c3*c2+c6*c5*c4*c3,
((c2+c6)*c1+c6*c5)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3+c6*c5*c4,
(c1+c6)*c0+c2*c1+c3*c2+c4*c3+c5*c4+c6*c5,
c0+c1+c2+c3+c4+c5+c6>;
time B := GroebnerBasis(I);

Output: Magma V2.11-6     Sun Sep 19 2004 22:47:50 on modular  [Seed = 2560073061]
-------------------------------------

>> P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(31991),7,"grev-lex");
^
Runtime error in 'PolynomialRing': Bad order "grev-lex"

>> 4*c3*c2*c1,
^

>> c0+c1+c2+c3+c4+c5+c6>;
^

>> time B := GroebnerBasis(I);
^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 22:50:48 2004

Input: P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(31991),7);
I:= ideal<P | c6*c5*c4*c3*c2*c1*c0-1,
(((((c5+c6)*c4+c6*c5)*c3+c6*c5*c4)*c2+c6*c5*c4*c3)*c1+c6*c5*c4*c3*c2)*c0+c6*c5*c4*c3*c2*c1,
((((c4+c6)*c3+c6*c5)*c2+c6*c5*c4)*c1+c6*c5*c4*c3)*c0+c5*c4*c3*c2*c1+c6*c5*c4*c3*c2,
(((c3+c6)*c2+c6*c5)*c1+c6*c5*c4)*c0+c4*c3*c2*c1+c5*c4*c3*c2+c6*c5*c4*c3,
((c2+c6)*c1+c6*c5)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3+c6*c5*c4,
(c1+c6)*c0+c2*c1+c3*c2+c4*c3+c5*c4+c6*c5,
c0+c1+c2+c3+c4+c5+c6>;
time B := GroebnerBasis(I);

Output: Magma V2.11-6     Sun Sep 19 2004 22:50:45 on modular  [Seed = 2543358777]
-------------------------------------

Time: 2.570

Total time: 2.759 seconds, Total memory usage: 21.19MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 22:51:13 2004

Input: P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(31991),7);
I:= ideal<P | c6*c5*c4*c3*c2*c1*c0-1,
(((((c5+c6)*c4+c6*c5)*c3+c6*c5*c4)*c2+c6*c5*c4*c3)*c1+c6*c5*c4*c3*c2)*c0+c6*c5*c4*c3*c2*c1,
((((c4+c6)*c3+c6*c5)*c2+c6*c5*c4)*c1+c6*c5*c4*c3)*c0+c5*c4*c3*c2*c1+c6*c5*c4*c3*c2,
(((c3+c6)*c2+c6*c5)*c1+c6*c5*c4)*c0+c4*c3*c2*c1+c5*c4*c3*c2+c6*c5*c4*c3,
((c2+c6)*c1+c6*c5)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3+c6*c5*c4,
(c1+c6)*c0+c2*c1+c3*c2+c4*c3+c5*c4+c6*c5,
c0+c1+c2+c3+c4+c5+c6>;
time B := GroebnerBasis(I);
B;

Output: Magma V2.11-6     Sun Sep 19 2004 22:51:10 on modular  [Seed = 3940937311]
-------------------------------------

Time: 2.550
[
c0 + c1 + c2 + c3 + c4 + c5 + c6,
c1^2 + c1*c5^2*c6^6 + 15998*c1*c5 + 15997*c1*c6 + 9140*c2*c5*c6^7 +
6858*c2*c5 + 10244*c2*c6^15 + 11587*c2*c6^8 + 26153*c2*c6 + c3^2 +
2*c3*c4^2*c6^6 + 15995*c3*c4 + 15998*c3*c5^2*c6^6 + 23755*c3*c5*c6^14 +
7508*c3*c5*c6^7 + 16726*c3*c5 + 26869*c3*c6^15 + 14771*c3*c6^8 +
6345*c3*c6 + 22853*c4^4*c6^5 + 4582*c4^3*c6^6 + 25139*c4^2 +
7998*c4*c5^2*c6^6 + 12038*c4*c5*c6^14 + 10723*c4*c5*c6^7 + 1233*c4*c5 +
22761*c4*c6^15 + 5837*c4*c6^8 + 7953*c4*c6 + 29384*c5^22*c6 +
58*c5^21*c6^2 + 1781*c5^20*c6^3 + 26031*c5^19*c6^4 + 24683*c5^18*c6^5 +
9490*c5^17*c6^6 + 20458*c5^16 + 22083*c5^15*c6 + 1786*c5^14*c6^2 +
3870*c5^13*c6^3 + 9566*c5^12*c6^4 + 30620*c5^11*c6^5 + 14750*c5^10*c6^6
+ 6102*c5^9 + 4007*c5^8*c6 + 20780*c5^7*c6^2 + 5760*c5^6*c6^3 +
28380*c5^5*c6^4 + 7534*c5^4*c6^5 + 25599*c5^3*c6^90 + 28550*c5^3*c6^83 +
29065*c5^3*c6^76 + 22476*c5^3*c6^69 + 3537*c5^3*c6^62 + 19374*c5^3*c6^55
+ 10154*c5^3*c6^48 + 31770*c5^3*c6^41 + 22064*c5^3*c6^34 +
24898*c5^3*c6^27 + 12859*c5^3*c6^20 + 26272*c5^3*c6^13 + 31055*c5^3*c6^6
+ 11243*c5^2*c6^84 + 26547*c5^2*c6^77 + 26467*c5^2*c6^70 +
11277*c5^2*c6^63 + 15075*c5^2*c6^56 + 18600*c5^2*c6^49 +
24381*c5^2*c6^42 + 22476*c5^2*c6^35 + 31746*c5^2*c6^28 +
22930*c5^2*c6^21 + 160*c5^2*c6^14 + 24855*c5^2*c6^7 + 21043*c5^2 +
29443*c5*c6^197 + 18007*c5*c6^190 + 30644*c5*c6^183 + 27918*c5*c6^176 +
26338*c5*c6^169 + 10099*c5*c6^162 + 7163*c5*c6^155 + 6149*c5*c6^148 +
6826*c5*c6^141 + 20428*c5*c6^134 + 17578*c5*c6^127 + 3230*c5*c6^120 +
1532*c5*c6^113 + 26078*c5*c6^106 + 843*c5*c6^99 + 16868*c5*c6^92 +
14723*c5*c6^85 + 8715*c5*c6^78 + 28953*c5*c6^71 + 27496*c5*c6^64 +
24767*c5*c6^57 + 23902*c5*c6^50 + 24359*c5*c6^43 + 6347*c5*c6^36 +
7429*c5*c6^29 + 10188*c5*c6^22 + 17140*c5*c6^15 + 15897*c5*c6^8 +
6461*c5*c6 + 20259*c6^198 + 14178*c6^191 + 21080*c6^184 + 18703*c6^177 +
19902*c6^170 + 22173*c6^163 + 2163*c6^156 + 6158*c6^149 + 8389*c6^142 +
6645*c6^135 + 15509*c6^128 + 8741*c6^121 + 29741*c6^114 + 25556*c6^107 +
21749*c6^100 + 14550*c6^93 + 29766*c6^86 + 18116*c6^79 + 16541*c6^72 +
18562*c6^65 + 31374*c6^58 + 19491*c6^51 + 479*c6^44 + 13436*c6^37 +
23974*c6^30 + 11881*c6^23 + 22028*c6^16 + 14118*c6^9 + 13968*c6^2,
c1*c2 + 31990*c1*c6 + c2^2 + 2110*c2*c5*c6^7 + 24960*c2*c5 + 9393*c2*c6^15 +
18131*c2*c6^8 + 9392*c2*c6 + 31990*c3^2 + 31988*c3*c4^2*c6^6 +
31990*c3*c4 + 27067*c3*c5^2*c6^6 + 89*c3*c5*c6^14 + 6705*c3*c5*c6^7 +
25195*c3*c5 + 23450*c3*c6^15 + 20622*c3*c6^8 + 24835*c3*c6 +
25133*c4^4*c6^5 + 3413*c4^3*c6^6 + 22845*c4^2 + 2458*c4*c5^2*c6^6 +
12730*c4*c5*c6^14 + 1601*c4*c5*c6^7 + 15199*c4*c5 + 30421*c4*c6^15 +
10982*c4*c6^8 + 2025*c4*c6 + 3514*c5^22*c6 + 11890*c5^21*c6^2 +
8404*c5^20*c6^3 + 27745*c5^19*c6^4 + 13374*c5^18*c6^5 + 16609*c5^17*c6^6
+ 17420*c5^16 + 29171*c5^15*c6 + 1045*c5^14*c6^2 + 12029*c5^13*c6^3 +
14794*c5^12*c6^4 + 30543*c5^11*c6^5 + 10279*c5^10*c6^6 + 331*c5^9 +
10319*c5^8*c6 + 30587*c5^7*c6^2 + 8146*c5^6*c6^3 + 31290*c5^5*c6^4 +
21830*c5^4*c6^5 + 28697*c5^3*c6^90 + 18421*c5^3*c6^83 + 17794*c5^3*c6^76
+ 25755*c5^3*c6^69 + 24116*c5^3*c6^62 + 25450*c5^3*c6^55 +
16897*c5^3*c6^48 + 18423*c5^3*c6^41 + 9526*c5^3*c6^34 + 11408*c5^3*c6^27
+ 18775*c5^3*c6^20 + 30239*c5^3*c6^13 + 13066*c5^3*c6^6 +
6027*c5^2*c6^84 + 6862*c5^2*c6^77 + 6500*c5^2*c6^70 + 15081*c5^2*c6^63 +
7378*c5^2*c6^56 + 2667*c5^2*c6^49 + 6048*c5^2*c6^42 + 9222*c5^2*c6^35 +
1740*c5^2*c6^28 + 2885*c5^2*c6^21 + 18864*c5^2*c6^14 + 3465*c5^2*c6^7 +
12036*c5^2 + 12546*c5*c6^197 + 1630*c5*c6^190 + 15913*c5*c6^183 +
18068*c5*c6^176 + 21934*c5*c6^169 + 10972*c5*c6^162 + 29485*c5*c6^155 +
29622*c5*c6^148 + 14384*c5*c6^141 + 1659*c5*c6^134 + 15729*c5*c6^127 +
7116*c5*c6^120 + 7534*c5*c6^113 + 23912*c5*c6^106 + 24637*c5*c6^99 +
7186*c5*c6^92 + 6969*c5*c6^85 + 11467*c5*c6^78 + 16899*c5*c6^71 +
20528*c5*c6^64 + 14127*c5*c6^57 + 25637*c5*c6^50 + 9605*c5*c6^43 +
13873*c5*c6^36 + 1529*c5*c6^29 + 21733*c5*c6^22 + 8960*c5*c6^15 +
9780*c5*c6^8 + 8293*c5*c6 + 3710*c6^198 + 4437*c6^191 + 21838*c6^184 +
30842*c6^177 + 10776*c6^170 + 811*c6^163 + 6900*c6^156 + 11312*c6^149 +
7753*c6^142 + 11564*c6^135 + 7430*c6^128 + 22021*c6^121 + 3760*c6^114 +
22167*c6^107 + 22055*c6^100 + 9498*c6^93 + 23478*c6^86 + 25974*c6^79 +
25400*c6^72 + 28362*c6^65 + 6844*c6^58 + 7205*c6^51 + 13113*c6^44 +
9539*c6^37 + 6470*c6^30 + 28054*c6^23 + 10275*c6^16 + 11032*c6^9 +
11735*c6^2,
c1*c3 + 31990*c1*c5 + 29881*c2*c5*c6^7 + 23025*c2*c5 + 26869*c2*c6^15 +
30592*c2*c6^8 + 17597*c2*c6 + 20915*c3*c5^2*c6^6 + 9202*c3*c5*c6^14 +
16635*c3*c5*c6^7 + 22149*c3*c5 + 22503*c3*c6^15 + 9043*c3*c6^8 +
27516*c3*c6 + 21534*c4*c5^2*c6^6 + 21636*c4*c5*c6^14 + 1388*c4*c5*c6^7 +
19424*c4*c5 + 7184*c4*c6^15 + 11133*c4*c6^8 + 13674*c4*c6 + 199*c5^22*c6
+ 2919*c5^21*c6^2 + 14871*c5^20*c6^3 + 12592*c5^19*c6^4 +
16279*c5^18*c6^5 + 14005*c5^17*c6^6 + 14485*c5^16 + 19201*c5^15*c6 +
16477*c5^14*c6^2 + 19588*c5^13*c6^3 + 10825*c5^12*c6^4 +
30748*c5^11*c6^5 + 17091*c5^10*c6^6 + 10194*c5^9 + 6226*c5^8*c6 +
29191*c5^7*c6^2 + 29524*c5^6*c6^3 + 30726*c5^5*c6^4 + 341*c5^4*c6^5 +
30234*c5^3*c6^90 + 18234*c5^3*c6^83 + 28590*c5^3*c6^76 +
13496*c5^3*c6^69 + 13912*c5^3*c6^62 + 23915*c5^3*c6^55 +
19088*c5^3*c6^48 + 21303*c5^3*c6^41 + 823*c5^3*c6^34 + 11952*c5^3*c6^27
+ 2640*c5^3*c6^20 + 18543*c5^3*c6^13 + 16565*c5^3*c6^6 + 4453*c5^2*c6^84
+ 23790*c5^2*c6^77 + 25247*c5^2*c6^70 + 4260*c5^2*c6^63 +
2699*c5^2*c6^56 + 21274*c5^2*c6^49 + 1328*c5^2*c6^42 + 30735*c5^2*c6^35
+ 13246*c5^2*c6^28 + 26250*c5^2*c6^21 + 26372*c5^2*c6^14 +
29914*c5^2*c6^7 + 21681*c5^2 + 16487*c5*c6^197 + 5861*c5*c6^190 +
3660*c5*c6^183 + 27000*c5*c6^176 + 8189*c5*c6^169 + 21233*c5*c6^162 +
10411*c5*c6^155 + 13515*c5*c6^148 + 18298*c5*c6^141 + 8829*c5*c6^134 +
18428*c5*c6^127 + 24095*c5*c6^120 + 11928*c5*c6^113 + 1656*c5*c6^106 +
8892*c5*c6^99 + 28411*c5*c6^92 + 22525*c5*c6^85 + 13327*c5*c6^78 +
2118*c5*c6^71 + 6517*c5*c6^64 + 9765*c5*c6^57 + 24797*c5*c6^50 +
23042*c5*c6^43 + 29418*c5*c6^36 + 11019*c5*c6^29 + 18511*c5*c6^22 +
20979*c5*c6^15 + 3541*c5*c6^8 + 9795*c5*c6 + 14228*c6^198 + 1022*c6^191
+ 1286*c6^184 + 25760*c6^177 + 6752*c6^170 + 1459*c6^163 + 7189*c6^156 +
17437*c6^149 + 27591*c6^142 + 23207*c6^135 + 26669*c6^128 + 22841*c6^121
+ 20725*c6^114 + 28397*c6^107 + 10596*c6^100 + 14232*c6^93 + 23589*c6^86
+ 9102*c6^79 + 18210*c6^72 + 15774*c6^65 + 18829*c6^58 + 17913*c6^51 +
24673*c6^44 + 26251*c6^37 + 28343*c6^30 + 30168*c6^23 + 23283*c6^16 +
857*c6^9 + 8877*c6^2,
c1*c4 + 31990*c1*c5^2*c6^6 + 15995*c1*c5 + 15996*c1*c6 + 24961*c2*c5*c6^7 +
2109*c2*c5 + 5122*c2*c6^15 + 28821*c2*c6^8 + 2969*c2*c6 +
31990*c3*c4^2*c6^6 + c3*c4 + 27071*c3*c5^2*c6^6 + 2097*c3*c5*c6^14 +
25803*c3*c5*c6^7 + 20086*c3*c5 + 28019*c3*c6^15 + 20908*c3*c6^8 +
3980*c3*c6 + 18455*c4*c5^2*c6^6 + 855*c4*c5*c6^14 + 9524*c4*c5*c6^7 +
3155*c4*c5 + 3371*c4*c6^15 + 6518*c4*c6^8 + 22104*c4*c6 + 10541*c5^22*c6
+ 31908*c5^21*c6^2 + 21169*c5^20*c6^3 + 11422*c5^19*c6^4 +
30985*c5^18*c6^5 + 1458*c5^17*c6^6 + 15223*c5^16 + 4507*c5^15*c6 +
31082*c5^14*c6^2 + 6891*c5^13*c6^3 + 24033*c5^12*c6^4 + 26123*c5^11*c6^5
+ 18078*c5^10*c6^6 + 16679*c5^9 + 7183*c5^8*c6 + 9640*c5^7*c6^2 +
19927*c5^6*c6^3 + 22371*c5^5*c6^4 + 31485*c5^4*c6^5 + 12327*c5^3*c6^90 +
10594*c5^3*c6^83 + 29823*c5^3*c6^76 + 28451*c5^3*c6^69 +
24254*c5^3*c6^62 + 6249*c5^3*c6^55 + 9049*c5^3*c6^48 + 17653*c5^3*c6^41
+ 764*c5^3*c6^34 + 13898*c5^3*c6^27 + 20123*c5^3*c6^20 + 1793*c5^3*c6^13
+ 26964*c5^3*c6^6 + 5644*c5^2*c6^84 + 2429*c5^2*c6^77 + 21047*c5^2*c6^70
+ 26764*c5^2*c6^63 + 3577*c5^2*c6^56 + 4645*c5^2*c6^49 +
16476*c5^2*c6^42 + 30073*c5^2*c6^35 + 18100*c5^2*c6^28 + 7591*c5^2*c6^21
+ 21148*c5^2*c6^14 + 6840*c5^2*c6^7 + 27699*c5^2 + 16696*c5*c6^197 +
10830*c5*c6^190 + 18379*c5*c6^183 + 4987*c5*c6^176 + 24802*c5*c6^169 +
22310*c5*c6^162 + 1087*c5*c6^155 + 19595*c5*c6^148 + 3709*c5*c6^141 +
22706*c5*c6^134 + 16415*c5*c6^127 + 8111*c5*c6^120 + 1386*c5*c6^113 +
17278*c5*c6^106 + 15200*c5*c6^99 + 19143*c5*c6^92 + 14933*c5*c6^85 +
16516*c5*c6^78 + 7846*c5*c6^71 + 20316*c5*c6^64 + 4115*c5*c6^57 +
804*c5*c6^50 + 4321*c5*c6^43 + 3599*c5*c6^36 + 20646*c5*c6^29 +
1716*c5*c6^22 + 12246*c5*c6^15 + 30282*c5*c6^8 + 1687*c5*c6 +
2685*c6^198 + 14040*c6^191 + 4609*c6^184 + 15257*c6^177 + 5175*c6^170 +
8929*c6^163 + 3166*c6^156 + 13826*c6^149 + 12357*c6^142 + 23611*c6^135 +
17867*c6^128 + 2935*c6^121 + 27069*c6^114 + 8121*c6^107 + 15357*c6^100 +
11606*c6^93 + 1982*c6^86 + 26281*c6^79 + 28483*c6^72 + 16666*c6^65 +
19855*c6^58 + 20342*c6^51 + 2271*c6^44 + 31687*c6^37 + 4851*c6^30 +
4111*c6^23 + 12768*c6^16 + 1187*c6^9 + 18151*c6^2,
c1*c5^3 + 15996*c1*c5^2*c6 + 15995*c1*c5*c6^2 + 31990*c1*c6^3 +
22147*c2*c5*c6^9 + 16148*c2*c5*c6^2 + 7032*c2*c6^17 + 11701*c2*c6^10 +
6954*c2*c6^3 + 6304*c3*c5^2*c6 + 23903*c3*c5*c6^16 + 19240*c3*c5*c6^9 +
20839*c3*c5*c6^2 + 15285*c3*c6^17 + 17538*c
** WARNING: Output too long, hence truncated.
'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 22:52:29 2004

Input: P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(99999989),7);
I:= ideal<P | c6*c5*c4*c3*c2*c1*c0-1,
(((((c5+c6)*c4+c6*c5)*c3+c6*c5*c4)*c2+c6*c5*c4*c3)*c1+c6*c5*c4*c3*c2)*c0+c6*c5*c4*c3*c2*c1,
((((c4+c6)*c3+c6*c5)*c2+c6*c5*c4)*c1+c6*c5*c4*c3)*c0+c5*c4*c3*c2*c1+c6*c5*c4*c3*c2,
(((c3+c6)*c2+c6*c5)*c1+c6*c5*c4)*c0+c4*c3*c2*c1+c5*c4*c3*c2+c6*c5*c4*c3,
((c2+c6)*c1+c6*c5)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3+c6*c5*c4,
(c1+c6)*c0+c2*c1+c3*c2+c4*c3+c5*c4+c6*c5,
c0+c1+c2+c3+c4+c5+c6>;
time B := GroebnerBasis(I);
B;

Output: Magma V2.11-6     Sun Sep 19 2004 22:52:23 on modular  [Seed = 4193713461]
-------------------------------------

Time: 5.520
[
c0 + c1 + c2 + c3 + c4 + c5 + c6,
c1^2 + c1*c5^2*c6^6 + 49999997*c1*c5 + 49999996*c1*c6 + 85714276*c2*c5*c6^7
+ 64285710*c2*c5 + 70800619*c2*c6^15 + 51530605*c2*c6^8 + 27668757*c2*c6
+ c3^2 + 2*c3*c4^2*c6^6 + 49999994*c3*c4 + 49999997*c3*c5^2*c6^6 +
29356355*c3*c5*c6^14 + 41836730*c3*c5*c6^7 + 78806901*c3*c5 +
14599685*c3*c6^15 + 67091829*c3*c6^8 + 68308468*c3*c6 +
14285715*c4^4*c6^5 + 42857150*c4^3*c6^6 + 35714285*c4^2 +
74999992*c4*c5^2*c6^6 + 24512219*c4*c5*c6^14 + 31195329*c4*c5*c6^7 +
69292439*c4*c5 + 55707548*c4*c6^15 + 24161801*c4*c6^8 + 62987768*c4*c6 +
27233731*c5^22*c6 + 61486208*c5^21*c6^2 + 47696372*c5^20*c6^3 +
25299090*c5^19*c6^4 + 83241301*c5^18*c6^5 + 49291974*c5^17*c6^6 +
86627228*c5^16 + 42693434*c5^15*c6 + 42279833*c5^14*c6^2 +
71197631*c5^13*c6^3 + 661001*c5^12*c6^4 + 10981940*c5^11*c6^5 +
36623811*c5^10*c6^6 + 849547*c5^9 + 1761319*c5^8*c6 + 71130502*c5^7*c6^2
+ 88248817*c5^6*c6^3 + 74039893*c5^5*c6^4 + 95062450*c5^4*c6^5 +
91145975*c5^3*c6^90 + 18853292*c5^3*c6^83 + 69169527*c5^3*c6^76 +
32767557*c5^3*c6^69 + 61079562*c5^3*c6^62 + 68994279*c5^3*c6^55 +
14054107*c5^3*c6^48 + 9574507*c5^3*c6^41 + 53187127*c5^3*c6^34 +
26484453*c5^3*c6^27 + 95812783*c5^3*c6^20 + 77590435*c5^3*c6^13 +
20370532*c5^3*c6^6 + 480962*c5^2*c6^84 + 70902869*c5^2*c6^77 +
17549749*c5^2*c6^70 + 94009147*c5^2*c6^63 + 70004084*c5^2*c6^56 +
81819858*c5^2*c6^49 + 258842*c5^2*c6^42 + 68594908*c5^2*c6^35 +
95374695*c5^2*c6^28 + 81864696*c5^2*c6^21 + 3464667*c5^2*c6^14 +
54044613*c5^2*c6^7 + 31296920*c5^2 + 1420387*c5*c6^197 +
90026581*c5*c6^190 + 76182222*c5*c6^183 + 65386784*c5*c6^176 +
253987*c5*c6^169 + 91030623*c5*c6^162 + 46142765*c5*c6^155 +
90119189*c5*c6^148 + 49333510*c5*c6^141 + 89969920*c5*c6^134 +
51260654*c5*c6^127 + 70320309*c5*c6^120 + 49846957*c5*c6^113 +
609650*c5*c6^106 + 80318720*c5*c6^99 + 88731292*c5*c6^92 +
83520130*c5*c6^85 + 98468996*c5*c6^78 + 80298773*c5*c6^71 +
59221420*c5*c6^64 + 15187102*c5*c6^57 + 40733036*c5*c6^50 +
92099832*c5*c6^43 + 9053375*c5*c6^36 + 41965131*c5*c6^29 +
72387392*c5*c6^22 + 76321829*c5*c6^15 + 57225873*c5*c6^8 +
46589165*c5*c6 + 62189794*c6^198 + 99043429*c6^191 + 75739147*c6^184 +
59402088*c6^177 + 7574732*c6^170 + 27939043*c6^163 + 98392087*c6^156 +
63253546*c6^149 + 13087273*c6^142 + 33343543*c6^135 + 37592532*c6^128 +
98277367*c6^121 + 65495914*c6^114 + 88100150*c6^107 + 63855878*c6^100 +
69775174*c6^93 + 74551880*c6^86 + 64812685*c6^79 + 64149790*c6^72 +
7767068*c6^65 + 98753947*c6^58 + 75860536*c6^51 + 4896692*c6^44 +
31871406*c6^37 + 94966850*c6^30 + 18290076*c6^23 + 41434679*c6^16 +
28251172*c6^9 + 56434779*c6^2,
c1*c2 + 99999988*c1*c6 + c2^2 + 35164832*c2*c5*c6^7 + 49450544*c2*c5 +
23233908*c2*c6^15 + 68916791*c2*c6^8 + 23233907*c2*c6 + 99999988*c3^2 +
99999986*c3*c4^2*c6^6 + 99999988*c3*c4 + 84615373*c3*c5^2*c6^6 +
96353087*c3*c5*c6^14 + 61773934*c3*c5*c6^7 + 41872955*c3*c5 +
11447892*c3*c6^15 + 81299049*c3*c6^8 + 22637665*c3*c6 +
35714279*c4^4*c6^5 + 32142839*c4^3*c6^6 + 14285707*c4^2 +
7692304*c4*c5^2*c6^6 + 43357423*c4*c5*c6^14 + 52803318*c4*c5*c6^7 +
96146930*c4*c5 + 68283674*c4*c6^15 + 85991809*c4*c6^8 + 52867363*c4*c6 +
64464284*c5^22*c6 + 67639242*c5^21*c6^2 + 5522292*c5^20*c6^3 +
21960050*c5^19*c6^4 + 64569527*c5^18*c6^5 + 33970818*c5^17*c6^6 +
87068377*c5^16 + 31652863*c5^15*c6 + 85473857*c5^14*c6^2 +
97062712*c5^13*c6^3 + 68274982*c5^12*c6^4 + 67654201*c5^11*c6^5 +
6871445*c5^10*c6^6 + 83620164*c5^9 + 72444739*c5^8*c6 +
84289590*c5^7*c6^2 + 65272136*c5^6*c6^3 + 40534188*c5^5*c6^4 +
30413624*c5^4*c6^5 + 16843566*c5^3*c6^90 + 24615051*c5^3*c6^83 +
69823475*c5^3*c6^76 + 94340314*c5^3*c6^69 + 84177456*c5^3*c6^62 +
27729607*c5^3*c6^55 + 42306082*c5^3*c6^48 + 6973858*c5^3*c6^41 +
39221424*c5^3*c6^34 + 78831795*c5^3*c6^27 + 10717279*c5^3*c6^20 +
53202292*c5^3*c6^13 + 2683162*c5^3*c6^6 + 17640650*c5^2*c6^84 +
2103370*c5^2*c6^77 + 4605216*c5^2*c6^70 + 19204335*c5^2*c6^63 +
31545363*c5^2*c6^56 + 27276870*c5^2*c6^49 + 92047019*c5^2*c6^42 +
56657071*c5^2*c6^35 + 32630927*c5^2*c6^28 + 61001182*c5^2*c6^21 +
7397634*c5^2*c6^14 + 45277123*c5^2*c6^7 + 24781764*c5^2 +
78508266*c5*c6^197 + 45591507*c5*c6^190 + 42782037*c5*c6^183 +
56138568*c5*c6^176 + 15351969*c5*c6^169 + 6013016*c5*c6^162 +
27980672*c5*c6^155 + 39978797*c5*c6^148 + 48441128*c5*c6^141 +
57055472*c5*c6^134 + 80320788*c5*c6^127 + 76661617*c5*c6^120 +
55728070*c5*c6^113 + 29142946*c5*c6^106 + 32568766*c5*c6^99 +
41411052*c5*c6^92 + 21582610*c5*c6^85 + 80617418*c5*c6^78 +
95624782*c5*c6^71 + 78975107*c5*c6^64 + 3028670*c5*c6^57 +
56268159*c5*c6^50 + 34534747*c5*c6^43 + 20268985*c5*c6^36 +
76196675*c5*c6^29 + 897418*c5*c6^22 + 83292864*c5*c6^15 +
61452470*c5*c6^8 + 49309082*c5*c6 + 46466634*c6^198 + 61426125*c6^191 +
42187424*c6^184 + 65473613*c6^177 + 5864203*c6^170 + 75625931*c6^163 +
36967366*c6^156 + 95772726*c6^149 + 19343416*c6^142 + 47043706*c6^135 +
56141464*c6^128 + 41265834*c6^121 + 70104755*c6^114 + 43643558*c6^107 +
40838218*c6^100 + 88815977*c6^93 + 93961080*c6^86 + 20421713*c6^79 +
56864584*c6^72 + 70598384*c6^65 + 96225571*c6^58 + 29665746*c6^51 +
23420767*c6^44 + 80011868*c6^37 + 52853391*c6^30 + 68424620*c6^23 +
82379920*c6^16 + 13669267*c6^9 + 37119255*c6^2,
c1*c3 + 99999988*c1*c5 + 64835157*c2*c5*c6^7 + 549449*c2*c5 +
14599685*c2*c6^15 + 30828098*c2*c6^8 + 89187589*c2*c6 +
65384606*c3*c5^2*c6^6 + 91872952*c3*c5*c6^14 + 85675029*c3*c5*c6^7 +
72451991*c3*c5 + 54643153*c3*c6^15 + 61175425*c3*c6^8 + 68796788*c3*c6 +
17307692*c4*c5^2*c6^6 + 5756723*c4*c5*c6^14 + 44572769*c4*c5*c6^7 +
32362805*c4*c5 + 15726188*c4*c6^15 + 16249438*c4*c6^8 + 68024363*c4*c6 +
55620967*c5^22*c6 + 57440752*c5^21*c6^2 + 9214573*c5^20*c6^3 +
98500343*c5^19*c6^4 + 40979080*c5^18*c6^5 + 40981054*c5^17*c6^6 +
78891859*c5^16 + 49481300*c5^15*c6 + 23182028*c5^14*c6^2 +
4629641*c5^13*c6^3 + 80973117*c5^12*c6^4 + 51276028*c5^11*c6^5 +
98856549*c5^10*c6^6 + 87550208*c5^9 + 39934289*c5^8*c6 +
34674329*c5^7*c6^2 + 86155776*c5^6*c6^3 + 89757284*c5^5*c6^4 +
5821801*c5^4*c6^5 + 77780218*c5^3*c6^90 + 74774502*c5^3*c6^83 +
90642706*c5^3*c6^76 + 8626435*c5^3*c6^69 + 2792444*c5^3*c6^62 +
26183094*c5^3*c6^55 + 9746518*c5^3*c6^48 + 78313708*c5^3*c6^41 +
74603722*c5^3*c6^34 + 44370628*c5^3*c6^27 + 57772726*c5^3*c6^20 +
84170690*c5^3*c6^13 + 63077222*c5^3*c6^6 + 71550798*c5^2*c6^84 +
56857085*c5^2*c6^77 + 9389292*c5^2*c6^70 + 18510118*c5^2*c6^63 +
51252613*c5^2*c6^56 + 87158343*c5^2*c6^49 + 31867800*c5^2*c6^42 +
38373616*c5^2*c6^35 + 72928863*c5^2*c6^28 + 91211151*c5^2*c6^21 +
25909757*c5^2*c6^14 + 66774755*c5^2*c6^7 + 11773654*c5^2 +
37186132*c5*c6^197 + 71921231*c5*c6^190 + 78513923*c5*c6^183 +
34551502*c5*c6^176 + 67126652*c5*c6^169 + 89933207*c5*c6^162 +
31919467*c5*c6^155 + 10236949*c5*c6^148 + 52442411*c5*c6^141 +
54076218*c5*c6^134 + 69617496*c5*c6^127 + 69038103*c5*c6^120 +
33312631*c5*c6^113 + 10561419*c5*c6^106 + 40621604*c5*c6^99 +
30327541*c5*c6^92 + 72836321*c5*c6^85 + 33256258*c5*c6^78 +
20421049*c5*c6^71 + 4279558*c5*c6^64 + 88802298*c5*c6^57 +
14481436*c5*c6^50 + 91294333*c5*c6^43 + 67240919*c5*c6^36 +
93202231*c5*c6^29 + 59260361*c5*c6^22 + 64988229*c5*c6^15 +
87860869*c5*c6^8 + 75652908*c5*c6 + 99166670*c6^198 + 35210922*c6^191 +
35619066*c6^184 + 16202825*c6^177 + 2123219*c6^170 + 40426441*c6^163 +
33762464*c6^156 + 32520476*c6^149 + 76154918*c6^142 + 55441905*c6^135 +
99188623*c6^128 + 88025116*c6^121 + 40186079*c6^114 + 87843129*c6^107 +
66170626*c6^100 + 60644593*c6^93 + 31809621*c6^86 + 35854033*c6^79 +
59797162*c6^72 + 5870300*c6^65 + 70020041*c6^58 + 12186640*c6^51 +
90369146*c6^44 + 63816714*c6^37 + 76979381*c6^30 + 49879293*c6^23 +
70679752*c6^16 + 28260708*c6^9 + 20492852*c6^2,
c1*c4 + 99999988*c1*c5^2*c6^6 + 49999994*c1*c5 + 49999995*c1*c6 +
49450545*c2*c5*c6^7 + 35164831*c2*c5 + 85400304*c2*c6^15 +
26314754*c2*c6^8 + 3669544*c2*c6 + 99999988*c3*c4^2*c6^6 + c3*c4 +
84615377*c3*c5^2*c6^6 + 96510072*c3*c5*c6^14 + 55141283*c3*c5*c6^7 +
98348617*c3*c5 + 54305029*c3*c6^15 + 33977626*c3*c6^8 + 77101941*c3*c6 +
57692300*c4*c5^2*c6^6 + 97786660*c4*c5*c6^14 + 80208558*c4*c5*c6^7 +
64312447*c4*c5 + 98312823*c4*c6^15 + 26826359*c4*c6^8 + 74860798*c4*c6 +
98769578*c5^22*c6 + 52982163*c5^21*c6^2 + 42141417*c5^20*c6^3 +
62074892*c5^19*c6^4 + 74080796*c5^18*c6^5 + 386343*c5^17*c6^6 +
93673858*c5^16 + 83223559*c5^15*c6 + 70739239*c5^14*c6^2 +
93042922*c5^13*c6^3 + 80472491*c5^12*c6^4 + 28941475*c5^11*c6^5 +
19686276*c5^10*c6^6 + 22213185*c5^9 + 64252929*c5^8*c6 +
93054939*c5^7*c6^2 + 14815645*c5^6*c6^3 + 38221824*c5^5*c6^4 +
73900789*c5^4*c6^5 + 93242430*c5^3*c6^90 + 29040192*c5^3*c6^83 +
45169434*c5^3*c6^76 + 80382296*c5^3*c6^69 + 68791345*c5^3*c6^62 +
55229625*c5^3*c6^55 + 16620772*c5^3*c6^48 + 56109116*c5^3*c6^41 +
5389584*c5^3*c6
** WARNING: Output too long, hence truncated.
'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 22:56:10 2004

Input: P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(99999989),7,"glevlex");
I:= ideal<P | c6*c5*c4*c3*c2*c1*c0-1,
(((((c5+c6)*c4+c6*c5)*c3+c6*c5*c4)*c2+c6*c5*c4*c3)*c1+c6*c5*c4*c3*c2)*c0+c6*c5*c4*c3*c2*c1,
((((c4+c6)*c3+c6*c5)*c2+c6*c5*c4)*c1+c6*c5*c4*c3)*c0+c5*c4*c3*c2*c1+c6*c5*c4*c3*c2,
(((c3+c6)*c2+c6*c5)*c1+c6*c5*c4)*c0+c4*c3*c2*c1+c5*c4*c3*c2+c6*c5*c4*c3,
((c2+c6)*c1+c6*c5)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3+c6*c5*c4,
(c1+c6)*c0+c2*c1+c3*c2+c4*c3+c5*c4+c6*c5,
c0+c1+c2+c3+c4+c5+c6>;
time B := GroebnerBasis(I);
B;

Output: Magma V2.11-6     Sun Sep 19 2004 22:56:10 on modular  [Seed = 134680552]
-------------------------------------

>> P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(99999989),7,"glevlex"
^
Runtime error in 'PolynomialRing': Bad order "glevlex"

>> I:= ideal<P | c6*c5*c4*c3*c2*c1*c0-1,
^
User error: Identifier 'P' has not been declared or assigned

>> time B := GroebnerBasis(I);
^
User error: Identifier 'I' has not been declared or assigned

>> B;
^
User error: Identifier 'B' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 22:56:33 2004

Input: P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(99999989),7,"grevlex");
I:= ideal<P | c6*c5*c4*c3*c2*c1*c0-1,
(((((c5+c6)*c4+c6*c5)*c3+c6*c5*c4)*c2+c6*c5*c4*c3)*c1+c6*c5*c4*c3*c2)*c0+c6*c5*c4*c3*c2*c1,
((((c4+c6)*c3+c6*c5)*c2+c6*c5*c4)*c1+c6*c5*c4*c3)*c0+c5*c4*c3*c2*c1+c6*c5*c4*c3*c2,
(((c3+c6)*c2+c6*c5)*c1+c6*c5*c4)*c0+c4*c3*c2*c1+c5*c4*c3*c2+c6*c5*c4*c3,
((c2+c6)*c1+c6*c5)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3+c6*c5*c4,
(c1+c6)*c0+c2*c1+c3*c2+c4*c3+c5*c4+c6*c5,
c0+c1+c2+c3+c4+c5+c6>;
time B := GroebnerBasis(I);
B;

Output: Magma V2.11-6     Sun Sep 19 2004 22:56:29 on modular  [Seed = 420880110]
-------------------------------------

Time: 4.010
[
c4^3*c6^9 + 22092720*c2*c3*c4^2*c5 + 85081467*c3^2*c4^2*c5 +
38315779*c1*c4^3*c5 + 28773981*c2*c4^3*c5 + 55182145*c3*c4^3*c5 +
73702796*c4^4*c5 + 58119125*c2^3*c5^2 + 85238848*c1*c2*c3*c5^2 +
83577205*c2^2*c3*c5^2 + 836559*c1*c3^2*c5^2 + 53383791*c2*c3^2*c5^2 +
57000405*c3^3*c5^2 + 91252002*c1*c2*c4*c5^2 + 408725*c2^2*c4*c5^2 +
18994961*c1*c3*c4*c5^2 + 67709574*c2*c3*c4*c5^2 + 4033006*c3^2*c4*c5^2 +
42951688*c1*c4^2*c5^2 + 73755871*c2*c4^2*c5^2 + 5083742*c3*c4^2*c5^2 +
40888622*c4^3*c5^2 + 92656369*c1*c2*c5^3 + 8397647*c2^2*c5^3 +
94299427*c1*c3*c5^3 + 94804469*c2*c3*c5^3 + 58920247*c3^2*c5^3 +
80950266*c1*c4*c5^3 + 2657541*c2*c4*c5^3 + 19064928*c3*c4*c5^3 +
57647148*c4^2*c5^3 + 75873645*c1*c5^4 + 80423453*c2*c5^4 +
4644699*c3*c5^4 + 74174385*c4*c5^4 + 89447365*c5^5 + 47423040*c2^4*c6 +
98492839*c1*c3^3*c6 + 61878371*c2*c3^3*c6 + 50224244*c3^4*c6 +
43175574*c2^3*c4*c6 + 53597203*c1*c2*c3*c4*c6 + 18273272*c2^2*c3*c4*c6 +
97317619*c1*c3^2*c4*c6 + 74115769*c2*c3^2*c4*c6 + 82051189*c3^3*c4*c6 +
24588055*c1*c2*c4^2*c6 + 96408495*c2^2*c4^2*c6 + 38025474*c1*c3*c4^2*c6
+ 12913745*c2*c3*c4^2*c6 + 52929700*c3^2*c4^2*c6 + 87720903*c1*c4^3*c6 +
96867733*c2*c4^3*c6 + 76565149*c3*c4^3*c6 + 85535482*c4^4*c6 +
79020399*c2^3*c5*c6 + 75267540*c1*c2*c3*c5*c6 + 39043365*c2^2*c3*c5*c6 +
1122366*c1*c3^2*c5*c6 + 14270107*c2*c3^2*c5*c6 + 46842224*c3^3*c5*c6 +
20646562*c1*c2*c4*c5*c6 + 5205393*c2^2*c4*c5*c6 +
83433068*c1*c3*c4*c5*c6 + 17669688*c2*c3*c4*c5*c6 +
71118198*c3^2*c4*c5*c6 + 67461139*c1*c4^2*c5*c6 + 67434134*c2*c4^2*c5*c6
+ 56781347*c3*c4^2*c5*c6 + 54281774*c4^3*c5*c6 + 91916713*c1*c2*c5^2*c6
+ 11204602*c2^2*c5^2*c6 + 77275494*c1*c3*c5^2*c6 +
69189337*c2*c3*c5^2*c6 + 53252633*c3^2*c5^2*c6 + 7945797*c1*c4*c5^2*c6 +
59048797*c2*c4*c5^2*c6 + 35407223*c3*c4*c5^2*c6 + 93498935*c4^2*c5^2*c6
+ 51023329*c1*c5^3*c6 + 66587675*c2*c5^3*c6 + 85839165*c3*c5^3*c6 +
67811767*c4*c5^3*c6 + 35343*c5^4*c6 + 66671662*c2^3*c6^2 +
73452263*c1*c2*c3*c6^2 + 20372321*c2^2*c3*c6^2 + 11575262*c1*c3^2*c6^2 +
70588415*c2*c3^2*c6^2 + 51832679*c3^3*c6^2 + 33386187*c1*c2*c4*c6^2 +
36659833*c2^2*c4*c6^2 + 681917*c1*c3*c4*c6^2 + 52229503*c2*c3*c4*c6^2 +
31068385*c3^2*c4*c6^2 + 68375779*c1*c4^2*c6^2 + 37698991*c2*c4^2*c6^2 +
14186634*c3*c4^2*c6^2 + 42033897*c4^3*c6^2 + 96674307*c1*c2*c5*c6^2 +
31069630*c2^2*c5*c6^2 + 85391241*c1*c3*c5*c6^2 + 96470211*c2*c3*c5*c6^2
+ 37286687*c3^2*c5*c6^2 + 51226279*c1*c4*c5*c6^2 + 152035*c2*c4*c5*c6^2
+ 61852919*c3*c4*c5*c6^2 + 73220249*c4^2*c5*c6^2 + 17179336*c1*c5^2*c6^2
+ 9600279*c2*c5^2*c6^2 + 94185492*c3*c5^2*c6^2 + 59925479*c4*c5^2*c6^2 +
89527001*c5^3*c6^2 + 99077225*c1*c2*c6^3 + 26619081*c2^2*c6^3 +
56671984*c1*c3*c6^3 + 20173224*c2*c3*c6^3 + 44932554*c3^2*c6^3 +
4348360*c1*c4*c6^3 + 40570907*c2*c4*c6^3 + 49425282*c3*c4*c6^3 +
75188764*c4^2*c6^3 + 15485826*c1*c5*c6^3 + 51077021*c2*c5*c6^3 +
5516726*c3*c5*c6^3 + 41917768*c4*c5*c6^3 + 5286277*c5^2*c6^3 +
89270147*c1*c6^4 + 32274501*c2*c6^4 + 84974301*c3*c6^4 +
50823930*c4*c6^4 + 54226390*c5*c6^4 + 49481539*c6^5,
c1*c2*c5*c6^9 + 69046102*c2*c3*c4^2*c5 + 15188328*c3^2*c4^2*c5 +
12449905*c1*c4^3*c5 + 74984891*c2*c4^3*c5 + 55359938*c3*c4^3*c5 +
73668377*c4^4*c5 + 78578377*c2^3*c5^2 + 84333929*c1*c2*c3*c5^2 +
99357949*c2^2*c3*c5^2 + 25538351*c1*c3^2*c5^2 + 25678502*c2*c3^2*c5^2 +
59444562*c3^3*c5^2 + 76406521*c1*c2*c4*c5^2 + 9164490*c2^2*c4*c5^2 +
12093048*c1*c3*c4*c5^2 + 28891569*c2*c3*c4*c5^2 + 89023811*c3^2*c4*c5^2
+ 89586904*c1*c4^2*c5^2 + 3091677*c2*c4^2*c5^2 + 90960403*c3*c4^2*c5^2 +
88668655*c4^3*c5^2 + 97383810*c1*c2*c5^3 + 51810837*c2^2*c5^3 +
65567701*c1*c3*c5^3 + 47677270*c2*c3*c5^3 + 80989980*c3^2*c5^3 +
23460249*c1*c4*c5^3 + 49334556*c2*c4*c5^3 + 52888861*c3*c4*c5^3 +
28507028*c4^2*c5^3 + 75270103*c1*c5^4 + 23686282*c2*c5^4 +
42185063*c3*c5^4 + 79739852*c4*c5^4 + 77168661*c5^5 + 96611513*c2^4*c6 +
21756672*c1*c3^3*c6 + 84658780*c2*c3^3*c6 + 99632839*c3^4*c6 +
13663278*c2^3*c4*c6 + 54533605*c1*c2*c3*c4*c6 + 81105292*c2^2*c3*c4*c6 +
61476840*c1*c3^2*c4*c6 + 92533575*c2*c3^2*c4*c6 + 64000998*c3^3*c4*c6 +
92120715*c1*c2*c4^2*c6 + 57499322*c2^2*c4^2*c6 + 67789173*c1*c3*c4^2*c6
+ 79518106*c2*c3*c4^2*c6 + 27026792*c3^2*c4^2*c6 + 56205496*c1*c4^3*c6 +
78830600*c2*c4^3*c6 + 53535734*c3*c4^3*c6 + 25366256*c4^4*c6 +
50624713*c2^3*c5*c6 + 77391435*c1*c2*c3*c5*c6 + 62844893*c2^2*c3*c5*c6 +
45739261*c1*c3^2*c5*c6 + 60507699*c2*c3^2*c5*c6 + 12529280*c3^3*c5*c6 +
79147183*c1*c2*c4*c5*c6 + 54508509*c2^2*c4*c5*c6 +
10958202*c1*c3*c4*c5*c6 + 5671289*c2*c3*c4*c5*c6 +
36682495*c3^2*c4*c5*c6 + 63675662*c1*c4^2*c5*c6 + 55374815*c2*c4^2*c5*c6
+ 2314557*c3*c4^2*c5*c6 + 60051703*c4^3*c5*c6 + 48701135*c1*c2*c5^2*c6 +
14254105*c2^2*c5^2*c6 + 94850570*c1*c3*c5^2*c6 + 98297621*c2*c3*c5^2*c6
+ 24965455*c3^2*c5^2*c6 + 26686108*c1*c4*c5^2*c6 +
84829574*c2*c4*c5^2*c6 + 56044504*c3*c4*c5^2*c6 + 55448721*c4^2*c5^2*c6
+ 67811872*c1*c5^3*c6 + 19153785*c2*c5^3*c6 + 39125176*c3*c5^3*c6 +
69615647*c4*c5^3*c6 + 57218728*c5^4*c6 + 63671096*c2^3*c6^2 +
15308935*c1*c2*c3*c6^2 + 51482728*c2^2*c3*c6^2 + 88044998*c1*c3^2*c6^2 +
12175118*c2*c3^2*c6^2 + 78641105*c3^3*c6^2 + 1687790*c1*c2*c4*c6^2 +
32993064*c2^2*c4*c6^2 + 24089133*c1*c3*c4*c6^2 + 89887540*c2*c3*c4*c6^2
+ 99512336*c3^2*c4*c6^2 + 73762560*c1*c4^2*c6^2 + 83997353*c2*c4^2*c6^2
+ 67419675*c3*c4^2*c6^2 + 31343849*c4^3*c6^2 + 20240868*c1*c2*c5*c6^2 +
24805407*c2^2*c5*c6^2 + 5399155*c1*c3*c5*c6^2 + 7411699*c2*c3*c5*c6^2 +
10362983*c3^2*c5*c6^2 + 65785811*c1*c4*c5*c6^2 + 10373888*c2*c4*c5*c6^2
+ 61409765*c3*c4*c5*c6^2 + 64891643*c4^2*c5*c6^2 + 81831322*c1*c5^2*c6^2
+ 23450321*c2*c5^2*c6^2 + 49780816*c3*c5^2*c6^2 + 43913731*c4*c5^2*c6^2
+ 24923130*c5^3*c6^2 + 17032635*c1*c2*c6^3 + 18381452*c2^2*c6^3 +
49626072*c1*c3*c6^3 + 68880977*c2*c3*c6^3 + 27783838*c3^2*c6^3 +
83094395*c1*c4*c6^3 + 34289291*c2*c4*c6^3 + 10753215*c3*c4*c6^3 +
68403798*c4^2*c6^3 + 98728470*c1*c5*c6^3 + 73374578*c2*c5*c6^3 +
34803331*c3*c5*c6^3 + 71829024*c4*c5*c6^3 + 52341261*c5^2*c6^3 +
44433174*c1*c6^4 + 94569827*c2*c6^4 + 98298331*c3*c6^4 +
20718511*c4*c6^4 + 4753688*c5*c6^4 + 19228728*c6^5,
c2^2*c5*c6^9 + 20797274*c2*c3*c4^2*c5 + 55155238*c3^2*c4^2*c5 +
13130112*c1*c4^3*c5 + 63977373*c2*c4^3*c5 + 73955745*c3*c4^3*c5 +
99787604*c4^4*c5 + 7024644*c2^3*c5^2 + 7053203*c1*c2*c3*c5^2 +
14002929*c2^2*c3*c5^2 + 41756685*c1*c3^2*c5^2 + 8998372*c2*c3^2*c5^2 +
61160108*c3^3*c5^2 + 61442288*c1*c2*c4*c5^2 + 47889298*c2^2*c4*c5^2 +
17311338*c1*c3*c4*c5^2 + 56771689*c2*c3*c4*c5^2 + 48148230*c3^2*c4*c5^2
+ 79030564*c1*c4^2*c5^2 + 72237057*c2*c4^2*c5^2 + 76210719*c3*c4^2*c5^2
+ 53755036*c4^3*c5^2 + 4040975*c1*c2*c5^3 + 66976628*c2^2*c5^3 +
21876852*c1*c3*c5^3 + 9145172*c2*c3*c5^3 + 44280470*c3^2*c5^3 +
84669862*c1*c4*c5^3 + 4647084*c2*c4*c5^3 + 6712468*c3*c4*c5^3 +
45743146*c4^2*c5^3 + 47347818*c1*c5^4 + 71989727*c2*c5^4 +
84803418*c3*c5^4 + 27356482*c4*c5^4 + 40741619*c5^5 + 85517531*c2^4*c6 +
80947539*c1*c3^3*c6 + 23110327*c2*c3^3*c6 + 91349752*c3^4*c6 +
90791946*c2^3*c4*c6 + 98963417*c1*c2*c3*c4*c6 + 75356949*c2^2*c3*c4*c6 +
90446696*c1*c3^2*c4*c6 + 12961613*c2*c3^2*c4*c6 + 48810992*c3^3*c4*c6 +
11469668*c1*c2*c4^2*c6 + 7024367*c2^2*c4^2*c6 + 55214671*c1*c3*c4^2*c6 +
69178271*c2*c3*c4^2*c6 + 60177328*c3^2*c4^2*c6 + 31716030*c1*c4^3*c6 +
29930002*c2*c4^3*c6 + 67493250*c3*c4^3*c6 + 73308977*c4^4*c6 +
33122898*c2^3*c5*c6 + 74801173*c1*c2*c3*c5*c6 + 38699329*c2^2*c3*c5*c6 +
63902199*c1*c3^2*c5*c6 + 38658054*c2*c3^2*c5*c6 + 79743246*c3^3*c5*c6 +
74689275*c1*c2*c4*c5*c6 + 22977972*c2^2*c4*c5*c6 +
5166966*c1*c3*c4*c5*c6 + 27897774*c2*c3*c4*c5*c6 +
16592280*c3^2*c4*c5*c6 + 81162412*c1*c4^2*c5*c6 + 61740553*c2*c4^2*c5*c6
+ 64282897*c3*c4^2*c5*c6 + 62734155*c4^3*c5*c6 + 59541132*c1*c2*c5^2*c6
+ 7331850*c2^2*c5^2*c6 + 31523293*c1*c3*c5^2*c6 + 32660261*c2*c3*c5^2*c6
+ 46478153*c3^2*c5^2*c6 + 4559768*c1*c4*c5^2*c6 + 66063963*c2*c4*c5^2*c6
+ 1528904*c3*c4*c5^2*c6 + 92177379*c4^2*c5^2*c6 + 59369452*c1*c5^3*c6 +
71088844*c2*c5^3*c6 + 3859240*c3*c5^3*c6 + 85556082*c4*c5^3*c6 +
33347943*c5^4*c6 + 1930513*c2^3*c6^2 + 6429775*c1*c2*c3*c6^2 +
95329465*c2^2*c3*c6^2 + 25761279*c1*c3^2*c6^2 + 38342297*c2*c3^2*c6^2 +
39619670*c3^3*c6^2 + 23828631*c1*c2*c4*c6^2 + 46149522*c2^2*c4*c6^2 +
50639996*c1*c3*c4*c6^2 + 26079538*c2*c3*c4*c6^2 + 96984443*c3^2*c4*c6^2
+ 86985561*c1*c4^2*c6^2 + 1085194*c2*c4^2*c6^2 + 81614330*c3*c4^2*c6^2 +
29500192*c4^3*c6^2 + 13813435*c1*c2*c5*c6^2 + 21440413*c2^2*c5*c6^2 +
69665444*c1*c3*c5*c6^2 + 26280157*c2*c3*c5*c6^2 + 85122156*c3^2*c5*c6^2
+ 26123484*c1*c4*c5*c6^2 + 54506415*c2*c4*c5*c6^2 +
47173810*c3*c4*c5*c6^2 + 78432181*c4^2*c5*c6^2 + 2203007*c1*c5^2*c6^2 +
47477635*c2*c5^2*c6^2 + 77474224*c3*c5^2*c6^2 + 88664164*c4*c5^2*c6^2 +
16844993*c5^3*c6^2 + 92735616*c1*c2*c6^3 + 6759128*c2^2*c6^3 +
1079043*c1*c3*c6^3 + 96788097*c2*c3*c6^3 + 45379959*c3^2*c6^3 +
** WARNING: Output too long, hence truncated.
'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 22:57:16 2004

Input: P<c0,c1,c2,c3,c4,c5,c6> := PolynomialRing(FiniteField(31991),7,"grevlex");
I:= ideal<P | c6*c5*c4*c3*c2*c1*c0-1,
(((((c5+c6)*c4+c6*c5)*c3+c6*c5*c4)*c2+c6*c5*c4*c3)*c1+c6*c5*c4*c3*c2)*c0+c6*c5*c4*c3*c2*c1,
((((c4+c6)*c3+c6*c5)*c2+c6*c5*c4)*c1+c6*c5*c4*c3)*c0+c5*c4*c3*c2*c1+c6*c5*c4*c3*c2,
(((c3+c6)*c2+c6*c5)*c1+c6*c5*c4)*c0+c4*c3*c2*c1+c5*c4*c3*c2+c6*c5*c4*c3,
((c2+c6)*c1+c6*c5)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3+c6*c5*c4,
(c1+c6)*c0+c2*c1+c3*c2+c4*c3+c5*c4+c6*c5,
c0+c1+c2+c3+c4+c5+c6>;
time B := GroebnerBasis(I);
B;

Output: Magma V2.11-6     Sun Sep 19 2004 22:57:14 on modular  [Seed = 2054519898]
-------------------------------------

Time: 1.280
[
c4^3*c6^9 + 4830*c2*c3*c4^2*c5 + 20140*c3^2*c4^2*c5 + 2071*c1*c4^3*c5 +
4271*c2*c4^3*c5 + 25190*c3*c4^3*c5 + 7979*c4^4*c5 + 22388*c2^3*c5^2 +
30660*c1*c2*c3*c5^2 + 17*c2^2*c3*c5^2 + 11041*c1*c3^2*c5^2 +
12580*c2*c3^2*c5^2 + 10118*c3^3*c5^2 + 9652*c1*c2*c4*c5^2 +
70*c2^2*c4*c5^2 + 23774*c1*c3*c4*c5^2 + 16808*c2*c3*c4*c5^2 +
14687*c3^2*c4*c5^2 + 25911*c1*c4^2*c5^2 + 5606*c2*c4^2*c5^2 +
11249*c3*c4^2*c5^2 + 5536*c4^3*c5^2 + 13527*c1*c2*c5^3 + 20989*c2^2*c5^3
+ 27433*c1*c3*c5^3 + 6080*c2*c3*c5^3 + 9083*c3^2*c5^3 + 3949*c1*c4*c5^3
+ 12586*c2*c4*c5^3 + 20570*c3*c4*c5^3 + 19586*c4^2*c5^3 + 22430*c1*c5^4
+ 17571*c2*c5^4 + 29945*c3*c5^4 + 18590*c4*c5^4 + 27064*c5^5 +
5468*c2^4*c6 + 28026*c1*c3^3*c6 + 18855*c2*c3^3*c6 + 29223*c3^4*c6 +
26275*c2^3*c4*c6 + 31803*c1*c2*c3*c4*c6 + 23729*c2^2*c3*c4*c6 +
9324*c1*c3^2*c4*c6 + 20605*c2*c3^2*c4*c6 + 5528*c3^3*c4*c6 +
3106*c1*c2*c4^2*c6 + 23734*c2^2*c4^2*c6 + 2829*c1*c3*c4^2*c6 +
29051*c2*c3*c4^2*c6 + 12393*c3^2*c4^2*c6 + 11640*c1*c4^3*c6 +
8695*c2*c4^3*c6 + 28728*c3*c4^3*c6 + 31237*c4^4*c6 + 11090*c2^3*c5*c6 +
21010*c1*c2*c3*c5*c6 + 13899*c2^2*c3*c5*c6 + 5631*c1*c3^2*c5*c6 +
3210*c2*c3^2*c5*c6 + 10155*c3^3*c5*c6 + 22045*c1*c2*c4*c5*c6 +
8093*c2^2*c4*c5*c6 + 26776*c1*c3*c4*c5*c6 + 6582*c2*c3*c4*c5*c6 +
31522*c3^2*c4*c5*c6 + 11764*c1*c4^2*c5*c6 + 25311*c2*c4^2*c5*c6 +
14063*c3*c4^2*c5*c6 + 696*c4^3*c5*c6 + 29416*c1*c2*c5^2*c6 +
30121*c2^2*c5^2*c6 + 7573*c1*c3*c5^2*c6 + 3644*c2*c3*c5^2*c6 +
17081*c3^2*c5^2*c6 + 20796*c1*c4*c5^2*c6 + 6893*c2*c4*c5^2*c6 +
17279*c3*c4*c5^2*c6 + 559*c4^2*c5^2*c6 + 21946*c1*c5^3*c6 +
14990*c2*c5^3*c6 + 12045*c3*c5^3*c6 + 23996*c4*c5^3*c6 + 24639*c5^4*c6 +
18402*c2^3*c6^2 + 4422*c1*c2*c3*c6^2 + 31602*c2^2*c3*c6^2 +
20391*c1*c3^2*c6^2 + 27644*c2*c3^2*c6^2 + 17877*c3^3*c6^2 +
22351*c1*c2*c4*c6^2 + 19612*c2^2*c4*c6^2 + 20992*c1*c3*c4*c6^2 +
9998*c2*c3*c4*c6^2 + 1838*c3^2*c4*c6^2 + 15573*c1*c4^2*c6^2 +
11404*c2*c4^2*c6^2 + 1715*c3*c4^2*c6^2 + 5587*c4^3*c6^2 +
21475*c1*c2*c5*c6^2 + 3747*c2^2*c5*c6^2 + 9698*c1*c3*c5*c6^2 +
5965*c2*c3*c5*c6^2 + 4004*c3^2*c5*c6^2 + 24928*c1*c4*c5*c6^2 +
26134*c2*c4*c5*c6^2 + 18341*c3*c4*c5*c6^2 + 27219*c4^2*c5*c6^2 +
4598*c1*c5^2*c6^2 + 20304*c2*c5^2*c6^2 + 19282*c3*c5^2*c6^2 +
24534*c4*c5^2*c6^2 + 30287*c5^3*c6^2 + 16506*c1*c2*c6^3 +
29683*c2^2*c6^3 + 20287*c1*c3*c6^3 + 21829*c2*c3*c6^3 + 29509*c3^2*c6^3
+ 3828*c1*c4*c6^3 + 1834*c2*c4*c6^3 + 3566*c3*c4*c6^3 + 10658*c4^2*c6^3
+ 9343*c1*c5*c6^3 + 31837*c2*c5*c6^3 + 77*c3*c5*c6^3 + 22740*c4*c5*c6^3
+ 30547*c5^2*c6^3 + 21295*c1*c6^4 + 10256*c2*c6^4 + 2374*c3*c6^4 +
5177*c4*c6^4 + 26926*c5*c6^4 + 4163*c6^5,
c1*c2*c5*c6^9 + 24346*c2*c3*c4^2*c5 + 21894*c3^2*c4^2*c5 + 29124*c1*c4^3*c5
+ 20453*c2*c4^3*c5 + 15991*c3*c4^3*c5 + 23594*c4^4*c5 + 7158*c2^3*c5^2 +
18285*c1*c2*c3*c5^2 + 11579*c2^2*c3*c5^2 + 6325*c1*c3^2*c5^2 +
25476*c2*c3^2*c5^2 + 15349*c3^3*c5^2 + 11185*c1*c2*c4*c5^2 +
14857*c2^2*c4*c5^2 + 8011*c1*c3*c4*c5^2 + 24148*c2*c3*c4*c5^2 +
16195*c3^2*c4*c5^2 + 9496*c1*c4^2*c5^2 + 28814*c2*c4^2*c5^2 +
9458*c3*c4^2*c5^2 + 13766*c4^3*c5^2 + 17805*c1*c2*c5^3 + 29127*c2^2*c5^3
+ 8084*c1*c3*c5^3 + 18035*c2*c3*c5^3 + 23790*c3^2*c5^3 +
28830*c1*c4*c5^3 + 9309*c2*c4*c5^3 + 17929*c3*c4*c5^3 + 11618*c4^2*c5^3
+ 16105*c1*c5^4 + 1976*c2*c5^4 + 4794*c3*c5^4 + 5464*c4*c5^4 +
18441*c5^5 + 12793*c2^4*c6 + 16381*c1*c3^3*c6 + 9164*c2*c3^3*c6 +
6470*c3^4*c6 + 10149*c2^3*c4*c6 + 10963*c1*c2*c3*c4*c6 +
21638*c2^2*c3*c4*c6 + 15541*c1*c3^2*c4*c6 + 29681*c2*c3^2*c4*c6 +
20721*c3^3*c4*c6 + 16725*c1*c2*c4^2*c6 + 14626*c2^2*c4^2*c6 +
12581*c1*c3*c4^2*c6 + 24737*c2*c3*c4^2*c6 + 30284*c3^2*c4^2*c6 +
19086*c1*c4^3*c6 + 6879*c2*c4^3*c6 + 9709*c3*c4^3*c6 + 3169*c4^4*c6 +
13268*c2^3*c5*c6 + 9357*c1*c2*c3*c5*c6 + 24672*c2^2*c3*c5*c6 +
3205*c1*c3^2*c5*c6 + 27767*c2*c3^2*c5*c6 + 13714*c3^3*c5*c6 +
13347*c1*c2*c4*c5*c6 + 1062*c2^2*c4*c5*c6 + 26180*c1*c3*c4*c5*c6 +
6106*c2*c3*c4*c5*c6 + 29779*c3^2*c4*c5*c6 + 2630*c1*c4^2*c5*c6 +
4954*c2*c4^2*c5*c6 + 113*c3*c4^2*c5*c6 + 20203*c4^3*c5*c6 +
18769*c1*c2*c5^2*c6 + 11649*c2^2*c5^2*c6 + 20433*c1*c3*c5^2*c6 +
31740*c2*c3*c5^2*c6 + 21363*c3^2*c5^2*c6 + 26791*c1*c4*c5^2*c6 +
25019*c2*c4*c5^2*c6 + 9208*c3*c4*c5^2*c6 + 9210*c4^2*c5^2*c6 +
18481*c1*c5^3*c6 + 19534*c2*c5^3*c6 + 14198*c3*c5^3*c6 +
17377*c4*c5^3*c6 + 19626*c5^4*c6 + 31867*c2^3*c6^2 + 13468*c1*c2*c3*c6^2
+ 28213*c2^2*c3*c6^2 + 1339*c1*c3^2*c6^2 + 9783*c2*c3^2*c6^2 +
790*c3^3*c6^2 + 29950*c1*c2*c4*c6^2 + 20366*c2^2*c4*c6^2 +
20954*c1*c3*c4*c6^2 + 14547*c2*c3*c4*c6^2 + 17955*c3^2*c4*c6^2 +
5866*c1*c4^2*c6^2 + 23333*c2*c4^2*c6^2 + 26242*c3*c4^2*c6^2 +
9475*c4^3*c6^2 + 977*c1*c2*c5*c6^2 + 447*c2^2*c5*c6^2 +
4066*c1*c3*c5*c6^2 + 14004*c2*c3*c5*c6^2 + 15367*c3^2*c5*c6^2 +
6670*c1*c4*c5*c6^2 + 26884*c2*c4*c5*c6^2 + 20014*c3*c4*c5*c6^2 +
8052*c4^2*c5*c6^2 + 2286*c1*c5^2*c6^2 + 14666*c2*c5^2*c6^2 +
12374*c3*c5^2*c6^2 + 2319*c4*c5^2*c6^2 + 14137*c5^3*c6^2 +
6112*c1*c2*c6^3 + 14607*c2^2*c6^3 + 17723*c1*c3*c6^3 + 22090*c2*c3*c6^3
+ 14363*c3^2*c6^3 + 30102*c1*c4*c6^3 + 5920*c2*c4*c6^3 +
14091*c3*c4*c6^3 + 5931*c4^2*c6^3 + 15845*c1*c5*c6^3 + 7262*c2*c5*c6^3 +
24329*c3*c5*c6^3 + 22447*c4*c5*c6^3 + 30226*c5^2*c6^3 + 4768*c1*c6^4 +
5312*c2*c6^4 + 31685*c3*c6^4 + 27843*c4*c6^4 + 27829*c5*c6^4 +
4664*c6^5,
c2^2*c5*c6^9 + 3362*c2*c3*c4^2*c5 + 9322*c3^2*c4^2*c5 + 16153*c1*c4^3*c5 +
7906*c2*c4^3*c5 + 29852*c3*c4^3*c5 + 16573*c4^4*c5 + 20798*c2^3*c5^2 +
15676*c1*c2*c3*c5^2 + 7614*c2^2*c3*c5^2 + 28442*c1*c3^2*c5^2 +
26091*c2*c3^2*c5^2 + 2891*c3^3*c5^2 + 495*c1*c2*c4*c5^2 +
1531*c2^2*c4*c5^2 + 13919*c1*c3*c4*c5^2 + 13873*c2*c3*c4*c5^2 +
6005*c3^2*c4*c5^2 + 8923*c1*c4^2*c5^2 + 16186*c2*c4^2*c5^2 +
7056*c3*c4^2*c5^2 + 30483*c4^3*c5^2 + 23049*c1*c2*c5^3 + 405*c2^2*c5^3 +
7857*c1*c3*c5^3 + 24015*c2*c3*c5^3 + 7926*c3^2*c5^3 + 8377*c1*c4*c5^3 +
5346*c2*c4*c5^3 + 15259*c3*c4*c5^3 + 7995*c4^2*c5^3 + 2067*c1*c5^4 +
40*c2*c5^4 + 22568*c3*c5^4 + 12997*c4*c5^4 + 21391*c5^5 + 3415*c2^4*c6 +
17138*c1*c3^3*c6 + 22285*c2*c3^3*c6 + 1358*c3^4*c6 + 19576*c2^3*c4*c6 +
10050*c1*c2*c3*c4*c6 + 542*c2^2*c3*c4*c6 + 11513*c1*c3^2*c4*c6 +
11374*c2*c3^2*c4*c6 + 25508*c3^3*c4*c6 + 25775*c1*c2*c4^2*c6 +
22811*c2^2*c4^2*c6 + 30660*c1*c3*c4^2*c6 + 22507*c2*c3*c4^2*c6 +
13327*c3^2*c4^2*c6 + 12819*c1*c4^3*c6 + 25319*c2*c4^3*c6 +
19034*c3*c4^3*c6 + 16326*c4^4*c6 + 12933*c2^3*c5*c6 +
24491*c1*c2*c3*c5*c6 + 24391*c2^2*c3*c5*c6 + 10366*c1*c3^2*c5*c6 +
4395*c2*c3^2*c5*c6 + 11646*c3^3*c5*c6 + 8322*c1*c2*c4*c5*c6 +
6445*c2^2*c4*c5*c6 + 2259*c1*c3*c4*c5*c6 + 19507*c2*c3*c4*c5*c6 +
4809*c3^2*c4*c5*c6 + 23060*c1*c4^2*c5*c6 + 4359*c2*c4^2*c5*c6 +
26135*c3*c4^2*c5*c6 + 10387*c4^3*c5*c6 + 16367*c1*c2*c5^2*c6 +
11221*c2^2*c5^2*c6 + 18407*c1*c3*c5^2*c6 + 19752*c2*c3*c5^2*c6 +
21935*c3^2*c5^2*c6 + 12749*c1*c4*c5^2*c6 + 28193*c2*c4*c5^2*c6 +
17317*c3*c4*c5^2*c6 + 1988*c4^2*c5^2*c6 + 22207*c1*c5^3*c6 +
3676*c2*c5^3*c6 + 30340*c3*c5^3*c6 + 31373*c4*c5^3*c6 + 4859*c5^4*c6 +
27422*c2^3*c6^2 + 27651*c1*c2*c3*c6^2 + 20041*c2^2*c3*c6^2 +
16585*c1*c3^2*c6^2 + 19838*c2*c3^2*c6^2 + 26975*c3^3*c6^2 +
5013*c1*c2*c4*c6^2 + 4087*c2^2*c4*c6^2 + 13045*c1*c3*c4*c6^2 +
513*c2*c3*c4*c6^2 + 25267*c3^2*c4*c6^2 + 93*c1*c4^2*c6^2 +
17185*c2*c4^2*c6^2 + 5697*c3*c4^2*c6^2 + 4805*c4^3*c6^2 +
24239*c1*c2*c5*c6^2 + 4485*c2^2*c5*c6^2 + 12279*c1*c3*c5*c6^2 +
15372*c2*c3*c5*c6^2 + 21577*c3^2*c5*c6^2 + 26885*c1*c4*c5*c6^2 +
11034*c2*c4*c5*c6^2 + 2574*c3*c4*c5*c6^2 + 23267*c4^2*c5*c6^2 +
30372*c1*c5^2*c6^2 + 873*c2*c5^2*c6^2 + 429*c3*c5^2*c6^2 +
30350*c4*c5^2*c6^2 + 31733*c5^3*c6^2 + 18420*c1*c2*c6^3 +
30680*c2^2*c6^3 + 13495*c1*c3*c6^3 + 3074*c2*c3*c6^3 + 27424*c3^2*c6^3 +
22873*c1*c4*c6^3 + 10228*c2*c4*c6^3 + 31521*c3*c4*c6^3 + 8525*c4^2*c6^3
+ 30609*c1*c5*c6^3 + 331*c2*c5*c6^3 + 31157*c3*c5*c6^3 +
10924*c4*c5*c6^3 + 23207*c5^2*c6^3 + 27120*c1*c6^4 + 29912*c2*c6^4 +
9122*c3*c6^4 + 2887*c4*c6^4 + 30448*c5*c6^4 + 16120*c6^5,
c1*c3*c5*c6^9 + 30544*c2*c3*c4^2*c5 + 13201*c3^2*c4^2*c5 + 2665*c1*c4^3*c5 +
4318*c2*c4^3*c5 + 20693*c3*c4^3*c5 + 1219*c4^4*c5 + 5306*c2^3*c5^2 +
18383*c1*c2*c3*c5^2 + 26589*c2^2*c3*c5^2 + 29457*c1*c3^2*c5^2 +
23939*c2*c3^2*c5^2 + 18017*c3^3*c5^2 + 30266*c1*c2*c4*c5^2 +
21184*c2^2*c4*c5^2 + 8428*c1*c3*c4*c5^2 + 4721*c2*c3*c4*c5^2 +
9663*c3^2*c4*c5^2 + 27633*c1*c4^2*c5^2 + 100*c2*c4^2*c5^2 +
20011*c3*c4^2*c5^2 + 1998*c4^3*c5^2 + 8925*c1*c2*c5^3 + 4881*c2^2*c5^3 +
829*c1*c3*c5^3 + 8042*c2*c3*c5^3 + 464*c3^2*c5^3 + 6591*c1*c4*c5^3 +
22155*c2*c4*c5^3 + 15549*c3*c4*c5^3 + 11422*c4^2*c5^3 + 18497*c1*c5^4 +
10701*c2*c5^4 + 28127*c3*c5^4 + 6791*c4*c5^4 + 7014*c5^5 + 6066*c2^4*c6
+ 14180*c1*c3^3*c6 + 3634*c2*c3^3*c6 + 25454*c3^4*c6 + 5877*c2^3*c4*c6 +
30417*c1*c2*c3*c4*c6 + 15893*c2^2*c3*c4*c6 + 27841*c1*c3^2*c4*c6 +
5032*c2*c3^2*c4*c6 + 18468*c3^3*c4*c6 + 26476*c1*c2*c4^2*c6 +
28312*c2^2*c4^2*c6 + 9235*c1*c3*c4^2*c6 + 16485*c2*
** WARNING: Output too long, hence truncated.
'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 23:07:11 2004

Input: P<c0,c1,c2,c3> := PolynomialRing(FiniteField(31991),4,"grevlex");
I:= ideal<P |c3*c2*c1*c0-1,((c2+c3)*c1+c3*c2)*c0+c3*c2*c1,(c1+c3)*c0+c2*c1+c3*c2,c0+c1+c2+c3>;
time B := GroebnerBasis(I);

Output: Magma V2.11-6     Sun Sep 19 2004 23:07:11 on modular  [Seed = 4227134350]
-------------------------------------

Time: 0.000

Total time: 0.180 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 23:07:26 2004

Input: P<c0,c1,c2,c3> := PolynomialRing(FiniteField(31991),4,"grevlex");
I:= ideal<P |c3*c2*c1*c0-1,((c2+c3)*c1+c3*c2)*c0+c3*c2*c1,(c1+c3)*c0+c2*c1+c3*c2,c0+c1+c2+c3>;
time B := GroebnerBasis(I);
B;

Output: Magma V2.11-6     Sun Sep 19 2004 23:07:25 on modular  [Seed = 4243846331]
-------------------------------------

Time: 0.000
[
c2^2*c3^4 + c1*c2 + 31990*c1*c3 + c2*c3 + 31989*c3^2,
c2^3*c3^2 + c2^2*c3^3 + 31990*c2 + 31990*c3,
c1*c3^4 + c3^5 + 31990*c1 + 31990*c3,
c1*c2*c3^2 + c2^2*c3^2 + 31990*c1*c3^3 + c2*c3^3 + 31990*c3^4 + 31990,
c1*c2^2 + c2^2*c3 + 31990*c1*c3^2 + 31990*c3^3,
c1^2 + 2*c1*c3 + c3^2,
c0 + c1 + c2 + c3
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Sun Sep 19 23:10:14 2004

Input: P<c0,c1,c2,c3,c4,c5,c6,c7> := PolynomialRing(FiniteField(31991),8,"grevlex");
I:= ideal<P |
c7*c6*c5*c4*c3*c2*c1*c0-1,
((((((c6+c7)*c5+c7*c6)*c4+c7*c6*c5)*c3+c7*c6*c5*c4)*c2+c7*c6*c5*c4*c3)*c1+c7*c6*c5*c4*c3*c2)*c0+c7*c6*c5*c4*c3*c2*c1,
(((((c5+c7)*c4+c7*c6)*c3+c7*c6*c5)*c2+c7*c6*c5*c4)*c1+c7*c6*c5*c4*c3)*c0+c6*c5*c4*c3*c2*c1+c7*c6*c5*c4*c3*c2,
((((c4+c7)*c3+c7*c6)*c2+c7*c6*c5)*c1+c7*c6*c5*c4)*c0+c5*c4*c3*c2*c1+c6*c5*c4*c3*c2+c7*c6*c5*c4*c3,
(((c3+c7)*c2+c7*c6)*c1+c7*c6*c5)*c0+c4*c3*c2*c1+c5*c4*c3*c2+c6*c5*c4*c3+c7*c6*c5*c4,
((c2+c7)*c1+c7*c6)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3+c6*c5*c4+c7*c6*c5,
(c1+c7)*c0+c2*c1+c3*c2+c4*c3+c5*c4+c6*c5+c7*c6,
c0+c1+c2+c3+c4+c5+c6+c7>;

time B := GroebnerBasis(I);
B;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Sun Sep 19 2004 23:09:53 on modular  [Seed = 4110155743]
-------------------------------------

Errors: /bin/sh: line 1: 27614 Killed                  nice -n 19 /usr/local/bin/magma

'203.199'
************** MAGMA *****************
Host 203.199.51.149 (203.199.51.149)
Time: Mon Sep 20 02:14:07 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Mon Sep 20 2004 02:14:07 on modular  [Seed = 521153308]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.199'
************** MAGMA *****************
Host 203.199.51.149 (203.199.51.149)
Time: Mon Sep 20 02:15:13 2004

Input: A := Matrix(K, 5,
[ 0, 2, 4, 2, 0,
2, 2, 2, 3, 3,
3, 4, 4, 1, 3,
0, 0, 0, 0, 1,
0, 0, 0, 1, 0 ]);
FrobeniusForm(A)

Output: Magma V2.11-6     Mon Sep 20 2004 02:15:13 on modular  [Seed = 1818449969]
-------------------------------------

>> A := Matrix(K, 5,
^
User error: Identifier 'K' has not been declared or assigned

>> FrobeniusForm(A);
^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.199'
************** MAGMA *****************
Host 203.199.51.149 (203.199.51.149)
Time: Mon Sep 20 02:15:35 2004

Input: K := GF(5);
A := Matrix(K, 5,
[ 0, 2, 4, 2, 0,
2, 2, 2, 3, 3,
3, 4, 4, 1, 3,
0, 0, 0, 0, 1,
0, 0, 0, 1, 0 ]);
FrobeniusForm(A)

Output: Magma V2.11-6     Mon Sep 20 2004 02:15:35 on modular  [Seed = 1634620874]
-------------------------------------

FrobeniusForm(
M: [0 2 4 2 0] [2 2 2 3 3] [3 4 4 1 3] [0 0 0 0 1] [0 0 0 1 0]
)
In file "/usr/local/magma/package/Geometry/CrvAnJac/frobenius.m", line 95,
column 23:
>>   require BaseRing(M) eq IntegerRing():
^
Runtime error in 'eq': Bad argument types
Argument types given: FldFin, RngInt

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:43:29 2004

Input: factorize(x~10-1);

Output: Magma V2.11-6     Mon Sep 20 2004 02:43:29 on modular  [Seed = 2862978967]
-------------------------------------

>> factorize(x~10-1);;
^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:43:45 2004

Input: factorize(x^10-1);

Output: Magma V2.11-6     Mon Sep 20 2004 02:43:45 on modular  [Seed = 2695863725]
-------------------------------------

>> factorize(x^10-1);;
^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:44:50 2004

Input: P<x>:=PolynomialRing(RationalField(),1);
factorize(x);

Output: Magma V2.11-6     Mon Sep 20 2004 02:44:50 on modular  [Seed = 3182592243]
-------------------------------------

>> factorize(x);;
^
User error: Identifier 'factorize' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:45:06 2004

Input: P<x>:=PolynomialRing(RationalField(),1);
Factorize(x);

Output: Magma V2.11-6     Mon Sep 20 2004 02:45:06 on modular  [Seed = 3132458980]
-------------------------------------

>> Factorize(x);;
^
User error: Identifier 'Factorize' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:45:19 2004

Input: P<x>:=PolynomialRing(RationalField(),1);
Factor(x);

Output: Magma V2.11-6     Mon Sep 20 2004 02:45:19 on modular  [Seed = 3082324708]
-------------------------------------

>> Factor(x);;
^
Runtime error in 'Factor': Bad argument types
Argument types given: RngMPolElt

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:48:24 2004

Input: P<x>:=PolynomialRing(RationalField(),1);
Factorization(x);

Output: Magma V2.11-6     Mon Sep 20 2004 02:48:24 on modular  [Seed = 2290594972]
-------------------------------------

[
<x, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:48:32 2004

Input: P<x>:=PolynomialRing(RationalField(),1);
time Factorization(x);

Output: Magma V2.11-6     Mon Sep 20 2004 02:48:32 on modular  [Seed = 2257173226]
-------------------------------------

[
<x, 1>
]
Time: 0.000

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:49:33 2004

Input: P<x,y,z,w>:=PolynomialRing(RationalField(),4);
time Factorization(29*w^4*z^3*x^33+21*z^2*x^24+(3*w^15*y^20-15*z^16*y^2)*x^21+29*w^4*z^3*y^2*x^14+(29*w^4*z^3*y^18-29*w^4*z^3*y^14-29*w^4*z^34-29*w^16*z^23+29*w^6*z^3)*x^12+21*z^2*y^2*x^5+(21*z^2*y^18-21*z^2*y^14-21*z^33-21*w^12*z^22+21*w^2*z^2)*x^3+(3*w^15*y^22-15*z^16*y^4)*x^2+3*w^15*y^38-3*w^15*y^34+(-3*w^15*z^31-3*w^27*z^20-15*z^16+3*w^17)*y^20+15*z^16*y^16+(15*z^47+15*w^12*z^36-15*w^2*z^16)*y^2
);

Output: Magma V2.11-6     Mon Sep 20 2004 02:49:32 on modular  [Seed = 2660344526]
-------------------------------------

[
<x^12*z^3*w^4 + 21/29*x^3*z^2 + 3/29*y^20*w^15 - 15/29*y^2*z^16, 1>,
<x^21 + x^2*y^2 + y^18 - y^14 - z^31 - z^20*w^12 + w^2, 1>
]
Time: 0.030

Total time: 0.220 seconds, Total memory usage: 3.56MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:58:31 2004

Input: A:=Matrix(RationalField,20,
4,0,14,17,0,0,0,0,0,0,21,1,0,-8,-7,0,0,170,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,91,0,0,0,0,0,0,0,0,0,1,0,0,
0,900,0,-10,0,-6,0,0,2,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,7,2,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,-8,0,0,0,0,0,0,4,0,1,0,0,0,0,8,0,0,0,0,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,42,0,0,1,0,0,0,0,2,0,0,0
,-36,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,-1,0,-28,-32,0,0,0,0,0
,0,-7,0,0,0,0,0,0,-320,1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,1,0,0,0,0,0,0,0,0,2,1,8,0,0,0,0,30,0,0,153,
32,0,0,0,-1,0,0,1,-30,32,34,264,0,0,0,0,0,0,0,-20,-4,0,0,0,0,0,0,0,0,-4,-4,-31,0
,0,0,0,0,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,-89,0,1,-6,0,-41,-72,0,0,0,0,0,0,-42,-3,
0,24,21,0,0,-720,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1);
time JordanForm(A);

Output: Magma V2.11-6     Mon Sep 20 2004 02:58:30 on modular  [Seed = 3924219731]
-------------------------------------

>> A:=Matrix(RationalField,20,
^
Runtime error in 'Matrix': Bad argument types

>> time JordanForm(A);
^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:58:52 2004

Input: A:=Matrix(RationalField(),20,
4,0,14,17,0,0,0,0,0,0,21,1,0,-8,-7,0,0,170,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,91,0,0,0,0,0,0,0,0,0,1,0,0,
0,900,0,-10,0,-6,0,0,2,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,7,2,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,-8,0,0,0,0,0,0,4,0,1,0,0,0,0,8,0,0,0,0,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,42,0,0,1,0,0,0,0,2,0,0,0
,-36,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,-1,0,-28,-32,0,0,0,0,0
,0,-7,0,0,0,0,0,0,-320,1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,1,0,0,0,0,0,0,0,0,2,1,8,0,0,0,0,30,0,0,153,
32,0,0,0,-1,0,0,1,-30,32,34,264,0,0,0,0,0,0,0,-20,-4,0,0,0,0,0,0,0,0,-4,-4,-31,0
,0,0,0,0,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,-89,0,1,-6,0,-41,-72,0,0,0,0,0,0,-42,-3,
0,24,21,0,0,-720,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1);
time JordanForm(A);

Output: Magma V2.11-6     Mon Sep 20 2004 02:58:51 on modular  [Seed = 3874084966]
-------------------------------------

>> A:=Matrix(RationalField(),20,
^
Runtime error in 'Matrix': Bad argument types

>> time JordanForm(A);
^
User error: Identifier 'A' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:59:31 2004

Input: A:=Matrix(RationalField(),20,[
4,0,14,17,0,0,0,0,0,0,21,1,0,-8,-7,0,0,170,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,91,0,0,0,0,0,0,0,0,0,1,0,0,
0,900,0,-10,0,-6,0,0,2,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,7,2,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,-8,0,0,0,0,0,0,4,0,1,0,0,0,0,8,0,0,0,0,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,42,0,0,1,0,0,0,0,2,0,0,0
,-36,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,-1,0,-28,-32,0,0,0,0,0
,0,-7,0,0,0,0,0,0,-320,1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,1,0,0,0,0,0,0,0,0,2,1,8,0,0,0,0,30,0,0,153,
32,0,0,0,-1,0,0,1,-30,32,34,264,0,0,0,0,0,0,0,-20,-4,0,0,0,0,0,0,0,0,-4,-4,-31,0
,0,0,0,0,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,-89,0,1,-6,0,-41,-72,0,0,0,0,0,0,-42,-3,
0,24,21,0,0,-720,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1]);
time JordanForm(A);

Output: Magma V2.11-6     Mon Sep 20 2004 02:59:31 on modular  [Seed = 3823951132]
-------------------------------------

[2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
Time: 0.010

Total time: 0.200 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 02:59:50 2004

Input: A:=Matrix(RationalField(),20,[
4,0,14,18,0,0,0,0,0,0,21,1,0,-8,-7,0,0,170,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,91,0,0,0,0,0,0,0,0,0,1,0,0,
0,900,0,-10,0,-6,0,0,2,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,7,2,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,-8,0,0,0,0,0,0,4,0,1,0,0,0,0,8,0,0,0,0,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,42,0,0,1,0,0,0,0,2,0,0,0
,-36,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,-1,0,-28,-32,0,0,0,0,0
,0,-7,0,0,0,0,0,0,-320,1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,1,0,0,0,0,0,0,0,0,2,1,8,0,0,0,0,30,0,0,153,
32,0,0,0,-1,0,0,1,-30,32,34,264,0,0,0,0,0,0,0,-20,-4,0,0,0,0,0,0,0,0,-4,-4,-31,0
,0,0,0,0,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,-89,0,1,-6,0,-41,-72,0,0,0,0,0,0,-42,-3,
0,24,21,0,0,-720,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1]);
time JordanForm(A);

Output: Magma V2.11-6     Mon Sep 20 2004 02:59:50 on modular  [Seed = 4176987698]
-------------------------------------

[2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
Time: 0.020

Total time: 0.210 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 03:00:08 2004

Input: A:=Matrix(RationalField(),20,[
4,0,14,30,0,0,0,0,0,0,21,1,0,-8,-7,0,0,170,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,91,0,0,0,0,0,0,0,0,0,1,0,0,
0,900,0,-10,0,-6,0,0,2,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,7,2,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,-8,0,0,0,0,0,0,4,0,1,0,0,0,0,8,0,0,0,0,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,42,0,0,1,0,0,0,0,2,0,0,0
,-36,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,-1,0,-28,-32,0,0,0,0,0
,0,-7,0,0,0,0,0,0,-320,1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,1,0,0,0,0,0,0,0,0,2,1,8,0,0,0,0,30,0,0,153,
32,0,0,0,-1,0,0,1,-30,32,34,264,0,0,0,0,0,0,0,-20,-4,0,0,0,0,0,0,0,0,-4,-4,-31,0
,0,0,0,0,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,-89,0,1,-6,0,-41,-72,0,0,0,0,0,0,-42,-3,
0,24,21,0,0,-720,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1]);
time JordanForm(A);

Output: Magma V2.11-6     Mon Sep 20 2004 03:00:08 on modular  [Seed = 4126853921]
-------------------------------------

[2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
Time: 0.030

Total time: 0.210 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 03:01:04 2004

Input: A:=Matrix(RationalField(),20,[
30,0,14,30,0,0,0,0,0,0,21,1,0,-8,-7,0,0,170,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,91,0,0,0,0,0,0,0,0,0,1,0,0,
0,900,0,-10,0,-6,0,0,2,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,7,2,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,-8,0,0,0,0,0,0,4,0,1,0,0,0,0,8,0,0,0,0,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,42,0,0,1,0,0,0,0,2,0,0,0
,-36,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,-1,0,-28,-32,0,0,0,0,0
,0,-7,0,0,0,0,0,0,-320,1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,5,1,0,0,0,0,0,0,0,0,2,1,8,0,0,0,0,30,0,0,153,
32,0,0,0,-1,0,0,1,-30,32,34,264,0,0,0,0,0,0,0,-20,-4,0,0,0,0,0,0,0,0,-4,-4,-31,0
,0,0,0,0,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,-89,0,1,-6,0,-41,-72,0,0,0,0,0,0,-42,-3,
0,24,21,0,0,-720,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1]);
time JordanForm(A);

Output: Magma V2.11-6     Mon Sep 20 2004 03:01:04 on modular  [Seed = 4076680174]
-------------------------------------

[2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 86 -64 32]
Time: 0.020

Total time: 0.210 seconds, Total memory usage: 3.51MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 03:03:48 2004

Input: A:=Matrix(RationalField(),20,[0,0,14,30,0,0,0,0,0,0,21,1,0,-8,-7,0,0,170,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,1,0,0,0,900,0,-10,0,-6,0,0,4,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,7,5,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,-8,0,0,0,0,0,0,4,0,1,0,0,0,0,8,0,0,0,0,1,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,1,0,0,0,0,0,0,0,0,0,0,42,0,0,1,0,0,0,0,9,0,0,0,-36,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,10,0,0,0,0,0,0,10,0,0,-1,0,-28,-32,0,0,0,0,0,0,-7,11,0,0,0,0,0,-320,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,0,5,1,0,0,0,0,0,0,0,0,14,1,8,0,0,0,0,30,0,0,153,32,0,0,0,-1,0,0,1,-30,32,15,264,0,0,0,0,0,0,0,-20,-4,0,0,0,0,0,0,0,0,-4,-4,16,0,0,0,0,0,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,17,0,1,-6,0,-41,-72,0,0,0,0,0,0,-42,-3,0,24,21,0,0,-720,18,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,19]);
time JordanForm(A);

Output: Magma V2.11-6     Mon Sep 20 2004 03:03:48 on modular  [Seed = 3418622515]
-------------------------------------

[2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 12 -202 29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 12391460 -3470122 311547 -9313 57 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 1461107520 -25800503784 27134868792 -12581845556 3323089260
-550255877 59378286 -4209963 193800 -5659 102]
Time: 0.080

Total time: 0.270 seconds, Total memory usage: 3.56MB

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 03:19:22 2004

Input:
P<x,y,z,t> := PolynomialRing(FiniteField(2),4);
I:= ideal<P |
x^12+x^10+x^8+x^2+t,
y^12+y^10+y^8+y^2+t,
z^12+z^10+z^8+z^2+t>;
time B := PrimaryDecomposition(I);
B;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Mon Sep 20 2004 03:19:01 on modular  [Seed = 606855534]
-------------------------------------

Errors: /bin/sh: line 1: 28171 Killed                  nice -n 19 /usr/local/bin/magma

'219.164'
************** MAGMA *****************
Host 219.164.138.41 (219.164.138.41)
Time: Mon Sep 20 03:19:52 2004

Input: P<x,y,z,t> := PolynomialRing(FiniteField(31991),4);
I:= ideal<P |
x^12+x^10+x^8+x^2+t,
y^12+y^10+y^8+y^2+t,
z^12+z^10+z^8+z^2+t>;
time B := PrimaryDecomposition(I);
B;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Mon Sep 20 2004 03:19:31 on modular  [Seed = 1010039184]
-------------------------------------

Errors: /bin/sh: line 1: 28179 Killed                  nice -n 19 /usr/local/bin/magma

'134.60.'
************** MAGMA *****************
Host 134.60.67.219 (134.60.67.219)
Time: Mon Sep 20 03:47:49 2004

Input: M2:= MatrixRing(Integers(), 2);
Z1:=[ M2!1, M2!1];
Z2:=[ M2!1, M2![2,1,1,2] ];
ok, T:= IsIsometric(Z1, Z2);
T;

Output: Magma V2.11-6     Mon Sep 20 2004 03:47:48 on modular  [Seed = 1634642794]
-------------------------------------

[1 0]
[0 1]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'147.210'
************** MAGMA *****************
Host 147.210.17.33 (147.210.17.33)
Time: Mon Sep 20 08:05:48 2004

Input: TransitiveGroup(9,T_{33}^+);

Output: Magma V2.11-6     Mon Sep 20 2004 08:05:48 on modular  [Seed = 809481887]
-------------------------------------

>> TransitiveGroup(9,T_{33}^+);;
^

Total time: 0.190 seconds, Total memory usage: 3.51MB

'147.210'
************** MAGMA *****************
Host 147.210.17.33 (147.210.17.33)
Time: Mon Sep 20 08:06:29 2004

Input: TransitiveGroup(9,T33+);

Output: Magma V2.11-6     Mon Sep 20 2004 08:06:29 on modular  [Seed = 993312205]
-------------------------------------

>> TransitiveGroup(9,T33+);;
^

Total time: 0.190 seconds, Total memory usage: 3.51MB

'195.130'
************** MAGMA *****************
Host 195.130.112.43 (195.130.112.43)
Time: Mon Sep 20 11:35:56 2004

Input: K<w> := GF(3);
R<x, y, z, w > := PolynomialRing(K, [3^2 -3, 3^2 -1, 3^4 -3^3, 3^4 -3^2 ]);
R;
P := [ z, w, y*(w-y^9 -x^3 *(z-x^9)), y^3 *(z-x^9) +x*(w-y^9 -x^3 *(z-x^9)) ] ;

I:=ideal<R | P>;

V,phi:=VectorSpace(quo<R | I>);
S:=[R!([email protected]@phi ): v in Basis(V)];

S;

Output: Magma V2.11-6     Mon Sep 20 2004 11:35:55 on modular  [Seed = 1262809762]
-------------------------------------

Graded Polynomial ring of rank 4 over GF(3)
Lexicographical Order
Variables: x, y, z, w
Variable weights: 6 8 54 72
[
1,
y,
y^2,
y^3,
y^4,
y^5,
y^6,
y^7,
y^8,
y^9,
y^10,
y^11,
y^12,
x,
x*y,
x*y^2,
x*y^3,
x*y^4,
x*y^5,
x*y^6,
x*y^7,
x*y^8,
x*y^9,
x*y^10,
x*y^11,
x*y^12,
x^2,
x^2*y,
x^2*y^2,
x^2*y^3,
x^2*y^4,
x^2*y^5,
x^2*y^6,
x^2*y^7,
x^2*y^8,
x^2*y^9,
x^2*y^10,
x^2*y^11,
x^2*y^12,
x^3,
x^3*y,
x^3*y^2,
x^3*y^3,
x^3*y^4,
x^3*y^5,
x^3*y^6,
x^3*y^7,
x^3*y^8,
x^3*y^9,
x^3*y^10,
x^3*y^11,
x^3*y^12,
x^4,
x^4*y,
x^4*y^2,
x^4*y^3,
x^4*y^4,
x^4*y^5,
x^4*y^6,
x^4*y^7,
x^4*y^8,
x^4*y^9,
x^4*y^10,
x^4*y^11,
x^4*y^12,
x^5,
x^5*y,
x^5*y^2,
x^5*y^3,
x^5*y^4,
x^5*y^5,
x^5*y^6,
x^5*y^7,
x^5*y^8,
x^5*y^9,
x^5*y^10,
x^5*y^11,
x^5*y^12,
x^6,
x^6*y,
x^6*y^2,
x^6*y^3,
x^6*y^4,
x^6*y^5,
x^6*y^6,
x^6*y^7,
x^6*y^8,
x^6*y^9,
x^6*y^10,
x^6*y^11,
x^6*y^12,
x^7,
x^7*y,
x^7*y^2,
x^7*y^3,
x^7*y^4,
x^7*y^5,
x^7*y^6,
x^7*y^7,
x^7*y^8,
x^7*y^9,
x^7*y^10,
x^7*y^11,
x^7*y^12,
x^8,
x^8*y,
x^8*y^2,
x^8*y^3,
x^8*y^4,
x^8*y^5,
x^8*y^6,
x^8*y^7,
x^8*y^8,
x^8*y^9,
x^8*y^10,
x^8*y^11,
x^8*y^12,
x^9,
x^9*y,
x^9*y^2,
x^9*y^3,
x^10,
x^10*y,
x^10*y^2,
x^10*y^3,
x^11,
x^11*y,
x^11*y^2,
x^11*y^3,
x^12
]

Total time: 0.200 seconds, Total memory usage: 3.66MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Mon Sep 20 12:45:39 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,1,
-1020589392,-12549449883218]))));

Output: Magma V2.11-6     Mon Sep 20 2004 12:45:39 on modular  [Seed = 1548883033]
-------------------------------------

[ <3, 11>, <5, 4>, <11, 1>, <131, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Mon Sep 20 12:46:34 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-1576045728,24082487013852]))));

Output: Magma V2.11-6     Mon Sep 20 2004 12:46:34 on modular  [Seed = 1498878213]
-------------------------------------

[ <2, 8>, <3, 9>, <5, 4>, <29, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Mon Sep 20 12:47:12 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,0,
-1331364250,-18697482798839]))));

Output: Magma V2.11-6     Mon Sep 20 2004 12:47:11 on modular  [Seed = 1095698936]
-------------------------------------

[ <2, 4>, <3, 6>, <11, 9>, <43, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Mon Sep 20 12:47:53 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,1,
-8059714329,278504219221139]))));

Output: Magma V2.11-6     Mon Sep 20 2004 12:47:53 on modular  [Seed = 1245971141]
-------------------------------------

[ <3, 9>, <11, 10>, <13, 8> ]

Total time: 0.200 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Mon Sep 20 12:48:36 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-6181569372,187066592189768]))));

Output: Magma V2.11-6     Mon Sep 20 2004 12:48:36 on modular  [Seed = 3082420069]
-------------------------------------

[ <2, 10>, <3, 21>, <107, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Mon Sep 20 12:49:14 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,1,
-358510449,2612782268914]))));

Output: Magma V2.11-6     Mon Sep 20 2004 12:49:14 on modular  [Seed = 2982148749]
-------------------------------------

[ <3, 15>, <83, 8> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Mon Sep 20 12:49:51 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,1,
-14461288257,669358199975026]))));

Output: Magma V2.11-6     Mon Sep 20 2004 12:49:50 on modular  [Seed = 3115840161]
-------------------------------------

[ <3, 7>, <13, 10>, <41, 3> ]

Total time: 0.200 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:22:04 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() | 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() | 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:22:03 on modular  [Seed = 287293543]
-------------------------------------

>>   [ IntegerRing() | 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^

>> FourDescendentAscent(M,[-24,6,-7,-1]);
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:22:45 2004

Input: M :=
[ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() | 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() | 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:22:45 on modular  [Seed = 151509057]
-------------------------------------

>>   [ IntegerRing() | 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^

>> FourDescendentAscent(M,[-24,6,-7,-1]);;
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:25:56 2004

Input: help IntegerRing;

Output: Magma V2.11-6     Mon Sep 20 2004 22:25:55 on modular  [Seed = 34394635]
-------------------------------------

>> help IntegerRing;
^

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:26:13 2004

Input: help(IntegerRing);

Output: Magma V2.11-6     Mon Sep 20 2004 22:26:13 on modular  [Seed = 2121313798]
-------------------------------------

>> help(IntegerRing);;
^
User error: Identifier 'help' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:28:24 2004

Input: M :=
[ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() ! 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:28:23 on modular  [Seed = 2004461453]
-------------------------------------

>>   [ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^
Runtime error in '[]': Sequence element 0 not defined

>> FourDescendentAscent(M,[-24,6,-7,-1]);;
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:28:51 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() ! 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:28:51 on modular  [Seed = 1920770732]
-------------------------------------

>>   [ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^
Runtime error in '[]': Sequence element 0 not defined

>> FourDescendentAscent(M,[-24,6,-7,-1]);;
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:29:13 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) !
[ IntegerRing() ! 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:29:13 on modular  [Seed = 1851834026]
-------------------------------------

>>   [ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^
Runtime error in '[]': Sequence element 0 not defined

>> FourDescendentAscent(M,[-24,6,-7,-1]);;
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:29:47 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() | 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() | 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:29:46 on modular  [Seed = 1784985932]
-------------------------------------

>>   [ IntegerRing() | 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^

>> FourDescendentAscent(M,[-24,6,-7,-1]);;
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:29:58 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() ! 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:29:58 on modular  [Seed = 1718138237]
-------------------------------------

>>   [ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^
Runtime error in '[]': Sequence element 0 not defined

>> FourDescendentAscent(M,[-24,6,-7,-1]);;
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:36:20 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() ! 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);
FourDescendentAscent;

Output: Magma V2.11-6     Mon Sep 20 2004 22:36:20 on modular  [Seed = 1532332482]
-------------------------------------

>>   [ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^
Runtime error in '[]': Sequence element 0 not defined

>> FourDescendentAscent(M,[-24,6,-7,-1]);
^
User error: Identifier 'M' has not been declared or assigned
Intrinsic 'FourDescendentAscent'

Signatures:

(<SeqEnum[AlgMatElt]> A, <SeqEnum[RngIntElt]> pt) -> CrvEll, PtEll

Given a four-descendent with a point on it, construct the associated EC
and the point on that.

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:42:33 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() : 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() : 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);
FourDescendentAscent;

Output: Magma V2.11-6     Mon Sep 20 2004 22:42:32 on modular  [Seed = 1312856683]
-------------------------------------

>>   [ IntegerRing() : 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45
^

>>   [ IntegerRing() : 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^

>> FourDescendentAscent(M,[-24,6,-7,-1]);
^
User error: Identifier 'M' has not been declared or assigned
Intrinsic 'FourDescendentAscent'

Signatures:

(<SeqEnum[AlgMatElt]> A, <SeqEnum[RngIntElt]> pt) -> CrvEll, PtEll

Given a four-descendent with a point on it, construct the associated EC
and the point on that.

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:42:54 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);
FourDescendentAscent;

Output: Magma V2.11-6     Mon Sep 20 2004 22:42:54 on modular  [Seed = 1246010969]
-------------------------------------

>>   [ 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
^
Runtime error in '[]': Sequence element 0 not defined

>> FourDescendentAscent(M,[-24,6,-7,-1]);
^
User error: Identifier 'M' has not been declared or assigned
Intrinsic 'FourDescendentAscent'

Signatures:

(<SeqEnum[AlgMatElt]> A, <SeqEnum[RngIntElt]> pt) -> CrvEll, PtEll

Given a four-descendent with a point on it, construct the associated EC
and the point on that.

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:43:25 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:43:24 on modular  [Seed = 1179161143]
-------------------------------------

>>   [ IntegerRing() 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
^

>>   [ IntegerRing() 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36
^

>> FourDescendentAscent(M,[-24,6,-7,-1]);
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:43:51 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() : 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() : 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:43:51 on modular  [Seed = 3199232740]
-------------------------------------

>>   [ IntegerRing() : 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45
^

>>   [ IntegerRing() : 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^

>> FourDescendentAscent(M,[-24,6,-7,-1]);;
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 22:44:05 2004

Input: M := [ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() ! 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ]
[ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 22:44:05 on modular  [Seed = 3132387058]
-------------------------------------

>>   [ IntegerRing() ! 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90, -
^
Runtime error in '[]': Sequence element 0 not defined

>> FourDescendentAscent(M,[-24,6,-7,-1]);;
^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.51MB

'68.77.3'
************** MAGMA *****************
Host 68.77.37.223 (68.77.37.223)
Time: Mon Sep 20 23:14:59 2004

Input: 0.05^365

Output: Magma V2.11-6     Mon Sep 20 2004 23:14:59 on modular  [Seed = 3940824932]
-------------------------------------

1.330612450002547099971891786327284012790E-475

Total time: 0.200 seconds, Total memory usage: 3.51MB

'68.77.3'
************** MAGMA *****************
Host 68.77.37.223 (68.77.37.223)
Time: Mon Sep 20 23:20:40 2004

Input: 0.05*365*366/2

Output: Magma V2.11-6     Mon Sep 20 2004 23:20:40 on modular  [Seed = 3637905389]
-------------------------------------

3339.749999999999999999999999999999999975925

Total time: 0.190 seconds, Total memory usage: 3.51MB

'68.77.3'
************** MAGMA *****************
Host 68.77.37.223 (68.77.37.223)
Time: Mon Sep 20 23:22:55 2004

Input: 0.05*20*21/2

Output: Magma V2.11-6     Mon Sep 20 2004 23:22:55 on modular  [Seed = 3504213858]
-------------------------------------

10.499999999999999999999999999999999999952

Total time: 0.190 seconds, Total memory usage: 3.51MB

'68.77.3'
************** MAGMA *****************
Host 68.77.37.223 (68.77.37.223)
Time: Mon Sep 20 23:23:32 2004

Input: 0.05*365*366/2

Output: Magma V2.11-6     Mon Sep 20 2004 23:23:31 on modular  [Seed = 3385267783]
-------------------------------------

3339.749999999999999999999999999999999975925

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 23:41:27 2004

Input: M :=
[ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() | 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ],
[ IntegerRing() | 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90,
-36]];
FourDescendentAscent(M,[-24,6,-7,-1]);

Output: Magma V2.11-6     Mon Sep 20 2004 23:41:27 on modular  [Seed = 809423851]
-------------------------------------

FourDescendentAscent(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ -24, 6, -7, -1 ]
)
FourDescendentCover(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ -24, 6, -7, -1 ]
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/fourdesc.m", line
116, column 5:
>>     assert &and[QFFromMatrix(pt, a) eq 0 : a in A];
^
Runtime error in assert: Assertion failed

Total time: 0.200 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 23:42:28 2004

Input: M :=
[ MatrixAlgebra(IntegerRing(), 4) |
[ IntegerRing() | 2, 0, 4, 2, 0, -2, 2, 0, 4, 2, -43, -74, 2, 0, -74, 45 ],
[ IntegerRing() | 0, 4, 2, -4, 4, 0, 0, -2, 2, 0, 38, -90, -4, -2, -90,
-36]];
FourDescendentAscent(M,[-24,6,-7,-1]);
FourDescendentAscent(M,[-3,-248,-2,-8]);
FourDescendentAscent(M,[0,0,0,0]);
FourDescendentAscent(M,[9,-252,0,18]);
FourDescendentAscent(M,[20,-2,0,-4]);
FourDescendentAscent(M,[24,10,0,12]);

Output: Magma V2.11-6     Mon Sep 20 2004 23:42:28 on modular  [Seed = 757321525]
-------------------------------------

FourDescendentAscent(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ -24, 6, -7, -1 ]
)
FourDescendentCover(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ -24, 6, -7, -1 ]
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/fourdesc.m", line
116, column 5:
>>     assert &and[QFFromMatrix(pt, a) eq 0 : a in A];
^
Runtime error in assert: Assertion failed

FourDescendentAscent(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ -3, -248, -2, -8 ]
)
FourDescendentCover(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ -3, -248, -2, -8 ]
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/fourdesc.m", line
116, column 5:
>>     assert &and[QFFromMatrix(pt, a) eq 0 : a in A];
^
Runtime error in assert: Assertion failed

FourDescendentAscent(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ 0, 0, 0, 0 ]
)
FourDescendentCover(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ 0, 0, 0, 0 ]
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/fourdesc.m", line
123, column 20:
>>     ex := [-f(u)/f(u), f(u)/f(u)^2];
^
Runtime error in '/': Division by zero

FourDescendentAscent(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ 9, -252, 0, 18 ]
)
FourDescendentCover(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ 9, -252, 0, 18 ]
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/fourdesc.m", line
116, column 5:
>>     assert &and[QFFromMatrix(pt, a) eq 0 : a in A];
^
Runtime error in assert: Assertion failed

FourDescendentAscent(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ 20, -2, 0, -4 ]
)
FourDescendentCover(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ 20, -2, 0, -4 ]
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/fourdesc.m", line
116, column 5:
>>     assert &and[QFFromMatrix(pt, a) eq 0 : a in A];
^
Runtime error in assert: Assertion failed

FourDescendentAscent(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ 24, 10, 0, 12 ]
)
FourDescendentCover(
A: [ [  2   0   4   2] [  0  -2   2   0] [  4   2 -43 -74] [  2...,
pt: [ 24, 10, 0, 12 ]
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/fourdesc.m", line
116, column 5:
>>     assert &and[QFFromMatrix(pt, a) eq 0 : a in A];
^
Runtime error in assert: Assertion failed

Total time: 0.190 seconds, Total memory usage: 3.56MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Mon Sep 20 23:57:21 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-60076619,-176354810358]);
E;
f := P!Reverse([13697,-1424,25026,1424,13697]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Mon Sep 20 2004 23:57:00 on modular [Seed = 3807118638] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 60076619*x - 176354810358 over Rational Field 13697*x^4 - 1424*x^3 + 25026*x^2 + 1424*x + 13697 4 Errors: /bin/sh: line 1: 418 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.22 (66.63.133.22) Time: Mon Sep 20 23:58:14 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-60076619,-176354810358]); E; f := P!Reverse([13697,-1424,25026,1424,13697]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Mon Sep 20 2004 23:58:09 on modular  [Seed = 3890806902]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 60076619*x - 176354810358 over Rational
Field
13697*x^4 - 1424*x^3 + 25026*x^2 + 1424*x + 13697
4
Point [ 1, 448, 90, 315 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 454, 485, 385 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 768, 105, 918 ] was singular mod 1009 and ignored at the #3 lift
[
[ 7569, -4131, -1251, 1019 ],
[ 4457, -10449, 2270, 232 ],
[ 2880, 8588, 1019, 1251 ],
[ 12719, 4689, 232, -2270 ]
]
Scheme over Rational Field defined by
2*r1^2 + 2*r1*r3 - 2*r2^2 + 4*r2*r3 + 2*r2*r4 + 43*r3^2 + 74*r3*r4 - 45*r4^2,
4*r1*r2 + 2*r1*r4 - 2*r2*r3 + 4*r2*r4 + 38*r3^2 - 90*r3*r4 - 36*r4^2
(-2595840127566329121735993984048027691/527813643022911078884862253965601 :
-148735474405042246730990528626903251500148027053959420/12126093640313010487107\
907036563938265274448708401 : 1)
72.98759751512406523943

Total time: 4.900 seconds, Total memory usage: 9.13MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Tue Sep 21 00:14:32 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
E;
f := P!Reverse([-1069283275100,253352597540,-4944196555859,529370810346,-5718704313951]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 00:14:11 on modular [Seed = 2223664983] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x + 1112872991819139146923702415527076900 over Rational Field -1069283275100*x^4 + 253352597540*x^3 - 4944196555859*x^2 + 529370810346*x - 5718704313951 Errors: /bin/sh: line 1: 452 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.22 (66.63.133.22) Time: Tue Sep 21 00:15:59 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); E; f := P!Reverse([5,0,9930400468081,0,79409849685606720000000]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 00:15:38 on modular  [Seed = 2307351075]
-------------------------------------

Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x +
1112872991819139146923702415527076900 over Rational Field
5*x^4 + 9930400468081*x^2 + 79409849685606720000000

Errors: /bin/sh: line 1:   457 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.22 (66.63.133.22)
Time: Tue Sep 21 00:16:31 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
E;
f := P!Reverse([5,0,9930400468081,0,79409849685606720000000]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 00:16:10 on modular [Seed = 2390779076] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x + 1112872991819139146923702415527076900 over Rational Field 5*x^4 + 9930400468081*x^2 + 79409849685606720000000 Errors: /bin/sh: line 1: 462 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.22 (66.63.133.22) Time: Tue Sep 21 00:17:18 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); E; f := P!Reverse([7,0,9930400468081,0,56721321204004800000000]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 00:16:57 on modular  [Seed = 2509996012]
-------------------------------------

Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x +
1112872991819139146923702415527076900 over Rational Field
7*x^4 + 9930400468081*x^2 + 56721321204004800000000

Errors: /bin/sh: line 1:   469 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 00:19:34 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
E;
f := P!Reverse([35,0,9930400468081,0,11344264240800960000000]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 00:19:12 on modular [Seed = 2712619809] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x + 1112872991819139146923702415527076900 over Rational Field 35*x^4 + 9930400468081*x^2 + 11344264240800960000000 Errors: /bin/sh: line 1: 481 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:21:26 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-9230260848514469640007985630,334438337831884796715017914060851818910900]); E; f := P!Reverse([21,0,586851077698033,0,-1566005291005583770953194304]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 00:21:05 on modular  [Seed = 2929738719]
-------------------------------------

Elliptic Curve defined by y^2 + x*y = x^3 - 9230260848514469640007985630*x +
334438337831884796715017914060851818910900 over Rational Field
21*x^4 + 586851077698033*x^2 - 1566005291005583770953194304

Errors: /bin/sh: line 1:   494 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 00:22:23 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-9230260848514469640007985630,334438337831884796715017914060851818910900]);
E;
f := P!Reverse([9494,0,586851077698033,0,-3463883622405441246051936]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 00:22:02 on modular [Seed = 3015532185] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 9230260848514469640007985630*x + 334438337831884796715017914060851818910900 over Rational Field 9494*x^4 + 586851077698033*x^2 - 3463883622405441246051936 Errors: /bin/sh: line 1: 499 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:23:13 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-9230260848514469640007985630,334438337831884796715017914060851818910900]); E; f := P!Reverse([-9494,0,586851077698033,0,3463883622405441246051936]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 00:22:52 on modular  [Seed = 3098957156]
-------------------------------------

Elliptic Curve defined by y^2 + x*y = x^3 - 9230260848514469640007985630*x +
334438337831884796715017914060851818910900 over Rational Field
-9494*x^4 + 586851077698033*x^2 + 3463883622405441246051936

Errors: /bin/sh: line 1:   504 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 00:27:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,33236258933233,0,-3041245986244291199359212139584,0]);
E;
f := P!Reverse([7081614609,-1585505670,-1335324459483107,22415940428741300,53475326226066231844]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 00:27:12 on modular [Seed = 1112321697] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 33236258933233*x^2 - 3041245986244291199359212139584*x over Rational Field 7081614609*x^4 - 1585505670*x^3 - 1335324459483107*x^2 + 22415940428741300*x + 53475326226066231844 Errors: /bin/sh: line 1: 513 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:29:03 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,33236258933233,0,-3041245986244291199359212139584,0]); E; f := P!Reverse([60896770129,-80354628738,-1042987114325471,-26568661741559280,7178925450489669760]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 00:28:42 on modular  [Seed = 1246013171]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 + 33236258933233*x^2 -
3041245986244291199359212139584*x over Rational Field
60896770129*x^4 - 80354628738*x^3 - 1042987114325471*x^2 - 26568661741559280*x +
7178925450489669760

Errors: /bin/sh: line 1:   521 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 00:30:09 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,33236258933233,0,-3041245986244291199359212139584,0]);
E;
f := P!Reverse([9343387599841,15614278042646,-795444190357571,-5274667996568820,48587712742916100]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 00:29:48 on modular [Seed = 1279435571] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 33236258933233*x^2 - 3041245986244291199359212139584*x over Rational Field 9343387599841*x^4 + 15614278042646*x^3 - 795444190357571*x^2 - 5274667996568820*x + 48587712742916100 Errors: /bin/sh: line 1: 527 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:32:11 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,33236258933233,0,-3041245986244291199359212139584,0]); E; f := P!Reverse([7011619561,686613510,-743640309042827,-189558707599814940,68625448928056082596]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 00:31:50 on modular  [Seed = 1465497762]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 + 33236258933233*x^2 -
3041245986244291199359212139584*x over Rational Field
7011619561*x^4 + 686613510*x^3 - 743640309042827*x^2 - 189558707599814940*x +
68625448928056082596

Errors: /bin/sh: line 1:   532 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 00:34:24 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-1038427054499523341167676503880,407297544805282559416553418251079648077247552]);
E;
f := P!Reverse([-21,0,28240252302367492,0,-506961355131804394192896]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 00:34:03 on modular [Seed = 1498920737] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 1038427054499523341167676503880*x + 407297544805282559416553418251079648077247552 over Rational Field -21*x^4 + 28240252302367492*x^2 - 506961355131804394192896 Errors: /bin/sh: line 1: 538 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:36:19 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); E; f := P!Reverse([5,0,9930400468081,0,79409849685606720000000]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 00:35:58 on modular  [Seed = 1548923569]
-------------------------------------

Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x +
1112872991819139146923702415527076900 over Rational Field
5*x^4 + 9930400468081*x^2 + 79409849685606720000000

Errors: /bin/sh: line 1:   543 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 00:37:16 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
E;
f := P!Reverse([7,0,9930400468081,0,56721321204004800000000]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 00:36:55 on modular [Seed = 1734969795] ------------------------------------- Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x + 1112872991819139146923702415527076900 over Rational Field 7*x^4 + 9930400468081*x^2 + 56721321204004800000000 Errors: /bin/sh: line 1: 548 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:41:53 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([3109,348,-10608,2264,13220]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 00:41:44 on modular  [Seed = 1868668708]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
3109*x^4 + 348*x^3 - 10608*x^2 + 2264*x + 13220
2
Point [ 1, 338, 15, 394 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 581, 355, 788 ] was singular mod 1009 and ignored at the #1 lift
[
[ 2002, -72, -385, -215 ]
]
Scheme over Rational Field defined by
r1^2 + 20*r1*r2 + 4*r1*r3 + 2*r1*r4 + 14*r2^2 + 62*r2*r3 + 70*r2*r4 + 18*r3^2 -
72*r3*r4 + 70*r4^2,
r1^2 + 30*r1*r2 + 22*r1*r3 - 44*r1*r4 - 6*r2^2 + 142*r2*r3 + 30*r2*r4 + 70*r3^2
- 148*r3*r4 - 90*r4^2
(252577815405866106220347147925969/132858182474671836373869534025 :
-421988733621958724598767827675464358840960165922/48426430709924637308465095077\
859469576205125 : 1)
66.43307922758570782661

Total time: 8.089 seconds, Total memory usage: 6.91MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 00:47:12 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-1142761,0]);
E;
f := P!Reverse([1069,0,-6414,-17104,43829]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 00:47:09 on modular [Seed = 1987609976] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field 1069*x^4 - 6414*x^2 - 17104*x + 43829 2 [ [ 1899, -582, 577, 1637 ], [ 582, 1899, 1637, -577 ] ] Scheme over Rational Field defined by 12*r1*r2 + 6*r1*r3 + 4*r1*r4 - 4*r2*r3 + 6*r2*r4 + 3*r3^2 + 6*r3*r4 - 3*r4^2, 4*r1^2 - 8*r1*r2 + 22*r1*r3 - 10*r1*r4 - 4*r2^2 + 10*r2*r3 + 22*r2*r4 - 4*r3^2 + 4*r4^2 (-73975153990139974920200842127/27541173285562142868881521 : 25647697356660597659544931073115508448307290/1445352096157604700778580259092615\ 70569 : 1) 66.43307922758570782661 Total time: 3.089 seconds, Total memory usage: 5.14MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:51:28 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([-1,0,6414,0,-1142761]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 00:51:23 on modular  [Seed = 2021034608]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
-x^4 + 6414*x^2 - 1142761
4
Point [ 1, 60, 174, 127 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 70, 211, 528 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
2*r1*r3 + r2^2 - 2*r2*r3 - r3^2 + 2*r3*r4 + r4^2,
12*r1^2 + 18*r1*r2 + 34*r1*r3 + 22*r1*r4 + 24*r2^2 - 22*r2*r3 - 62*r2*r4 +
38*r3^2 + 4*r3*r4 - 46*r4^2

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: Sch[FldRat] Total time: 4.660 seconds, Total memory usage: 5.40MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:51:58 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([-1,0,6414,0,-1142761]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 00:51:53 on modular  [Seed = 51245353]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
-x^4 + 6414*x^2 - 1142761
4
[]
Scheme over Rational Field defined by
2*r1*r2 + r2^2 + 2*r2*r3 - r3^2 - r4^2,
12*r1^2 - 60*r1*r2 + 10*r1*r3 + 70*r1*r4 - 13*r2^2 + 14*r2*r4 - 25*r3^2 -
24*r3*r4 - 49*r4^2

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: Sch[FldRat] Total time: 4.570 seconds, Total memory usage: 5.32MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:52:30 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([-1,0,6414,0,-1142761]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($2);

Output: Magma V2.11-6     Tue Sep 21 2004 00:52:25 on modular  [Seed = 101250252]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
-x^4 + 6414*x^2 - 1142761
4
Point [ 1, 60, 174, 127 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 70, 211, 528 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
2*r1*r3 + r2^2 - 2*r2*r3 - r3^2 + 2*r3*r4 + r4^2,
12*r1^2 + 18*r1*r2 + 34*r1*r3 + 22*r1*r4 + 24*r2^2 - 22*r2*r3 - 62*r2*r4 +
38*r3^2 + 4*r3*r4 - 46*r4^2

>> m(pts);
^
Runtime error in '[]': Sequence element 2 not defined

>> Height($2); ^ Runtime error in 'Height': Bad argument types Argument types given: SeqEnum[Any] Total time: 4.650 seconds, Total memory usage: 5.39MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:53:01 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([-1,0,6414,0,-1142761]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($2);

Output: Magma V2.11-6     Tue Sep 21 2004 00:52:57 on modular  [Seed = 234945764]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
-x^4 + 6414*x^2 - 1142761
4
Point [ 1, 539, 904, 469 ] was singular mod 1009 and ignored at the #1 lift
[]
Scheme over Rational Field defined by
2*r1*r2 + r2^2 - 2*r2*r4 - r3^2 - r4^2,
24*r1^2 - 34*r1*r2 + 20*r1*r3 + 16*r1*r4 - 17*r2^2 + 22*r2*r3 - 40*r2*r4 +
35*r3^2 + 80*r3*r4 - 45*r4^2

>> m(pts);
^
Runtime error in '[]': Sequence element 2 not defined

>> Height($2); ^ Runtime error in 'Height': Bad argument types Argument types given: SeqEnum[Any] Total time: 4.639 seconds, Total memory usage: 5.32MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:53:27 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([-1,0,6414,0,-1142761]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 00:53:22 on modular  [Seed = 387573142]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
-x^4 + 6414*x^2 - 1142761
4
[]
Scheme over Rational Field defined by
2*r1*r2 + r2^2 + 2*r2*r3 - r3^2 - r4^2,
12*r1^2 - 60*r1*r2 + 10*r1*r3 + 70*r1*r4 - 13*r2^2 + 14*r2*r4 - 25*r3^2 -
24*r3*r4 - 49*r4^2

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: Sch[FldRat] Total time: 4.790 seconds, Total memory usage: 5.38MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:53:43 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([-1,0,6414,0,-1142761]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 00:53:39 on modular  [Seed = 437577866]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
-x^4 + 6414*x^2 - 1142761
4
[]
Scheme over Rational Field defined by
2*r1*r2 + r2^2 + 2*r2*r3 - r3^2 - r4^2,
12*r1^2 - 60*r1*r2 + 10*r1*r3 + 70*r1*r4 - 13*r2^2 + 14*r2*r4 - 25*r3^2 -
24*r3*r4 - 49*r4^2

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: Sch[FldRat] Total time: 4.710 seconds, Total memory usage: 5.36MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:54:06 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([-1,0,6414,0,-1142761]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($3);

Output: Magma V2.11-6     Tue Sep 21 2004 00:54:01 on modular  [Seed = 471002806]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
-x^4 + 6414*x^2 - 1142761
4
[]
Scheme over Rational Field defined by
2*r1*r2 + r2^2 + 2*r2*r3 - r3^2 - r4^2,
12*r1^2 - 60*r1*r2 + 10*r1*r3 + 70*r1*r4 - 13*r2^2 + 14*r2*r4 - 25*r3^2 -
24*r3*r4 - 49*r4^2

>> m(pts);
^
Runtime error in '[]': Sequence element 3 not defined

>> Height($3); ^ Runtime error in 'Height': Bad argument types Argument types given: RngIntElt Total time: 4.599 seconds, Total memory usage: 5.33MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 00:56:13 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1142761,0]); E; f := P!Reverse([3109,348,-10608,2264,13220]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 00:56:05 on modular  [Seed = 723901965]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1142761*x over Rational Field
3109*x^4 + 348*x^3 - 10608*x^2 + 2264*x + 13220
2
Point [ 1, 338, 15, 394 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 581, 355, 788 ] was singular mod 1009 and ignored at the #1 lift
[
[ 2002, -72, -385, -215 ]
]
Scheme over Rational Field defined by
r1^2 + 20*r1*r2 + 4*r1*r3 + 2*r1*r4 + 14*r2^2 + 62*r2*r3 + 70*r2*r4 + 18*r3^2 -
72*r3*r4 + 70*r4^2,
r1^2 + 30*r1*r2 + 22*r1*r3 - 44*r1*r4 - 6*r2^2 + 142*r2*r3 + 30*r2*r4 + 70*r3^2
- 148*r3*r4 - 90*r4^2
(252577815405866106220347147925969/132858182474671836373869534025 :
-421988733621958724598767827675464358840960165922/48426430709924637308465095077\
859469576205125 : 1)
66.43307922758570782661

Total time: 8.330 seconds, Total memory usage: 7.44MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 01:04:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-1194649,0]);
E;
f := P!Reverse([1093,0,-6558,-17488,44813]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 01:04:44 on modular [Seed = 876266267] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 1194649*x over Rational Field 1093*x^4 - 6558*x^2 - 17488*x + 44813 2 Point [ 1, 26, 0, 293 ] was singular mod 1009 and ignored at the #1 lift [ [ 169, -71, -157, 520 ], [ 71, 169, 520, 157 ] ] Scheme over Rational Field defined by r1^2 + 6*r1*r2 + 12*r1*r3 + 2*r1*r4 - r2^2 - 2*r2*r3 + 12*r2*r4 - 4*r3^2 + 4*r3*r4 + 4*r4^2, 3*r1^2 - 14*r1*r2 + 14*r1*r3 - 3*r2^2 + 14*r2*r4 + 4*r3^2 - 20*r3*r4 - 4*r4^2 (12493251233560917444763441/6396350846877039790681 : -4115201667608471287859832462212724410/511562164051420879260293302467421 : 1) 56.56757198997087243697 Total time: 3.180 seconds, Total memory usage: 5.14MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 01:07:00 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1194649,0]); E; f := P!Reverse([1093,0,-6558,-17488,44813]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 01:06:57 on modular  [Seed = 3621331045]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 1194649*x over Rational Field
1093*x^4 - 6558*x^2 - 17488*x + 44813
2
[
[ 363, 677, 240, 98 ],
[ 677, -363, -98, 240 ]
]
Scheme over Rational Field defined by
2*r1^2 + 8*r1*r2 + 2*r1*r3 + 12*r1*r4 - 2*r2^2 - 12*r2*r3 + 2*r2*r4 - 3*r3^2 +
2*r3*r4 + 3*r4^2,
10*r1^2 + 8*r1*r2 - 14*r1*r4 - 10*r2^2 + 14*r2*r3 - 7*r3^2 - 6*r3*r4 + 7*r4^2
(12493251233560917444763441/6396350846877039790681 :
4115201667608471287859832462212724410/511562164051420879260293302467421 : 1)
56.56757198997087243697

Total time: 3.180 seconds, Total memory usage: 5.14MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 01:18:58 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-1194649,0]);
E;
f := P!Reverse([1093,0,-6558,-17488,44813]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
AssociatedEC(f);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 01:18:55 on modular [Seed = 4143451658] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 1194649*x over Rational Field 1093*x^4 - 6558*x^2 - 17488*x + 44813 2 Elliptic Curve defined by y^2 = x^3 - 13141139*x + 18280518998 over Rational Field function(p) ... end function [ [ 363, 677, 240, 98 ], [ 677, -363, -98, 240 ] ] Scheme over Rational Field defined by 2*r1^2 + 8*r1*r2 + 2*r1*r3 + 12*r1*r4 - 2*r2^2 - 12*r2*r3 + 2*r2*r4 - 3*r3^2 + 2*r3*r4 + 3*r4^2, 10*r1^2 + 8*r1*r2 - 14*r1*r4 - 10*r2^2 + 14*r2*r3 - 7*r3^2 - 6*r3*r4 + 7*r4^2 (12493251233560917444763441/6396350846877039790681 : 4115201667608471287859832462212724410/511562164051420879260293302467421 : 1) 56.56757198997087243697 Total time: 3.160 seconds, Total memory usage: 5.14MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 01:31:14 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-86136961,0]); E; f := P!Reverse([9220,-1256,-29325,6021,17714]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); AssociatedEC(f); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 01:31:05 on modular  [Seed = 2459725640]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 86136961*x over Rational Field
9220*x^4 - 1256*x^3 - 29325*x^2 + 6021*x + 17714
4
Point [ 1, 651, 203, 333 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 792, 614, 649 ] was singular mod 1009 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 947506571*x + 11192119890574 over Rational
Field
function(p) ... end function
[
[ 54718, 9697, 9656, 47325 ]
]
Scheme over Rational Field defined by
6*r1*r2 + 4*r1*r3 + 6*r1*r4 + 2*r2^2 - 10*r2*r3 + 10*r2*r4 + 4*r3^2 + 4*r3*r4 -
12*r4^2,
r1^2 + 2*r1*r2 + 12*r1*r4 + 14*r2^2 + 60*r2*r3 + 8*r2*r4 - 17*r3^2 - 28*r3*r4 -
14*r4^2
(464916295297535948456575213384430976907266/20760717328910931771338833728916958\
881 : -103798259228391787147444846238077318247412914488117919745309928/94593987\
473435887557725725537489331963816188715535004529 : 1)
86.42078597927957162028

Total time: 8.220 seconds, Total memory usage: 13.34MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 01:42:30 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-12909649,0]);
E;
f := P!Reverse([793,-1200,55242,268288,294113]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
AssociatedEC(f);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 01:42:09 on modular [Seed = 2879739353] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 12909649*x over Rational Field 793*x^4 - 1200*x^3 + 55242*x^2 + 268288*x + 294113 Errors: /bin/sh: line 1: 744 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 01:43:15 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12909649,0]); E; f := P!Reverse([8388,14504,-30000,-31804,45029]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); AssociatedEC(f); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 01:43:02 on modular  [Seed = 2946584970]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 12909649*x over Rational Field
8388*x^4 + 14504*x^3 - 30000*x^2 - 31804*x + 45029
4
Point [ 1, 101, 768, 195 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 648, 357, 813 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 961, 4, 442 ] was singular mod 1009 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 142006139*x + 649381163998 over Rational
Field
function(p) ... end function
[]
Scheme over Rational Field defined by
36*r1^2 + 972*r1*r2 + 18*r1*r3 + 466*r1*r4 - 62*r2^2 - 2730*r2*r3 - 932*r2*r4 -
270*r3^2 - 1040*r3*r4 + 418*r4^2,
513*r1^2 + 1292*r1*r2 - 2940*r1*r3 - 1638*r1*r4 + 3156*r2^2 - 2720*r2*r3 +
232*r2*r4 + 4111*r3^2 + 3628*r3*r4 - 1059*r4^2

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: Sch[FldRat] Total time: 12.820 seconds, Total memory usage: 13.21MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 01:43:59 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12909649,0]); E; f := P!Reverse([8388,14504,-30000,-31804,45029]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); AssociatedEC(f); pts; X,m := Scheme(F); X; m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 01:43:46 on modular  [Seed = 3015527778]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 12909649*x over Rational Field
8388*x^4 + 14504*x^3 - 30000*x^2 - 31804*x + 45029
4
Elliptic Curve defined by y^2 = x^3 - 142006139*x + 649381163998 over Rational
Field
function(p) ... end function
[
[ 2109, 91, 1020, -617 ]
]
Scheme over Rational Field defined by
r1^2 + 2*r1*r2 + 8*r1*r3 + 6*r1*r4 + 5*r2^2 - 2*r2*r3 - 6*r3^2 + 4*r3*r4 -
14*r4^2,
2*r1^2 - 20*r1*r2 - 14*r1*r3 + 18*r1*r4 - 16*r2^2 - 10*r2*r3 + 2*r2*r4 + 34*r3^2
- 36*r3*r4 - 22*r4^2
(1104533762113852915474155368471643361/265298938227535665511809167207569 :
-1559971862838569967784182011829716732072382086943980262/4321189058839152146944\
653582387198970216320258503 : 1)
74.57368860628511697541

Total time: 12.730 seconds, Total memory usage: 13.22MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 01:56:10 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-90878089,0]);
E;
f := P!Reverse([3385,2404,47328,622856,1236724]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
AssociatedEC(f);
pts;
X,m := Scheme(F);
X;
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 01:55:49 on modular [Seed = 1229441646] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 90878089*x over Rational Field 3385*x^4 + 2404*x^3 + 47328*x^2 + 622856*x + 1236724 Errors: /bin/sh: line 1: 779 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 01:58:15 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-20079361,0]); E; f := P!Reverse([4481,0,-26886,-71696,183721]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 01:58:12 on modular  [Seed = 1348391910]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 20079361*x over Rational Field
4481*x^4 - 26886*x^2 - 71696*x + 183721
4
[
[ 647, 667, -1084, 1896 ],
[ 667, -647, 1896, 1084 ]
]
Scheme over Rational Field defined by
5*r1^2 + 8*r1*r2 + 4*r1*r4 - 5*r2^2 + 4*r2*r3 + 9*r3^2 - 8*r3*r4 - 9*r4^2,
7*r1^2 + 48*r1*r2 + 10*r1*r3 + 4*r1*r4 - 7*r2^2 + 4*r2*r3 - 10*r2*r4 - 9*r3^2 +
12*r3*r4 + 9*r4^2
Elliptic Curve defined by y^2 = x^3 - 220872971*x + 1259658632974 over Rational
Field
function(p) ... end function
(3792123088425339496675254690657/467748293701950006348603361 :
435939456737112409968141094970027749204477150/101162212201636578429216892511168\
35682641 : 1)
69.14270247488934728608

Total time: 3.189 seconds, Total memory usage: 5.16MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:06:15 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-87928129,0]);
E;
f := P!Reverse([8697,-10232,-89838,14200,363337]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:05:54 on modular [Seed = 1668146915] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 87928129*x over Rational Field 8697*x^4 - 10232*x^3 - 89838*x^2 + 14200*x + 363337 4 Errors: /bin/sh: line 1: 801 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:07:06 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-87928129,0]); E; f := P!Reverse([8157,8456,-89862,-1768,391341]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:06:45 on modular  [Seed = 1734992592]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 87928129*x over Rational Field
8157*x^4 + 8456*x^3 - 89862*x^2 - 1768*x + 391341

Errors: /bin/sh: line 1:   805 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:07:46 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-87928129,0]);
E;
f := P!Reverse([182,356,-28179,-38348,946253]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 02:07:38 on modular [Seed = 1801842435] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 87928129*x over Rational Field 182*x^4 + 356*x^3 - 28179*x^2 - 38348*x + 946253 4 Point [ 1, 60, 439, 278 ] was singular mod 1009 and ignored at the #3 lift [ [ 35246, -43163, 6490, -6218 ] ] Scheme over Rational Field defined by 2*r1*r2 + 4*r1*r3 + 2*r1*r4 + 2*r2*r3 + 10*r2*r4 + 2*r3^2 - 6*r3*r4 + 3*r4^2, 4*r1^2 - 4*r1*r2 - 18*r1*r3 - 72*r1*r4 - 16*r2^2 - 10*r2*r3 + 12*r2*r4 + 24*r3^2 - 58*r3*r4 - 59*r4^2 Elliptic Curve defined by y^2 = x^3 - 967209419*x + 11543028918862 over Rational Field function(p) ... end function (174709728899281887734310230864935711047296382594/92647059278743824632475168414\ 41913505738969 : -2778817899455917816071047217050704070805713029663567855017663\ 330170036/28199892861079355579311364920252567327554396781057022348355488797 : 1) 98.95549085537733446926 Total time: 8.060 seconds, Total memory usage: 15.60MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:20:21 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-89151364,0]); E; f := P!Reverse([1900,2712,-26934,-21296,89618]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 02:20:10 on modular  [Seed = 118066783]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 89151364*x over Rational Field
1900*x^4 + 2712*x^3 - 26934*x^2 - 21296*x + 89618
4
Point [ 1, 579, 671, 937 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 683, 946, 966 ] was singular mod 1009 and ignored at the #3 lift
[
[ 16608, 2101, -2455, 12717 ]
]
Scheme over Rational Field defined by
r1^2 + 4*r1*r2 + 2*r1*r4 - 4*r2^2 - 10*r2*r3 + 6*r3^2 - 2*r3*r4 - 6*r4^2,
9*r1^2 - 8*r1*r2 + 24*r1*r3 + 22*r1*r4 + 4*r2^2 + 26*r2*r3 - 22*r2*r4 - 26*r3^2
- 26*r3*r4 - 36*r4^2
Elliptic Curve defined by y^2 = x^3 - 980665004*x + 11784740504432 over Rational
Field
function(p) ... end function
(3083400032219274655565695394372849041/142317592664591845261526841174724 :
1428429439776046803810634832246047487687032932345082535/16978052939113373649975\
91644926199654016880034632 : 1)
75.117418401880584610808

Total time: 10.439 seconds, Total memory usage: 11.94MB

'62.2.79'
************** MAGMA *****************
Host 62.2.79.21 (62.2.79.21)
Time: Tue Sep 21 02:24:33 2004

Input: 111112111112111112111112111112111113 / 7

Output: Magma V2.11-6     Tue Sep 21 2004 02:24:33 on modular  [Seed = 303864433]
-------------------------------------

15873158730301587444444587301730159

Total time: 0.180 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:26:31 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1, 0, 1, -13729605380, 619204181234842]);
E;
f := P!Reverse([1155354261148416,679447196288,-459316592,0,14]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:26:10 on modular [Seed = 437555930] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 - 13729605380*x + 619204181234842 over Rational Field 1155354261148416*x^4 + 679447196288*x^3 - 459316592*x^2 + 14 1 Point [ 1, 777, 9348, 2364 ] was singular mod 10007 and ignored at the #3 lift Point [ 1, 4596, 8699, 8644 ] was singular mod 10007 and ignored at the #3 lift Errors: /bin/sh: line 1: 856 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:28:54 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1, 0, 1, -13729605380, 619204181234842]); E; f := P!Reverse([1155354261148416,679447196288,-459316592,0,14]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:28:33 on modular  [Seed = 504403277]
-------------------------------------

Elliptic Curve defined by y^2 + x*y + y = x^3 - 13729605380*x + 619204181234842
over Rational Field
1155354261148416*x^4 + 679447196288*x^3 - 459316592*x^2 + 14
1

Errors: /bin/sh: line 1:   860 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:33:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-2797457224628171888320,41434984034248969847835907992832]);
E;
f := P!Reverse([31,0,354865035938,0,22442884545360804031]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:33:26 on modular [Seed = 623619921] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x^2 - 2797457224628171888320*x + 41434984034248969847835907992832 over Rational Field 31*x^4 + 354865035938*x^2 + 22442884545360804031 Errors: /bin/sh: line 1: 871 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:37:51 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-1,0,-2797457224628171888320,41434984034248969847835907992832]); E; f := P!Reverse([-31,0,128281283906,0,-86706625018142569375]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:37:30 on modular  [Seed = 757309509]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - x^2 - 2797457224628171888320*x +
41434984034248969847835907992832 over Rational Field
-31*x^4 + 128281283906*x^2 - 86706625018142569375
8
Point [ 1, 3901, 29789, 97008 ] was singular mod 100003 and ignored at the #1
lift

Errors: /bin/sh: line 1:   879 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:39:14 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-182788794244,0,-5099736335381814297600,0]);
E;
f := P!Reverse([-31,0,128281283906,0,-86706625018142569375]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:38:53 on modular [Seed = 993375748] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 182788794244*x^2 - 5099736335381814297600*x over Rational Field -31*x^4 + 128281283906*x^2 - 86706625018142569375 8 Point [ 1, 3901, 29789, 97008 ] was singular mod 100003 and ignored at the #1 lift Errors: /bin/sh: line 1: 889 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:39:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-182788794244,0,-5099736335381814297600,0]); E; f := P!Reverse([-1881980649,3355444026,47587281419,45143152780,-54654792100]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:39:26 on modular  [Seed = 1060221667]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 182788794244*x^2 -
5099736335381814297600*x over Rational Field
-1881980649*x^4 + 3355444026*x^3 + 47587281419*x^2 + 45143152780*x - 54654792100

Errors: /bin/sh: line 1:   893 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:40:32 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-182788794244,0,-5099736335381814297600,0]);
E;
f := P!Reverse([31,62,32070321023,32070320992,5419164071651490832]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:40:11 on modular [Seed = 3285012042] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 182788794244*x^2 - 5099736335381814297600*x over Rational Field 31*x^4 + 62*x^3 + 32070321023*x^2 + 32070320992*x + 5419164071651490832 8 Errors: /bin/sh: line 1: 897 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:41:14 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-182788794244,0,-5099736335381814297600,0]); E; f := P!Reverse([2962028449,-5489026228,107910669368,-197375874824,1134257725156]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:40:53 on modular  [Seed = 3351857776]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 182788794244*x^2 -
5099736335381814297600*x over Rational Field
2962028449*x^4 - 5489026228*x^3 + 107910669368*x^2 - 197375874824*x +
1134257725156

Errors: /bin/sh: line 1:   901 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:41:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-182788794244,0,-5099736335381814297600,0]);
E;
f := P!Reverse([-227695,0,128281283906,0,-11804850240727375]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:41:26 on modular [Seed = 3468706458] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 182788794244*x^2 - 5099736335381814297600*x over Rational Field -227695*x^4 + 128281283906*x^2 - 11804850240727375 8 Errors: /bin/sh: line 1: 908 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:42:28 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-182788794244,0,-5099736335381814297600,0]); E; f := P!Reverse([-6273253089,6835831362,29581838507,-13671662724,-25093012356]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:42:07 on modular  [Seed = 3521076652]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 182788794244*x^2 -
5099736335381814297600*x over Rational Field
-6273253089*x^4 + 6835831362*x^3 + 29581838507*x^2 - 13671662724*x - 25093012356

Errors: /bin/sh: line 1:   915 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:43:01 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-182788794244,0,-5099736335381814297600,0]);
E;
f := P!Reverse([227695,455390,32070662519,32070434824,737811157639936]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:42:40 on modular [Seed = 3587922423] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 182788794244*x^2 - 5099736335381814297600*x over Rational Field 227695*x^4 + 455390*x^3 + 32070662519*x^2 + 32070434824*x + 737811157639936 Errors: /bin/sh: line 1: 919 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:43:41 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-182788794244,0,-5099736335381814297600,0]); E; f := P!Reverse([173736649,-268874544,124116920546,-383114961840,16123527628825]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:43:20 on modular  [Seed = 3654767891]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 182788794244*x^2 -
5099736335381814297600*x over Rational Field
173736649*x^4 - 268874544*x^3 + 124116920546*x^2 - 383114961840*x +
16123527628825

Errors: /bin/sh: line 1:   923 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:45:09 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]);
E;
f := P!Reverse([23,0,224741094914,0,519535132904052734375]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:44:48 on modular [Seed = 3790564675] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 54326190625369714087362857318400 over Rational Field 23*x^4 + 224741094914*x^2 + 519535132904052734375 Errors: /bin/sh: line 1: 931 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:45:40 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]); E; f := P!Reverse([-23,0,224741094914,0,-519535132904052734375]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:45:19 on modular  [Seed = 3857410392]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x -
54326190625369714087362857318400 over Rational Field
-23*x^4 + 224741094914*x^2 - 519535132904052734375

Errors: /bin/sh: line 1:   935 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:46:05 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]);
E;
f := P!Reverse([1154,0,-449482189828,0,2349503913319501824]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 02:45:51 on modular [Seed = 3924256436] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 54326190625369714087362857318400 over Rational Field 1154*x^4 - 449482189828*x^2 + 2349503913319501824 FourDescent( f: 1154*x^4 - 449482189828*x^2 + 2349503913319501824 ) Minimise( F: [ [894427314314045676083756344157798673842756337098647602659... ) MinimiseFDAtPrime( fd_in: [ [249307363221858595083957493413382261558150641260171807899..., prime: 577 ) MinimiseFDOnceAtPrime( fd_in: [ [483683963422406890721862522749025488369951841921058894738..., prime: 577 ) BoxMinimiseK1( fd_in: [ [483683963422406890721862522749025488369951841921058894738..., prime: 577 ) Extend3ToUnimodular( cc: [ ( 1 29 0 220), ( 0 1 0 412), ( 0 1 0 279) ] ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/utils.m", line 342, column 21: >> assert "Could not extend three rows to unimodular matri ^ Runtime error in assert: Logical expected >> #S; ^ User error: Identifier 'S' has not been declared or assigned >> F := S; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,100000); ^ User error: Identifier 'F' has not been declared or assigned >> pts; ^ User error: Identifier 'pts' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned >> X; ^ User error: Identifier 'X' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 54326190625369714087362857318400 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 13.449 seconds, Total memory usage: 15.66MB

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:49:07 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]);
E;
f := P!Reverse([6719013049,6546509920,-911029068478,4654759798880,-6250750633271]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:48:46 on modular [Seed = 4043210620] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 54326190625369714087362857318400 over Rational Field 6719013049*x^4 + 6546509920*x^3 - 911029068478*x^2 + 4654759798880*x - 6250750633271 Errors: /bin/sh: line 1: 946 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:49:50 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]); E; f := P!Reverse([-3707977031,-6234701952,387263549378,-143398144896,-1961519849399]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:49:29 on modular  [Seed = 4126898766]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x -
54326190625369714087362857318400 over Rational Field
-3707977031*x^4 - 6234701952*x^3 + 387263549378*x^2 - 143398144896*x -
1961519849399

Errors: /bin/sh: line 1:   951 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:50:29 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]);
E;
f := P!Reverse([3841494831,-3490747694,91683402539,-115091480500,161830562500]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:50:08 on modular [Seed = 4193744795] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 54326190625369714087362857318400 over Rational Field 3841494831*x^4 - 3490747694*x^3 + 91683402539*x^2 - 115091480500*x + 161830562500 Errors: /bin/sh: line 1: 955 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:51:09 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]); E; f := P!Reverse([44754796,-16997116,19297047419,-381991492330,26640976821775]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:50:48 on modular  [Seed = 2156793482]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x -
54326190625369714087362857318400 over Rational Field
44754796*x^4 - 16997116*x^3 + 19297047419*x^2 - 381991492330*x + 26640976821775

Errors: /bin/sh: line 1:   962 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:51:42 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]);
E;
f := P!Reverse([-176997025,304866430,67686479711,162409955616,-3618632630016]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:51:21 on modular [Seed = 2223639215] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 54326190625369714087362857318400 over Rational Field -176997025*x^4 + 304866430*x^3 + 67686479711*x^2 + 162409955616*x - 3618632630016 Errors: /bin/sh: line 1: 966 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:52:22 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]); E; f := P!Reverse([191805121,80068608,216589109762,-46199586816,63857487129409]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:52:01 on modular  [Seed = 2290484827]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x -
54326190625369714087362857318400 over Rational Field
191805121*x^4 + 80068608*x^3 + 216589109762*x^2 - 46199586816*x + 63857487129409

Errors: /bin/sh: line 1:   970 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:53:01 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]);
E;
f := P!Reverse([-8236775,2211840,224756992514,29353328640,-1450656208642775]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:52:40 on modular [Seed = 2357330550] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x - 54326190625369714087362857318400 over Rational Field -8236775*x^4 + 2211840*x^3 + 224756992514*x^2 + 29353328640*x - 1450656208642775 Errors: /bin/sh: line 1: 974 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:53:34 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-1,0,-4886878524254639331840,-54326190625369714087362857318400]); E; f := P!Reverse([8351975,-15598030,53906888411,-57568531956,91949381987004]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:53:13 on modular  [Seed = 2526550029]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - x^2 - 4886878524254639331840*x -
54326190625369714087362857318400 over Rational Field
8351975*x^4 - 15598030*x^3 + 53906888411*x^2 - 57568531956*x + 91949381987004

Errors: /bin/sh: line 1:   980 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:55:46 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-143733606079,0,-8905879752250573440000,0]);
E;
f := P!Reverse([-46,0,141996678977,0,-49300601327405203456]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:55:25 on modular [Seed = 2677083776] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 143733606079*x^2 - 8905879752250573440000*x over Rational Field -46*x^4 + 141996678977*x^2 - 49300601327405203456 Errors: /bin/sh: line 1: 989 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:56:31 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-143733606079,0,-8905879752250573440000,0]); E; f := P!Reverse([-24943339711,36961554126,124482871721,-71660335800,-79964470000]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:56:10 on modular  [Seed = 2746036843]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 143733606079*x^2 -
8905879752250573440000*x over Rational Field
-24943339711*x^4 + 36961554126*x^3 + 124482871721*x^2 - 71660335800*x -
79964470000

Errors: /bin/sh: line 1:   993 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:57:16 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-143733606079,0,-8905879752250573440000,0]);
E;
f := P!Reverse([46,0,141996678977,0,49300601327405203456]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:56:55 on modular [Seed = 2862889823] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 143733606079*x^2 - 8905879752250573440000*x over Rational Field 46*x^4 + 141996678977*x^2 + 49300601327405203456 Errors: /bin/sh: line 1: 1000 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:57:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-143733606079,0,-8905879752250573440000,0]); E; f := P!Reverse([30697793296,44034923192,148574801321,40775072050,83309730625]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:57:26 on modular  [Seed = 2929737530]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 143733606079*x^2 -
8905879752250573440000*x over Rational Field
30697793296*x^4 + 44034923192*x^3 + 148574801321*x^2 + 40775072050*x +
83309730625

Errors: /bin/sh: line 1:  1004 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:58:24 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-143733606079,0,-8905879752250573440000,0]);
E;
f := P!Reverse([-1186,0,141996678977,0,-1912164975599190016]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:58:03 on modular [Seed = 2998674187] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 143733606079*x^2 - 8905879752250573440000*x over Rational Field -1186*x^4 + 141996678977*x^2 - 1912164975599190016 Errors: /bin/sh: line 1: 1008 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:58:52 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-143733606079,0,-8905879752250573440000,0]); E; f := P!Reverse([1186,0,141996678977,0,1912164975599190016]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:58:31 on modular  [Seed = 3065521891]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 143733606079*x^2 -
8905879752250573440000*x over Rational Field
1186*x^4 + 141996678977*x^2 + 1912164975599190016

Errors: /bin/sh: line 1:  1012 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 02:59:22 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-143733606079,0,-8905879752250573440000,0]);
E;
f := P!Reverse([1128268361,-2230276326,-216047822767,538611539568,-214445926336]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 02:59:01 on modular [Seed = 3149212620] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 143733606079*x^2 - 8905879752250573440000*x over Rational Field 1128268361*x^4 - 2230276326*x^3 - 216047822767*x^2 + 538611539568*x - 214445926336 Errors: /bin/sh: line 1: 1017 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 02:59:59 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-143733606079,0,-8905879752250573440000,0]); E; f := P!Reverse([32027447104,41651774448,96713645393,82342066794,125706083161]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 02:59:38 on modular  [Seed = 1162597722]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 143733606079*x^2 -
8905879752250573440000*x over Rational Field
32027447104*x^4 + 41651774448*x^3 + 96713645393*x^2 + 82342066794*x +
125706083161

Errors: /bin/sh: line 1:  1024 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:02:15 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]);
E;
f := P!Reverse([-35,0,694431269681,0,-3116712510011660000000]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:01:54 on modular [Seed = 1095750118] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x - 2768741657274986655818438351454705 over Rational Field -35*x^4 + 694431269681*x^2 - 3116712510011660000000 Errors: /bin/sh: line 1: 1028 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:02:51 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]); E; f := P!Reverse([35,0,694431269681,0,3116712510011660000000]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:02:30 on modular  [Seed = 1312873741]
-------------------------------------

Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x
- 2768741657274986655818438351454705 over Rational Field
35*x^4 + 694431269681*x^2 + 3116712510011660000000

Errors: /bin/sh: line 1:  1035 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:03:23 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]);
E;
f := P!Reverse([-34078626,57293976,805462547381,17627959823550,-2801154735041625]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:03:02 on modular [Seed = 1246026025] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x - 2768741657274986655818438351454705 over Rational Field -34078626*x^4 + 57293976*x^3 + 805462547381*x^2 + 17627959823550*x - 2801154735041625 Errors: /bin/sh: line 1: 1039 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:04:07 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]); E; f := P!Reverse([68045167801,-118095562078,770977642241,-636409249280,1741880782600]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:03:46 on modular  [Seed = 1448658241]
-------------------------------------

Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x
- 2768741657274986655818438351454705 over Rational Field
68045167801*x^4 - 118095562078*x^3 + 770977642241*x^2 - 636409249280*x +
1741880782600

Errors: /bin/sh: line 1:  1043 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:04:39 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]);
E;
f := P!Reverse([-4105,0,694431269681,0,-26573675481220000000]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:04:18 on modular [Seed = 1565773418] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x - 2768741657274986655818438351454705 over Rational Field -4105*x^4 + 694431269681*x^2 - 26573675481220000000 Errors: /bin/sh: line 1: 1048 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:05:07 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]); E; f := P!Reverse([4105,0,694431269681,0,26573675481220000000]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:04:46 on modular  [Seed = 1498925714]
-------------------------------------

Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x
- 2768741657274986655818438351454705 over Rational Field
4105*x^4 + 694431269681*x^2 + 26573675481220000000

Errors: /bin/sh: line 1:  1052 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:05:39 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]);
E;
f := P!Reverse([12406234,-16792648,-4187008500307,1269502711400206,-106154568982753469]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:05:18 on modular [Seed = 1701574286] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x - 2768741657274986655818438351454705 over Rational Field 12406234*x^4 - 16792648*x^3 - 4187008500307*x^2 + 1269502711400206*x - 106154568982753469 Errors: /bin/sh: line 1: 1056 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:06:17 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]); E; f := P!Reverse([13938655761,-9242852286,663121253573,-376068336532,8142536011484]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:05:56 on modular  [Seed = 1651306995]
-------------------------------------

Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x
- 2768741657274986655818438351454705 over Rational Field
13938655761*x^4 - 9242852286*x^3 + 663121253573*x^2 - 376068336532*x +
8142536011484

Errors: /bin/sh: line 1:  1063 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:06:48 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]);
E;
f := P!Reverse([-5747,0,694431269681,0,-18981196772300000000]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:06:27 on modular [Seed = 1851850200] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x - 2768741657274986655818438351454705 over Rational Field -5747*x^4 + 694431269681*x^2 - 18981196772300000000 Errors: /bin/sh: line 1: 1067 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:07:17 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]); E; f := P!Reverse([5747,0,694431269681,0,18981196772300000000]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:06:56 on modular  [Seed = 1785002047]
-------------------------------------

Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x
- 2768741657274986655818438351454705 over Rational Field
5747*x^4 + 694431269681*x^2 + 18981196772300000000

Errors: /bin/sh: line 1:  1071 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:07:55 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]);
E;
f := P!Reverse([-184041,-227370,1015778068865,673824008626948,-343668591615468718]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:07:34 on modular [Seed = 1987634181] ------------------------------------- Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x - 2768741657274986655818438351454705 over Rational Field -184041*x^4 - 227370*x^3 + 1015778068865*x^2 + 673824008626948*x - 343668591615468718 Errors: /bin/sh: line 1: 1075 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:08:36 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,1,1,-37317792552409644788370,-2768741657274986655818438351454705]); E; f := P!Reverse([1070703286,990170228,683948465201,-175943019590,102965492879275]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:08:15 on modular  [Seed = 2087906918]
-------------------------------------

Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 37317792552409644788370*x
- 2768741657274986655818438351454705 over Rational Field
1070703286*x^4 + 990170228*x^3 + 683948465201*x^2 - 175943019590*x +
102965492879275

Errors: /bin/sh: line 1:  1081 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:10:13 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]);
E;
f := P!Reverse([-70232382351,105981528468,10965855732728,-6404632755256,-398839791615964]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:09:52 on modular [Seed = 51220870] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 - 7855839241258755277440000*x over Rational Field -70232382351*x^4 + 105981528468*x^3 + 10965855732728*x^2 - 6404632755256*x - 398839791615964 Errors: /bin/sh: line 1: 1094 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:10:51 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]); E; f := P!Reverse([-138021142871,-224213914128,11180513726498,13735078402416,-195731643087239]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:10:30 on modular  [Seed = 251764140]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 -
7855839241258755277440000*x over Rational Field
-138021142871*x^4 - 224213914128*x^3 + 11180513726498*x^2 + 13735078402416*x -
195731643087239

Errors: /bin/sh: line 1:  1098 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:11:27 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]);
E;
f := P!Reverse([31471441156,38411764156,2707809849299,1054139726630,56772995556775]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:11:06 on modular [Seed = 184917572] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 - 7855839241258755277440000*x over Rational Field 31471441156*x^4 + 38411764156*x^3 + 2707809849299*x^2 + 1054139726630*x + 56772995556775 Errors: /bin/sh: line 1: 1102 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:11:59 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]); E; f := P!Reverse([617830808975,-1102522104790,3408355865699,-2737953923292,3519109388844]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:11:38 on modular  [Seed = 270435711]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 -
7855839241258755277440000*x over Rational Field
617830808975*x^4 - 1102522104790*x^3 + 3408355865699*x^2 - 2737953923292*x +
3519109388844

Errors: /bin/sh: line 1:  1109 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:12:27 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]);
E;
f := P!Reverse([617830808975,-1102522104790,3408355865699,-2737953923292,3519109388844]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:12:06 on modular [Seed = 470976799] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 - 7855839241258755277440000*x over Rational Field 617830808975*x^4 - 1102522104790*x^3 + 3408355865699*x^2 - 2737953923292*x + 3519109388844 Errors: /bin/sh: line 1: 1113 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:12:59 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]); E; f := P!Reverse([-264980360025,-242525786610,2870835440759,2159645494376,-5924492746864]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:12:38 on modular  [Seed = 404131131]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 -
7855839241258755277440000*x over Rational Field
-264980360025*x^4 - 242525786610*x^3 + 2870835440759*x^2 + 2159645494376*x -
5924492746864

Errors: /bin/sh: line 1:  1117 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:13:44 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]);
E;
f := P!Reverse([-47009,94018,2745457789727,-2745457836736,-37428926194450397936]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:13:23 on modular [Seed = 556774647] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 - 7855839241258755277440000*x over Rational Field -47009*x^4 + 94018*x^3 + 2745457789727*x^2 - 2745457836736*x - 37428926194450397936 Errors: /bin/sh: line 1: 1124 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:14:21 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]); E; f := P!Reverse([2658776453281,711985966276,11052106237448,1423971932552,10635105813124]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:14:00 on modular  [Seed = 740473297]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 -
7855839241258755277440000*x over Rational Field
2658776453281*x^4 + 711985966276*x^3 + 11052106237448*x^2 + 1423971932552*x +
10635105813124

Errors: /bin/sh: line 1:  1129 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:14:53 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-20853211201924,0,-7855839241258755277440000,0]);
E;
f := P!Reverse([47009,0,10981831440962,0,598862830093037760929]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:14:32 on modular [Seed = 893100200] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 20853211201924*x^2 - 7855839241258755277440000*x over Rational Field 47009*x^4 + 10981831440962*x^2 + 598862830093037760929 Errors: /bin/sh: line 1: 1136 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:16:31 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-4245695279,0,-553320238017600,0]); E; f := P!Reverse([-15,0,548403121,0,-4591650240000000]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:16:10 on modular  [Seed = 826254670]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 4245695279*x^2 - 553320238017600*x over
Rational Field
-15*x^4 + 548403121*x^2 - 4591650240000000

Errors: /bin/sh: line 1:  1140 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:17:03 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-4245695279,0,-553320238017600,0]);
E;
f := P!Reverse([15,0,548403121,0,4591650240000000]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:16:42 on modular [Seed = 1026795810] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 4245695279*x^2 - 553320238017600*x over Rational Field 15*x^4 + 548403121*x^2 + 4591650240000000 Errors: /bin/sh: line 1: 1144 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:17:38 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-4245695279,0,-553320238017600,0]); E; f := P!Reverse([-28931,-43100,628733377,13151207100,-2103386551596]); f; S := FourDescent(f); #S; F := S; pts := Points(F,100000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:17:17 on modular  [Seed = 3301593340]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 4245695279*x^2 - 553320238017600*x over
Rational Field
-28931*x^4 - 43100*x^3 + 628733377*x^2 + 13151207100*x - 2103386551596
4

Errors: /bin/sh: line 1:  1153 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:18:51 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-548094724,0,-1071171346271846400,0]);
E;
f := P!Reverse([-18335,0,1468938626,0,-6163717745375]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,100000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:18:30 on modular [Seed = 3452131662] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 548094724*x^2 - 1071171346271846400*x over Rational Field -18335*x^4 + 1468938626*x^2 - 6163717745375 4 Point [ 1, 4117, 2892, 74510 ] was singular mod 100003 and ignored at the #1 lift Errors: /bin/sh: line 1: 1160 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:19:18 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-548094724,0,-1071171346271846400,0]); E; f := P!Reverse([-18335,0,1468938626,0,-6163717745375]); f; S := FourDescent(f); #S; F := S; pts := Points(F,10000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:18:57 on modular  [Seed = 3368442988]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 548094724*x^2 - 1071171346271846400*x over
Rational Field
-18335*x^4 + 1468938626*x^2 - 6163717745375
4

Errors: /bin/sh: line 1:  1165 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:19:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-548094724,0,-1071171346271846400,0]);
E;
f := P!Reverse([-5091984,4931208,2531926967,29151691254,94262126679]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:19:25 on modular [Seed = 3571073135] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 548094724*x^2 - 1071171346271846400*x over Rational Field -5091984*x^4 + 4931208*x^3 + 2531926967*x^2 + 29151691254*x + 94262126679 Errors: /bin/sh: line 1: 1169 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:20:20 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-548094724,0,-1071171346271846400,0]); E; f := P!Reverse([18335,36670,367262159,367243824,385324168896]); f; S := FourDescent(f); #S; F := S; pts := Points(F,10000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:19:59 on modular  [Seed = 3504228234]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 548094724*x^2 - 1071171346271846400*x over
Rational Field
18335*x^4 + 36670*x^3 + 367262159*x^2 + 367243824*x + 385324168896

Errors: /bin/sh: line 1:  1173 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:20:55 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-548094724,0,-1071171346271846400,0]);
E;
f := P!Reverse([7012657,-5662596,1421374184,-3320017608,18419279236]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:20:34 on modular [Seed = 3654766302] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 548094724*x^2 - 1071171346271846400*x over Rational Field 7012657*x^4 - 5662596*x^3 + 1421374184*x^2 - 3320017608*x + 18419279236 Errors: /bin/sh: line 1: 1180 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:21:55 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-36741577919,0,-35339220302400000000,0]); E; f := P!Reverse([-674,0,19777624897,0,-131652665964232704]); f; S := FourDescent(f); #S; F := S; pts := Points(F,10000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:21:34 on modular  [Seed = 3857412830]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 36741577919*x^2 - 35339220302400000000*x
over Rational Field
-674*x^4 + 19777624897*x^2 - 131652665964232704
4

Errors: /bin/sh: line 1:  1184 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:22:27 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-36741577919,0,-35339220302400000000,0]);
E;
f := P!Reverse([-8929799,-2591330,23523434797,202161250620,-8408528425404]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:22:06 on modular [Seed = 3790566970] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 36741577919*x^2 - 35339220302400000000*x over Rational Field -8929799*x^4 - 2591330*x^3 + 23523434797*x^2 + 202161250620*x - 8408528425404 Errors: /bin/sh: line 1: 1188 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:23:01 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-36741577919,0,-35339220302400000000,0]); E; f := P!Reverse([674,0,19777624897,0,131652665964232704]); f; S := FourDescent(f); #S; F := S; pts := Points(F,10000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:22:40 on modular  [Seed = 3991108200]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 36741577919*x^2 - 35339220302400000000*x
over Rational Field
674*x^4 + 19777624897*x^2 + 131652665964232704
4

Errors: /bin/sh: line 1:  1192 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:23:42 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-36741577919,0,-35339220302400000000,0]);
E;
f := P!Reverse([154609561,224185834,19683163633,8874208848,579148473024]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:23:21 on modular [Seed = 3957685319] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 36741577919*x^2 - 35339220302400000000*x over Rational Field 154609561*x^4 + 224185834*x^3 + 19683163633*x^2 + 8874208848*x + 579148473024 Errors: /bin/sh: line 1: 1198 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:24:31 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-36741577919,0,-35339220302400000000,0]); E; f := P!Reverse([674,0,76296827713,0,2158874733027723264]); f; S := FourDescent(f); #S; F := S; pts := Points(F,10000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:24:10 on modular  [Seed = 4093470124]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 36741577919*x^2 - 35339220302400000000*x
over Rational Field
674*x^4 + 76296827713*x^2 + 2158874733027723264

Errors: /bin/sh: line 1:  1206 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.132.174 (66.63.132.174)
Time: Tue Sep 21 03:25:08 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-36741577919,0,-35339220302400000000,0]);
E;
f := P!Reverse([393026,0,76296827713,0,3702252700993536]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 03:24:47 on modular [Seed = 4277168260] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 36741577919*x^2 - 35339220302400000000*x over Rational Field 393026*x^4 + 76296827713*x^2 + 3702252700993536 Errors: /bin/sh: line 1: 1211 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.132.174 (66.63.132.174) Time: Tue Sep 21 03:26:46 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,24479776636,0,-163775781014077440000,0]); E; f := P!Reverse([1479,0,32682680386,0,1263759858984375]); f; S := FourDescent(f); #S; F := S; pts := Points(F,10000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 03:26:25 on modular  [Seed = 4210322462]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 + 24479776636*x^2 - 163775781014077440000*x
over Rational Field
1479*x^4 + 32682680386*x^2 + 1263759858984375

Errors: /bin/sh: line 1:  1215 Killed                  nice -n 19 /usr/local/bin/magma

'196.11.'
************** MAGMA *****************
Host 196.11.235.1 (196.11.235.1)
Time: Tue Sep 21 04:54:35 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Tue Sep 21 2004 04:54:34 on modular  [Seed = 151495687]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

'194.95.'
************** MAGMA *****************
Host 194.95.179.177 (194.95.179.177)
Time: Tue Sep 21 08:14:40 2004

Input: 2^10;

Output: Magma V2.11-6     Tue Sep 21 2004 08:14:40 on modular  [Seed = 2626537185]
-------------------------------------

1024

Total time: 0.190 seconds, Total memory usage: 3.51MB

'24.225.'
************** MAGMA *****************
Host 24.225.143.141 (24.225.143.141)
Time: Tue Sep 21 09:41:23 2004

Input: sqrt(68.0);

Output: Magma V2.11-6     Tue Sep 21 2004 09:41:23 on modular  [Seed = 1297884033]
-------------------------------------

>> sqrt(68.0);
^
User error: Identifier 'sqrt' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'24.225.'
************** MAGMA *****************
Host 24.225.143.141 (24.225.143.141)
Time: Tue Sep 21 09:41:37 2004

Input: Sqrt(68.0);

Output: Magma V2.11-6     Tue Sep 21 2004 09:41:37 on modular  [Seed = 1213802134]
-------------------------------------

8.2462112512353210996428197119481540502758

Total time: 0.180 seconds, Total memory usage: 3.51MB

'24.225.'
************** MAGMA *****************
Host 24.225.143.141 (24.225.143.141)
Time: Tue Sep 21 09:42:31 2004

Input: 16486*6;

Output: Magma V2.11-6     Tue Sep 21 2004 09:42:31 on modular  [Seed = 1565275093]
-------------------------------------

98916

Total time: 0.190 seconds, Total memory usage: 3.51MB

'24.225.'
************** MAGMA *****************
Host 24.225.143.141 (24.225.143.141)
Time: Tue Sep 21 09:43:00 2004

Input: 16486*6-102400;

Output: Magma V2.11-6     Tue Sep 21 2004 09:43:00 on modular  [Seed = 1380138233]
-------------------------------------

-3484

Total time: 0.190 seconds, Total memory usage: 3.51MB

'24.225.'
************** MAGMA *****************
Host 24.225.143.141 (24.225.143.141)
Time: Tue Sep 21 09:43:14 2004

Input: Sqrt(68.0);

Output: Magma V2.11-6     Tue Sep 21 2004 09:43:14 on modular  [Seed = 1836843984]
-------------------------------------

8.2462112512353210996428197119481540502758

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Tue Sep 21 09:59:47 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+2);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-2)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Tue Sep 21 2004 09:59:47 on modular  [Seed = 152599445]
-------------------------------------

Abelian Group isomorphic to Z/24
Defined on 1 generator
Relations:
24*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/24 Defined on 1 generator Relations: 24*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/24
Defined on 1 generator
Relations:
24*$.1 = 0 given by a rule Total time: 0.490 seconds, Total memory usage: 13.88MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Tue Sep 21 10:00:24 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+x+2); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-2)*O); I := L; pl := Place(I); // SClassGroup({pl}) ClassGroup(F) Output: Magma V2.11-6 Tue Sep 21 2004 10:00:23 on modular [Seed = 68515516] ------------------------------------- Abelian Group isomorphic to Z/12 + Z Defined on 2 generators Relations: 12*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
12*$.1 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/12 + Z Defined on 2 generators Relations: 12*$.1 = 0 given by a rule

Total time: 0.490 seconds, Total memory usage: 13.88MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:35:00 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-6410,0,10272021,0]);
E;
f := P!Reverse([1077,-264,-6398,792,9501]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 11:34:38 on modular [Seed = 4125425333] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 6410*x^2 + 10272021*x over Rational Field 1077*x^4 - 264*x^3 - 6398*x^2 + 792*x + 9501 Errors: /bin/sh: line 1: 4027 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:36:42 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-6672,0,11128892,0]); E; f := P!Reverse([17,-4,-6342,-5356,676009]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:36:36 on modular  [Seed = 2375845447]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 6672*x^2 + 11128892*x over Rational Field
17*x^4 - 4*x^3 - 6342*x^2 - 5356*x + 676009
4
Point [ 1, 599, 620, 936 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 647, 797, 780 ] was singular mod 1009 and ignored at the #1 lift
[
[ 14, -22, 77, -207 ],
[ 22, 14, 207, 77 ]
]
Scheme over Rational Field defined by
2*r1*r2 + 2*r1*r3 + 2*r1*r4 + 2*r2*r3 - 2*r2*r4 + 3*r3^2 - 8*r3*r4 - 3*r4^2,
4*r1^2 + 40*r1*r2 - 6*r1*r3 + 6*r1*r4 - 4*r2^2 + 6*r2*r3 + 6*r2*r4 - 4*r3^2 +
8*r3*r4 + 4*r4^2
Elliptic Curve defined by y^2 = x^3 - 3709636*x + 2750064960 over Rational Field
function(p) ... end function
(117710185225138274114475026/116085551162147592355201 :
220527366186512645777998795746830950440/39551890940284904040403230813172801 : 1)
57.91715885335179336834

Total time: 5.809 seconds, Total memory usage: 5.42MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:39:44 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-6410,0,10272021,0]);
E;
f := P!Reverse([1077,-264,-6398,792,9501]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 11:39:23 on modular [Seed = 2609549822] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 6410*x^2 + 10272021*x over Rational Field 1077*x^4 - 264*x^3 - 6398*x^2 + 792*x + 9501 Errors: /bin/sh: line 1: 4053 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:40:31 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-6410,0,10272021,0]); E; f := P!Reverse([1069,0,-6398,0,9621]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 11:40:10 on modular  [Seed = 2542181763]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 6410*x^2 + 10272021*x over Rational Field
1069*x^4 - 6398*x^2 + 9621

Errors: /bin/sh: line 1:  4057 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:41:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-6410,0,10272021,0]);
E;
f := P!Reverse([5,4,-1925,4874,110415]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:40:47 on modular [Seed = 2474809762] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 6410*x^2 + 10272021*x over Rational Field 5*x^4 + 4*x^3 - 1925*x^2 + 4874*x + 110415 4 Point [ 1, 353, 145, 945 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 478, 728, 278 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 531, 281, 278 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 656, 864, 945 ] was singular mod 1009 and ignored at the #1 lift [] Scheme over Rational Field defined by 2*r1^2 + 6*r1*r4 - 3*r2^2 - 4*r2*r3 - 3*r3^2 + 5*r4^2, 3*r1^2 - 4*r1*r4 - 6*r2^2 + 18*r2*r3 - 15*r3^2 + 3*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 3424012*x + 2437504940 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.490 seconds, Total memory usage: 12.30MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:41:40 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-6410,0,10272021,0]);
E;
f := P!Reverse([5,4,-1925,4874,110415]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:41:20 on modular [Seed = 2948506945] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 6410*x^2 + 10272021*x over Rational Field 5*x^4 + 4*x^3 - 1925*x^2 + 4874*x + 110415 4 [] Scheme over Rational Field defined by 2*r1*r2 + 2*r1*r3 + 4*r1*r4 + 4*r2*r3 - 6*r2*r4 + 3*r3^2 + 6*r3*r4 - 11*r4^2, 2*r1^2 - 6*r1*r3 + 2*r1*r4 - 11*r2^2 + 6*r2*r3 + 6*r2*r4 + 3*r3^2 - 6*r3*r4 + 2*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 3424012*x + 2437504940 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.550 seconds, Total memory usage: 12.30MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:42:08 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-6410,0,10272021,0]);
E;
f := P!Reverse([5,4,-1925,4874,110415]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:41:54 on modular [Seed = 2881134887] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 6410*x^2 + 10272021*x over Rational Field 5*x^4 + 4*x^3 - 1925*x^2 + 4874*x + 110415 4 Point [ 1, 239, 1007, 966 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 278, 3, 236 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 330, 156, 826 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 679, 853, 826 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 731, 1006, 236 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 770, 2, 966 ] was singular mod 1009 and ignored at the #3 lift [] Scheme over Rational Field defined by r1^2 + 6*r1*r4 - 2*r2^2 - 6*r2*r3 - 5*r3^2 + 14*r4^2, r1^2 - 20*r1*r4 - r2^2 + 10*r2*r3 + 2*r3^2 + 15*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 3424012*x + 2437504940 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.490 seconds, Total memory usage: 12.30MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:42:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-6410,0,10272021,0]);
E;
f := P!Reverse([3,6,-1595,-1598,213868]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:42:39 on modular [Seed = 2813766918] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 6410*x^2 + 10272021*x over Rational Field 3*x^4 + 6*x^3 - 1595*x^2 - 1598*x + 213868 4 Point [ 1, 768, 646, 432 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 883, 247, 105 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 915, 20, 94 ] was singular mod 1009 and ignored at the #1 lift [] Scheme over Rational Field defined by 2*r1*r2 + r2^2 + 2*r2*r3 + r3^2 - 2*r3*r4 - 2*r4^2, 8*r1^2 + 2*r1*r2 + 22*r1*r3 + 16*r1*r4 + 23*r2^2 - 20*r2*r3 - 24*r2*r4 - 24*r3^2 - 12*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 3424012*x + 2437504940 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 8.169 seconds, Total memory usage: 18.73MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:43:27 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-6410,0,10272021,0]);
E;
f := P!Reverse([3,6,-1595,-1598,213868]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:43:20 on modular [Seed = 2746396405] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 6410*x^2 + 10272021*x over Rational Field 3*x^4 + 6*x^3 - 1595*x^2 - 1598*x + 213868 4 Point [ 1, 678, 252, 74 ] was singular mod 1009 and ignored at the #1 lift [ [ 41929, 24772, 33454, 32642 ] ] Scheme over Rational Field defined by 2*r1*r2 + r3^2 - 3*r4^2, 12*r1^2 - 10*r1*r2 + 2*r1*r3 + 24*r1*r4 + 16*r2^2 + 6*r2*r3 - 32*r2*r4 - 24*r3^2 + 4*r3*r4 - 12*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 3424012*x + 2437504940 over Rational Field function(p) ... end function (2522091452183958202641769119486436587097050469185406037/2366142904865156533474\ 727572778287423968857954934724 : 3989121267054070810300715086142123393383964478\ 417137158371149960113177811358135/115096324730196553928988919038574012817493975\ 586616976247781434778216407554632 : 1) 118.44173944480678528634 Total time: 6.940 seconds, Total memory usage: 18.58MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:46:05 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8390,0,17598021,0]); E; f := P!Reverse([37,-16,-2099,474,29661]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:45:57 on modular  [Seed = 3165499719]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8390*x^2 + 17598021*x over Rational Field
37*x^4 - 16*x^3 - 2099*x^2 + 474*x + 29661
4
Point [ 1, 427, 807, 578 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 778, 498, 535 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 880, 886, 993 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 974, 364, 588 ] was singular mod 1009 and ignored at the #3 lift
[
[ 60, 113, 72, 116 ],
[ 665, 396, -34, -191 ]
]
Scheme over Rational Field defined by
2*r1*r2 + 4*r1*r3 + 2*r1*r4 - 4*r2*r3 + 2*r2*r4 + r3^2 - 2*r3*r4 - 2*r4^2,
2*r1^2 - 22*r1*r3 + 4*r1*r4 + 8*r2^2 + 10*r2*r3 + 18*r2*r4 - 4*r3^2 - 18*r3*r4 -
14*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 5866012*x + 5466456800 over Rational
Field
function(p) ... end function
(2576091969715816833975638843/1825794536354834068948681 :
2046439542735441893843410915178526097260/2467049450202395883663987756820221829 :
1)
59.54231494617367559385

Total time: 8.349 seconds, Total memory usage: 9.97MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:48:22 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-8930,0,19936221,0]);
E;
f := P!Reverse([1473,312,-8918,-936,13497]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:48:12 on modular [Seed = 3098129610] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field 1473*x^4 + 312*x^3 - 8918*x^2 - 936*x + 13497 4 Point [ 1, 125, 954, 792 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 696, 507, 337 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 924, 503, 605 ] was singular mod 1009 and ignored at the #1 lift [] Scheme over Rational Field defined by 4*r1*r2 + 2*r1*r3 + 2*r1*r4 + 2*r2*r4 + 4*r3^2 + 40*r3*r4 + 4*r4^2, 2*r1^2 + 4*r1*r2 + 2*r1*r3 + 4*r1*r4 + 6*r2^2 + 6*r2*r3 + 8*r2*r4 - 23*r3^2 + 26*r3*r4 - 36*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 9.130 seconds, Total memory usage: 5.96MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:48:46 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-8930,0,19936221,0]);
E;
f := P!Reverse([1473,312,-8918,-936,13497]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:48:36 on modular [Seed = 3030759598] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field 1473*x^4 + 312*x^3 - 8918*x^2 - 936*x + 13497 4 Point [ 1, 836, 214, 826 ] was singular mod 1009 and ignored at the #3 lift [] Scheme over Rational Field defined by 4*r1^2 + 2*r1*r2 - 4*r2^2 + 8*r2*r3 + 6*r2*r4 - 5*r3^2 + 12*r3*r4 + 5*r4^2, 10*r1^2 + 8*r1*r2 + 8*r1*r3 + 8*r1*r4 - 12*r2^2 + 10*r2*r3 + 6*r2*r4 + 3*r3^2 - 10*r3*r4 - 3*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 9.330 seconds, Total memory usage: 6.00MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:49:21 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-8930,0,19936221,0]);
E;
f := P!Reverse([1473,312,-8918,-936,13497]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:49:12 on modular [Seed = 2963389574] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field 1473*x^4 + 312*x^3 - 8918*x^2 - 936*x + 13497 4 Point [ 1, 621, 922, 13 ] was singular mod 1009 and ignored at the #1 lift [] Scheme over Rational Field defined by 4*r1*r2 + 2*r1*r4 + 2*r2*r3 + 2*r3^2 - 38*r3*r4 + 6*r4^2, 2*r1^2 + 4*r1*r2 + 2*r1*r3 + 2*r1*r4 + 6*r2^2 + 2*r2*r3 + 6*r2*r4 - 17*r3^2 - 30*r3*r4 - 51*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 9.130 seconds, Total memory usage: 5.96MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:49:54 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-8930,0,19936221,0]);
E;
f := P!Reverse([1473,312,-8918,-936,13497]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:49:45 on modular [Seed = 1380146842] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field 1473*x^4 + 312*x^3 - 8918*x^2 - 936*x + 13497 4 Point [ 1, 210, 999, 822 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 283, 13, 370 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 479, 174, 479 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 655, 74, 376 ] was singular mod 1009 and ignored at the #3 lift Point [ 1, 859, 448, 788 ] was singular mod 1009 and ignored at the #1 lift Point [ 1, 949, 477, 710 ] was singular mod 1009 and ignored at the #1 lift [] Scheme over Rational Field defined by 3*r1^2 + 2*r1*r2 + 2*r1*r3 + 6*r1*r4 - 4*r2^2 - 10*r2*r3 + 4*r3^2 - 4*r3*r4 - 8*r4^2, 4*r1^2 + 2*r1*r2 + 16*r1*r3 - 2*r1*r4 - 6*r2^2 - 2*r2*r3 - 20*r2*r4 - 8*r3^2 - 4*r3*r4 + 8*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 9.310 seconds, Total memory usage: 6.03MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:50:19 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-8930,0,19936221,0]);
E;
f := P!Reverse([1473,312,-8918,-936,13497]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:50:12 on modular [Seed = 1531598782] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field 1473*x^4 + 312*x^3 - 8918*x^2 - 936*x + 13497 4 >> F := S; ^ Runtime error in '[]': Sequence element 0 not defined >> pts := Points(F,1000); ^ User error: Identifier 'F' has not been declared or assigned >> pts; ^ User error: Identifier 'pts' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned >> X; ^ User error: Identifier 'X' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 7.349 seconds, Total memory usage: 5.96MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:51:10 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-8930,0,19936221,0]);
E;
f := P!Reverse([1489,0,-8918,0,13401]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,1000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 11:50:49 on modular [Seed = 1598968791] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field 1489*x^4 - 8918*x^2 + 13401 Errors: /bin/sh: line 1: 4110 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:52:05 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8930,0,19936221,0]); E; f := P!Reverse([8,6,-2513,3594,142560]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:51:36 on modular  [Seed = 1129466906]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field
8*x^4 + 6*x^3 - 2513*x^2 + 3594*x + 142560
4
Point [ 1, 261, 614, 879 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 896, 194, 112 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 993, 715, 236 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
2*r1*r2 + 2*r1*r4 + r2^2 + 4*r2*r3 + 8*r2*r4 + r3^2 + 4*r3*r4 + 5*r4^2,
3*r1^2 + 8*r1*r2 + 20*r1*r3 - 20*r1*r4 - 4*r2*r3 - 8*r2*r4 - 11*r3^2 - 4*r3*r4 +
8*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 18.890 seconds, Total memory usage: 5.90MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:52:43 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8930,0,19936221,0]); E; f := P!Reverse([8,6,-2513,3594,142560]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:52:24 on modular  [Seed = 1196836910]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field
8*x^4 + 6*x^3 - 2513*x^2 + 3594*x + 142560
4
Point [ 1, 22, 912, 609 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 566, 106, 809 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
r1^2 + 2*r1*r2 + 2*r1*r3 + 2*r1*r4 - r2^2 + 2*r2*r3 + 8*r2*r4 + r3^2 + 4*r3*r4 -
3*r4^2,
2*r1^2 - 6*r1*r2 - 6*r1*r3 - 6*r1*r4 - 6*r2^2 + 20*r2*r3 - 22*r2*r4 - 9*r3^2 +
22*r3*r4 - 8*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.359 seconds, Total memory usage: 5.90MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:53:18 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8930,0,19936221,0]); E; f := P!Reverse([8,6,-2513,3594,142560]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:52:59 on modular  [Seed = 1264206913]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field
8*x^4 + 6*x^3 - 2513*x^2 + 3594*x + 142560
4
Point [ 1, 169, 254, 149 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 413, 379, 128 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 596, 630, 128 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 840, 755, 149 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
r1^2 + 4*r1*r4 - 2*r2^2 - 4*r2*r3 - 3*r3^2 + 5*r4^2,
2*r1^2 - 12*r1*r4 - 13*r2^2 + 28*r2*r3 - 9*r3^2 + 3*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 18.859 seconds, Total memory usage: 5.90MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:53:55 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8930,0,19936221,0]); E; f := P!Reverse([3,6,-2225,-2228,415153]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:53:39 on modular  [Seed = 1902149283]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field
3*x^4 + 6*x^3 - 2225*x^2 - 2228*x + 415153
4
Point [ 1, 84, 47, 138 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
2*r1*r2 + 2*r1*r3 + 2*r2*r3 + 2*r2*r4 + r3^2 + 2*r4^2,
8*r1^2 - 2*r1*r2 + 24*r1*r3 + 28*r1*r4 + 37*r2^2 + 36*r2*r3 + 4*r2*r4 + 4*r3^2 +
54*r3*r4 - 30*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.119 seconds, Total memory usage: 6.84MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:54:27 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8930,0,19936221,0]); E; f := P!Reverse([3,6,-2225,-2228,415153]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:54:13 on modular  [Seed = 1952807808]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field
3*x^4 + 6*x^3 - 2225*x^2 - 2228*x + 415153
4
Point [ 1, 416, 1004, 873 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 966, 414, 9 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
r1^2 - r2^2 + 2*r2*r4 - r3^2 + 2*r3*r4 + r4^2,
4*r1^2 + 28*r1*r2 + 16*r1*r3 + 38*r1*r4 + 5*r2^2 - 54*r2*r3 + 4*r2*r4 - 12*r3^2
- 2*r3*r4 - 16*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 13.699 seconds, Total memory usage: 6.48MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:54:55 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8930,0,19936221,0]); E; f := P!Reverse([3,6,-2225,-2228,415153]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:54:40 on modular  [Seed = 2070574314]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field
3*x^4 + 6*x^3 - 2225*x^2 - 2228*x + 415153
4
Point [ 1, 22, 552, 514 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 193, 514, 310 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 341, 648, 404 ] was singular mod 1009 and ignored at the #1 lift
Point [ 1, 906, 689, 103 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
2*r1*r3 + r2^2 + 2*r2*r3 + 2*r2*r4 - r3^2 - 2*r3*r4 - 2*r4^2,
3*r1^2 + 20*r1*r2 - 38*r1*r3 + 2*r1*r4 + 30*r2*r3 + 6*r2*r4 + 45*r3^2 + 4*r3*r4
- 24*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 15.179 seconds, Total memory usage: 6.78MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:55:27 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8930,0,19936221,0]); E; f := P!Reverse([3,6,-2225,-2228,415153]); f; S := FourDescent(f); #S; F := S; pts := Points(F,1000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:55:10 on modular  [Seed = 2137944304]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field
3*x^4 + 6*x^3 - 2225*x^2 - 2228*x + 415153
4
Point [ 1, 587, 874, 905 ] was singular mod 1009 and ignored at the #3 lift
Point [ 1, 835, 315, 872 ] was singular mod 1009 and ignored at the #3 lift
[]
Scheme over Rational Field defined by
127524266251402169898798081114874*r1^2 +
1739729812615017812610234503083600*r1*r2 +
143337519454071037505405039796514*r1*r3 +
1256185772111043616460924626062218*r1*r4 +
2147664299690755459783489150141562*r2^2 -
4007517730504251118386572994281330*r2*r3 +
9093729930645323006121490472014380*r2*r4 -
2947053844831163859534545473208589*r3^2 +
1728733407876908344464186717271618*r3*r4 +
2990199562705536788501140428037023*r4^2,
56831368651552945671223167327936*r1^2 - 3174095650983147877981643667544604*r1*r\
2 + 1928490611618238042831592616240590*r1*r3 -
289102171602793352702703894957480*r1*r4 +
15275947585382366276970429579650288*r2^2 -
6654051666882852007289270033178388*r2*r3 -
9385432261406282507500577656518658*r2*r4 +
1895970857118777151321936635277382*r3^2 +
6911282555626593282005015383368794*r3*r4 -
1958051192867999624741465707574709*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.339 seconds, Total memory usage: 6.94MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:56:26 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-8930,0,19936221,0]); E; f := P!Reverse([1473,312,-8918,-936,13497]); f; S := FourDescent(f); #S; F := S; pts := Points(F,10000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 11:56:05 on modular  [Seed = 1668443431]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field
1473*x^4 + 312*x^3 - 8918*x^2 - 936*x + 13497
4
Point [ 1, 132, 5992, 9275 ] was singular mod 10007 and ignored at the #3 lift

Errors: /bin/sh: line 1:  4146 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 11:56:58 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-8930,0,19936221,0]);
E;
f := P!Reverse([1473,312,-8918,-936,13497]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,5000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 11:56:40 on modular [Seed = 1735813390] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 8930*x^2 + 19936221*x over Rational Field 1473*x^4 + 312*x^3 - 8918*x^2 - 936*x + 13497 4 Point [ 1, 338, 2902, 2010 ] was singular mod 5003 and ignored at the #1 lift Point [ 1, 767, 947, 4939 ] was singular mod 5003 and ignored at the #1 lift [ [ 78767, -62794, -80021, 5603 ] ] Scheme over Rational Field defined by 4*r1^2 + 2*r1*r2 - 4*r2^2 + 8*r2*r3 + 6*r2*r4 - 5*r3^2 + 12*r3*r4 + 5*r4^2, 10*r1^2 + 8*r1*r2 + 8*r1*r3 + 8*r1*r4 - 12*r2^2 + 10*r2*r3 + 6*r2*r4 + 3*r3^2 - 10*r3*r4 - 3*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 6645412*x + 6591494780 over Rational Field function(p) ... end function (3911877699936918534138571607333065766582875327132501010/2472034840743742338887\ 561746213269332002583868619969 : 7837079943401965332876023994081875309660550317\ 32634205342244219899027916523006160/1229084894129790516579614763601918906513937\ 22803617867808410687953904823537953 : 1) 123.051571513152651959899 Total time: 18.160 seconds, Total memory usage: 5.96MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:59:12 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-9290,0,21576021,0]); E; f := P!Reverse([1657,-496,-9278,1488,12921]); f; S := FourDescent(f); #S; F := S; pts := Points(F,5000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Tue Sep 21 2004 11:58:53 on modular  [Seed = 1803183495]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 9290*x^2 + 21576021*x over Rational Field
1657*x^4 - 496*x^3 - 9278*x^2 + 1488*x + 12921
4
Point [ 1, 1347, 3197, 4229 ] was singular mod 5003 and ignored at the #1 lift
Point [ 1, 1808, 210, 3411 ] was singular mod 5003 and ignored at the #1 lift
Point [ 1, 2517, 4638, 3514 ] was singular mod 5003 and ignored at the #1 lift
Point [ 1, 4794, 4491, 1494 ] was singular mod 5003 and ignored at the #1 lift
[]
Scheme over Rational Field defined by
r1^2 + 12*r1*r2 + 16*r1*r3 + 6*r1*r4 - 2*r2^2 + 4*r2*r3 + 4*r2*r4 - 3*r3^2 +
15*r4^2,
r1^2 + 16*r1*r2 + 24*r1*r3 - 2*r2*r3 + 4*r2*r4 + r3^2 + 8*r3*r4 - 5*r4^2
Elliptic Curve defined by y^2 = x^3 + x^2 - 7192012*x + 7421341100 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 18.440 seconds, Total memory usage: 5.87MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 11:59:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-9290,0,21576021,0]); E; f := P!Reverse([1657,-496,-9278,1488,12921]); f; S := FourDescent(f); #S; F := S; pts := Points(F,7000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 11:59:26 on modular  [Seed = 1853841633]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 9290*x^2 + 21576021*x over Rational Field
1657*x^4 - 496*x^3 - 9278*x^2 + 1488*x + 12921
4
Point [ 1, 1128, 200, 4239 ] was singular mod 7001 and ignored at the #1 lift
Point [ 1, 5254, 4044, 64 ] was singular mod 7001 and ignored at the #3 lift

Errors: /bin/sh: line 1:  4159 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 12:00:22 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-9290,0,21576021,0]);
E;
f := P!Reverse([1657,-496,-9278,1488,12921]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Tue Sep 21 2004 12:00:01 on modular [Seed = 302187330] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 9290*x^2 + 21576021*x over Rational Field 1657*x^4 - 496*x^3 - 9278*x^2 + 1488*x + 12921 4 [] Scheme over Rational Field defined by r1^2 + 12*r1*r2 + 16*r1*r3 + 6*r1*r4 - 2*r2^2 + 4*r2*r3 + 4*r2*r4 - 3*r3^2 + 15*r4^2, r1^2 + 16*r1*r2 + 24*r1*r3 - 2*r2*r3 + 4*r2*r4 + r3^2 + 8*r3*r4 - 5*r4^2 Elliptic Curve defined by y^2 = x^3 + x^2 - 7192012*x + 7421341100 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 20.620 seconds, Total memory usage: 5.87MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 12:01:07 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-9290,0,21576021,0]);
E;
f := P!Reverse([1549,0,-9278,0,13941]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 12:00:46 on modular [Seed = 369559401] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 9290*x^2 + 21576021*x over Rational Field 1549*x^4 - 9278*x^2 + 13941 Errors: /bin/sh: line 1: 4167 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.247 (66.63.133.247) Time: Tue Sep 21 12:01:52 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-9290,0,21576021,0]); E; f := P!Reverse([33,28,-2387,-432,40005]); f; S := FourDescent(f); #S; F := S; pts := Points(F,6000); pts; X,m := Scheme(F); X; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Tue Sep 21 2004 12:01:31 on modular  [Seed = 436931344]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 9290*x^2 + 21576021*x over Rational Field
33*x^4 + 28*x^3 - 2387*x^2 - 432*x + 40005
4
Point [ 1, 191, 5031, 2587 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1:  4171 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.247 (66.63.133.247)
Time: Tue Sep 21 12:02:48 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-9290,0,21576021,0]);
E;
f := P!Reverse([3,6,-2315,-2318,449308]);
f;
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
pts;
X,m := Scheme(F);
X;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Tue Sep 21 2004 12:02:27 on modular [Seed = 504303580] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 9290*x^2 + 21576021*x over Rational Field 3*x^4 + 6*x^3 - 2315*x^2 - 2318*x + 449308 Errors: /bin/sh: line 1: 4175 Killed nice -n 19 /usr/local/bin/magma '204.214' ************** MAGMA ***************** Host 204.214.214.21 (204.214.214.21) Time: Tue Sep 21 18:33:43 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Tue Sep 21 2004 18:33:42 on modular [Seed = 487387144] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.190 seconds, Total memory usage: 3.51MB '69.199.' ************** MAGMA ***************** Host 69.199.8.11 (69.199.8.11) Time: Tue Sep 21 23:43:32 2004 Input: test Output: Magma V2.11-6 Tue Sep 21 2004 23:43:32 on modular [Seed = 4026423903] ------------------------------------- >> test; ^ User error: Identifier 'test' has not been declared or assigned Total time: 0.190 seconds, Total memory usage: 3.51MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.161 (66.63.132.161) Time: Wed Sep 22 00:14:37 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve( [0,0,0,-58094884,0] ); f := P!Reverse( [-5399,2012,-83910,14484,-366127] ); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:14:33 on modular  [Seed = 3148482246]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 1 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.509 seconds, Total memory usage: 5.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.161 (66.63.132.161) Time: Wed Sep 22 00:15:06 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve( [0,0,0,-58094884,0] ); f := P!Reverse( [-5399,2012,-83910,14484,-366127] ); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:15:03 on modular  [Seed = 2695962035]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 2 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.390 seconds, Total memory usage: 5.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.132.161 (66.63.132.161) Time: Wed Sep 22 00:15:21 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve( [0,0,0,-58094884,0] ); f := P!Reverse( [-5399,2012,-83910,14484,-366127] ); S := FourDescent(f); F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:15:18 on modular  [Seed = 2898071982]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 2 not defined

>> pts := Points(F,10000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.419 seconds, Total memory usage: 5.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:26:19 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-5399,2012,-83910,14484,-366127]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:26:15 on modular  [Seed = 1481238504]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 1 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.390 seconds, Total memory usage: 5.25MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:26:38 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-5399,2012,-83910,14484,-366127]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:26:35 on modular  [Seed = 1129512175]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 2 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.339 seconds, Total memory usage: 5.25MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:26:49 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-5399,2012,-83910,14484,-366127]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:26:46 on modular  [Seed = 1331622174]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 3 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.439 seconds, Total memory usage: 5.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:27:01 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-5399,2012,-83910,14484,-366127]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:26:57 on modular  [Seed = 1264252173]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 4 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.390 seconds, Total memory usage: 5.25MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:27:26 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-5399,2012,-83910,14484,-366127]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:27:23 on modular  [Seed = 2003224843]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 0 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 3.450 seconds, Total memory usage: 5.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:28:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-9290,0,21576021,0]); f := P!Reverse([3,6,-2315,-2318,449308]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 00:28:26 on modular  [Seed = 2137964866]
-------------------------------------

Point [ 1, 613, 3250, 2963 ] was singular mod 6007 and ignored at the #1 lift

Errors: /bin/sh: line 1:  5672 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:29:17 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-9290,0,21576021,0]);
f := P!Reverse([3,6,-2315,-2318,449308]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 00:28:56 on modular [Seed = 2070594980] ------------------------------------- Point [ 1, 3250, 3863, 2963 ] was singular mod 6007 and ignored at the #1 lift Errors: /bin/sh: line 1: 5676 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:29:50 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-9290,0,21576021,0]); f := P!Reverse([3,6,-2315,-2318,449308]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:29:29 on modular  [Seed = 1719130264]
-------------------------------------

Point [ 1, 1325, 2509, 4843 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 1885, 4350, 1508 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3318, 2289, 1161 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 9290*x^2 + 21576021*x over Rational Field
Elliptic Curve defined by y^2 = x^3 + x^2 - 7192012*x + 7421341100 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.300 seconds, Total memory usage: 6.51MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:30:04 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-18167,19240,-99012,51504,-109372]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:30:03 on modular  [Seed = 1651760382]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 1 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.820 seconds, Total memory usage: 4.80MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:30:11 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-18167,19240,-99012,51504,-109372]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:30:10 on modular  [Seed = 1853870315]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 2 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.850 seconds, Total memory usage: 4.79MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:30:18 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-18167,19240,-99012,51504,-109372]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:30:17 on modular  [Seed = 1786500324]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 3 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.850 seconds, Total memory usage: 4.79MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:30:26 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-18167,19240,-99012,51504,-109372]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:30:25 on modular  [Seed = 369600672]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 4 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.850 seconds, Total memory usage: 4.79MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:30:31 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-18167,19240,-99012,51504,-109372]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:30:30 on modular  [Seed = 521052590]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 5 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.820 seconds, Total memory usage: 4.78MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:30:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58094884,0]); f := P!Reverse([-18167,19240,-99012,51504,-109372]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:30:46 on modular  [Seed = 453682618]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 6 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.810 seconds, Total memory usage: 4.80MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:31:26 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-56025225,0]); f := P!Reverse([499,-499,2994,-15469,30439]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:31:11 on modular  [Seed = 118965855]
-------------------------------------

Point [ 1, 1406, 5836, 1775 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 1614, 4269, 3556 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4373, 3969, 2836 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 56025225*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 56025225*x over Rational Field
function(p) ... end function
(-11609012600895509592667935/100432223800480449340324 :
-2561006805546185505324691139828723181975/31828019730819832381028893792814168 :
1)
59.18339334970564635796

Total time: 14.990 seconds, Total memory usage: 19.62MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:32:16 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-15280281,0]);
f := P!Reverse([-16819,-4524,-43344,-5976,-31068]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:32:14 on modular [Seed = 51593754] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 15280281*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 168083091*x + 836228658006 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.960 seconds, Total memory usage: 4.79MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:32:34 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-15280281,0]);
f := P!Reverse([-16819,-4524,-43344,-5976,-31068]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:32:32 on modular [Seed = 253709880] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 2 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 15280281*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 168083091*x + 836228658006 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.960 seconds, Total memory usage: 4.73MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:32:48 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-15280281,0]);
f := P!Reverse([-6396,-11832,-54720,-42540,-85779]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:32:47 on modular [Seed = 186337843] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 15280281*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 168083091*x + 836228658006 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.540 seconds, Total memory usage: 4.92MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:33:06 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-15280281,0]);
f := P!Reverse([-6396,-11832,-54720,-42540,-85779]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:33:04 on modular [Seed = 925333216] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 2 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 15280281*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 168083091*x + 836228658006 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.520 seconds, Total memory usage: 4.94MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:33:14 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-15280281,0]);
f := P!Reverse([-6396,-11832,-54720,-42540,-85779]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:33:12 on modular [Seed = 857961196] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 3 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 15280281*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 168083091*x + 836228658006 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.520 seconds, Total memory usage: 4.92MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:33:25 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-15280281,0]);
f := P!Reverse([-6396,-11832,-54720,-42540,-85779]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:33:23 on modular [Seed = 1060077307] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 4 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 15280281*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 168083091*x + 836228658006 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.520 seconds, Total memory usage: 5.02MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:34:03 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:34:00 on modular [Seed = 942176727] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.379 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:34:17 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:34:13 on modular [Seed = 607413686] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 2 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.410 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:34:48 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:34:44 on modular [Seed = 792686236] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 3 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.450 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:34:57 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:34:54 on modular [Seed = 725314194] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 4 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.339 seconds, Total memory usage: 5.25MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:35:12 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
#S
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:35:08 on modular [Seed = 3620181628] ------------------------------------- >> F := S; ^ User error: bad syntax >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.509 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:35:32 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:35:29 on modular [Seed = 3552809877] ------------------------------------- 0 >> F := S; ^ Runtime error in '[]': Sequence element 4 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.500 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:35:46 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:35:43 on modular [Seed = 3754925975] ------------------------------------- 0 >> F := S; ^ Runtime error in '[]': Sequence element 0 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.410 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:36:44 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:36:41 on modular [Seed = 3637024982] ------------------------------------- 0 >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.330 seconds, Total memory usage: 5.25MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:37:04 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-18167,19240,-99012,51504,-109372]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:37:03 on modular [Seed = 3302262012] ------------------------------------- 0 >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 0.830 seconds, Total memory usage: 4.79MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:37:46 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-18167,19240,-99012,51504,-109372]);
S := FourDescent(f);
#S;
F := S[-1];
pts := Points(F,60000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:37:45 on modular [Seed = 3453848835] ------------------------------------- 0 >> F := S[-1]; ^ Runtime error in '[]': Sequence element -1 not defined >> pts := Points(F,60000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 0.840 seconds, Total memory usage: 4.80MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:38:28 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-29822521,0]);
f := P!Reverse([-20659,4252,-60336,7384,-49212]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:38:24 on modular [Seed = 4159158112] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 29822521*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 328047731*x + 2280051020534 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.149 seconds, Total memory usage: 5.57MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:38:49 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-29822521,0]);
f := P!Reverse([-2623,2924,-61920,25112,-385452]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:38:49 on modular [Seed = 4091786109] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 29822521*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 328047731*x + 2280051020534 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 0.710 seconds, Total memory usage: 5.24MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:39:03 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-29822521,0]);
f := P!Reverse([-2623,2924,-61920,25112,-385452]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:39:02 on modular [Seed = 4293902158] ------------------------------------- 0 >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 29822521*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 328047731*x + 2280051020534 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 0.710 seconds, Total memory usage: 5.24MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:39:22 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-3583449,0]);
f := P!Reverse([-443,408,-20934,8136,-275355]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:39:20 on modular [Seed = 4226530133] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 3583449*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 39417939*x + 94968565398 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.300 seconds, Total memory usage: 4.91MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:39:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-3583449,0]);
f := P!Reverse([-443,408,-20934,8136,-275355]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:39:32 on modular [Seed = 3858081462] ------------------------------------- 0 >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 3583449*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 39417939*x + 94968565398 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.310 seconds, Total memory usage: 5.01MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:40:15 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-67732900,0]);
f := P!Reverse([-44975,-35200,-105660,-32960,-52028]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:40:11 on modular [Seed = 3975982992] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 67732900*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 745061900*x + 7804184738000 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.839 seconds, Total memory usage: 4.77MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:41:06 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-77528025,0]);
f := P!Reverse([-341,191,30219,131126,147964]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:40:47 on modular [Seed = 3908611056] ------------------------------------- Point [ 1, 2692, 4565, 1587 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 77528025*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 77528025*x over Rational Field function(p) ... end function (744979999633874069046120041252015625/35363631152655502270617252902884 : 584149312809533493409928079762153531298084164420211875/210298065772567573019370\ 015480120495152931069848 : 1) 73.68273299523168873292 Total time: 18.719 seconds, Total memory usage: 34.49MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:41:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-97555129,0]); f := P!Reverse([-20551,-1036,-112560,8232,-157388]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

P

Output: Magma V2.11-6     Wed Sep 22 2004 00:41:42 on modular  [Seed = 2491733829]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 1 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 97555129*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 1073106419*x + 13489728127862 over
Rational Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Univariate Polynomial Ring in x over Integer Ring Total time: 4.759 seconds, Total memory usage: 4.98MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:42:30 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-24970009,0]); f := P!Reverse([-14987,9684,-57168,17800,-58012]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:42:29 on modular  [Seed = 2424361842]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 1 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 24970009*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 274670099*x + 1746851889622 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.970 seconds, Total memory usage: 5.05MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:43:23 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-76300225,0]); f := P!Reverse([4141,8191,6741,-194,3596]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 00:43:02 on modular  [Seed = 2575948312]
-------------------------------------

Errors: /bin/sh: line 1:  5838 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:43:51 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-76300225,0]);
f := P!Reverse([4141,8191,6741,-194,3596]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 00:43:30 on modular [Seed = 2241185312] ------------------------------------- Errors: /bin/sh: line 1: 5842 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:44:20 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-76300225,0]); f := P!Reverse([4141,8191,6741,-194,3596]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 00:43:59 on modular  [Seed = 2173813721]
-------------------------------------

Errors: /bin/sh: line 1:  5846 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:44:42 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-76300225,0]);
f := P!Reverse([-5241,6988,83856,97832,20964]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:44:27 on modular [Seed = 2359086832] ------------------------------------- Point [ 1, 1149, 3746, 4063 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5070, 1441, 1518 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 76300225*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 76300225*x over Rational Field function(p) ... end function (3061748340468507106760769058780180559065168225/3474329555049001284481782352528\ 18628598489 : 22416981413781173391135628611920153313980909528132811139004202670\ 300/204788948518382536097749162792083414019694686646075606137845987 : 1) 103.123485822657158905713 Total time: 15.089 seconds, Total memory usage: 10.32MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:45:26 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-10387729,0]); f := P!Reverse([97,-92,-39042,389476,-973507]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:45:09 on modular  [Seed = 2291714698]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 10387729*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 10387729*x over Rational Field
function(p) ... end function
(2112698274660747501458130868327941858915666239932/1996307426961778102674729388\
3447133593115209 : -30694087382666220675425453475215050960719968582490407258549\
21567363852190/8919512813919046278531379347985424411249387043837253453848389842\
7 : 1)
103.20774650870271216263

Total time: 17.070 seconds, Total memory usage: 8.94MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:46:16 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-4765489,0]);
f := P!Reverse([411,313,426,-1465,2583]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 00:45:55 on modular [Seed = 2980180837] ------------------------------------- Point [ 1, 1332, 1911, 1690 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 1585, 705, 3281 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 1984, 5273, 5559 ] was singular mod 6007 and ignored at the #3 lift Errors: /bin/sh: line 1: 5862 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:46:45 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-4765489,0]); f := P!Reverse([411,313,426,-1465,2583]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:46:25 on modular  [Seed = 3182296907]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 4765489*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 4765489*x over Rational Field
function(p) ... end function
(-821625709447072653205715513642079517914106241807/9483527628314863675739441646\
62413879424026404 : -1722438513733043884625222708951391546909645265937439909288\
634047224925025/292048426473928566763317930523866488036890460001067678637815235\
09208 : 1)
103.72295782120042417773

Total time: 20.769 seconds, Total memory usage: 9.66MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:47:36 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-76247824,0]);
f := P!Reverse([411,313,426,-1465,2583]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:47:18 on modular [Seed = 3114924856] ------------------------------------- Point [ 1, 407, 4153, 5553 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4076, 2189, 1194 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 76247824*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 4765489*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 17.949 seconds, Total memory usage: 9.49MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:48:14 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-76247824,0]);
f := P!Reverse([2065,2832,-12390,-2832,2065]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:47:57 on modular [Seed = 2780161807] ------------------------------------- Point [ 1, 1218, 2978, 2542 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 1408, 4985, 511 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2340, 4942, 1399 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2435, 948, 3203 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3951, 2608, 666 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5163, 1277, 5153 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 76247824*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 4765489*x over Rational Field function(p) ... end function (49014911706918769383383654662714051130453489521/969454546157179194552827005144\ 5064565700625 : 978793172344923559201295858107926834604555004284340339042216641\ 4189556/30184999802194462963708769360584516180173474818105737563436234375 : 1) 103.72295782120043838858 Total time: 17.339 seconds, Total memory usage: 9.12MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:49:08 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-69338929,0]); f := P!Reverse([218,-248,-296916,6051736,-34148828]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:48:49 on modular  [Seed = 2931747784]
-------------------------------------

Point [ 1, 2682, 3911, 3496 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 69338929*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 69338929*x over Rational Field
function(p) ... end function
(19296109512565722172201227390811101784010591926463/167074819299367015428535370\
2717879038841208881 : -58735825321828709980970405393673214584593111384466436257\
831570231425853180/682914761247747487942638579260789686182825010273446831066745\
67848279 : 1)
104.37653522530644067956

Total time: 18.210 seconds, Total memory usage: 14.61MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:49:54 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-61701025,0]);
f := P!Reverse([3191,-2520,1470,-12600,79775]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 00:49:33 on modular [Seed = 2847534243] ------------------------------------- Point [ 1, 301, 838, 5433 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3534, 683, 4426 ] was singular mod 6007 and ignored at the #3 lift Errors: /bin/sh: line 1: 5886 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:50:24 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-61701025,0]); f := P!Reverse([3191,-2520,1470,-12600,79775]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:50:03 on modular  [Seed = 1413747070]
-------------------------------------

Point [ 1, 895, 3236, 4703 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 1230, 5598, 3712 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 2143, 5170, 4718 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 2652, 4132, 671 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 61701025*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 61701025*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.730 seconds, Total memory usage: 6.05MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:50:53 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-61701025,0]); f := P!Reverse([1571,-1571,-14139,21994,-6284]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:50:40 on modular  [Seed = 1346377126]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 61701025*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 61701025*x over Rational Field
function(p) ... end function
(11680932397278332488319592834100718466902068225/745089780369074174682509259879\
71807775844 : 12608703704892033197176381518399481578551206670543675324121111437\
07225/20338218556796220722654265717986920747519299819211504541284328 : 1)
104.48733690626032455384

Total time: 12.390 seconds, Total memory usage: 10.17MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:51:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-41667025,0]);
f := P!Reverse([1291,-1291,-11619,18074,-5164]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:51:19 on modular [Seed = 1548491213] ------------------------------------- Point [ 1, 300, 2689, 2897 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4428, 1094, 5585 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4790, 2298, 3249 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5114, 5856, 5728 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5173, 1643, 4627 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5681, 5758, 440 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 41667025*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 41667025*x over Rational Field function(p) ... end function (10138636200333783225446470131688914521255430625/123689210341183160373960065093\ 1877447525924 : -62918032088575145721262683442879441105245500701149841264298395\ 6403625/1375617605353221701068670637604343041858146284664943752729482968 : 1) 104.60959752722831694882 Total time: 13.980 seconds, Total memory usage: 10.20MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:52:17 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-73239364,0]); f := P!Reverse([1945,2334,2334,-4668,7780]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:52:02 on modular  [Seed = 1196884707]
-------------------------------------

Point [ 1, 520, 1317, 2203 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 2174, 4734, 336 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 73239364*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 73239364*x over Rational Field
function(p) ... end function
(-1359773087029279051915474607515574443583579/439719355136997298248641728904241\
5816641225 : 438814616299604357391757219790164283697379217669964812200566293465\
31/9220688987635124699133877129044723847840941679787522676962549125 : 1)
104.84628344930541743451

Total time: 14.720 seconds, Total memory usage: 9.40MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:52:50 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-55086084,0]);
f := P!Reverse([1237,2474,7422,-4948,4948]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:52:36 on modular [Seed = 1129514753] ------------------------------------- Point [ 1, 3323, 4437, 2510 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4186, 1719, 3210 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4923, 1529, 4904 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5795, 3671, 3663 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 55086084*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 55086084*x over Rational Field function(p) ... end function (-7509294851980876251855022894754650893877615683/188654084663370991274467104396\ 1701877136689 : 102409821687059452128421988305752846511816444974827443635806598\ 9212985/2591190359496325016113240873745738463567669517053008699850563113 : 1) 105.36455764503480736493 Total time: 14.339 seconds, Total memory usage: 11.67MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:53:32 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-44076321,0]); f := P!Reverse([769,688,-74568,306448,-304748]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:53:12 on modular  [Seed = 1297942819]
-------------------------------------

Point [ 1, 1285, 3225, 4274 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3230, 4705, 391 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3570, 2557, 577 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4691, 5133, 4243 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 44076321*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 44076321*x over Rational Field
function(p) ... end function
(57619881008648125486558123499013925216579391168316/836570085625113930068488187\
4096698781855453169 : -11645634185121541743040291894708635171634283057155846721\
3083660753860356130/76516218082734343325921622991784321378427252252617936368263\
5240820553 : 1)
106.113938348674324174680

Total time: 19.449 seconds, Total memory usage: 19.44MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:54:04 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-31528225,0]);
f := P!Reverse([281,-75,15,-750,28100]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:53:46 on modular [Seed = 1230572869] ------------------------------------- Point [ 1, 376, 5527, 3556 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2237, 3518, 3812 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 31528225*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 31528225*x over Rational Field function(p) ... end function (-2042374348421878496470549137671993302708775286815/129245967809540978714607744\ 01324669466927864164 : 10367221646391525160575681820734384753301125913708462498\ 1125633116036208425/14693508360497215817598544676307417810971159912636900151189\ 20267885288 : 1) 106.18819119873477063720 Total time: 17.850 seconds, Total memory usage: 6.97MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:54:45 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-93373569,0]); f := P!Reverse([-6383,9252,82206,69156,4653]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 00:54:24 on modular  [Seed = 1935882149]
-------------------------------------

Point [ 1, 1613, 1892, 2097 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 2659, 239, 646 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3104, 4167, 278 ] was singular mod 6007 and ignored at the #1 lift

Errors: /bin/sh: line 1:  5925 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:55:23 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-93373569,0]);
f := P!Reverse([-6383,9252,82206,69156,4653]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 00:55:02 on modular [Seed = 2053783178] ------------------------------------- Point [ 1, 2457, 3943, 1250 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4324, 1789, 4996 ] was singular mod 6007 and ignored at the #3 lift Errors: /bin/sh: line 1: 5932 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:55:45 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-93373569,0]); f := P!Reverse([6442,0,0,0,57978]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 00:55:30 on modular  [Seed = 1719018226]
-------------------------------------

Point [ 1, 1399, 1650, 5465 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 1939, 2916, 2964 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3498, 5193, 3029 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4401, 4457, 5489 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 5185, 3240, 2161 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 93373569*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 93373569*x over Rational Field
function(p) ... end function
(-60789526060246980867658270306398623884154273529/65404964924886366110831761493\
83311766000225 : -4263175117392001045159428806523495713530447818238976599160169\
883117644/16726923691191016537351281611456597417084683498031008758973284625 : 1)
106.65359746389111705866

Total time: 14.720 seconds, Total memory usage: 5.42MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:56:44 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17952169,0]);
f := P!Reverse([266,152,-5415,37012,181697]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:56:27 on modular [Seed = 1651648207] ------------------------------------- Point [ 1, 3320, 2673, 5090 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5187, 2244, 868 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 17952169*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 197473859*x + 1064886760742 over Rational Field function(p) ... end function (35663914397826226187717806/5502634826262181134121 : -97678953631027449726872760408316392158/408184057809329862542839571381419 : 1) 53.35228922191927125595 Total time: 16.519 seconds, Total memory usage: 8.03MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 00:58:07 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-1394761,0]); f := P!Reverse([601,-884,240,-48808,120052]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 00:57:46 on modular  [Seed = 1836919409]
-------------------------------------

Errors: /bin/sh: line 1:  5947 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:58:31 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-1394761,0]);
f := P!Reverse([601,-884,240,-48808,120052]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:58:22 on modular [Seed = 1769549393] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 3 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 1394761*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 15342371*x + 23060978374 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 8.400 seconds, Total memory usage: 11.15MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 00:59:20 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-1394761,0]);
f := P!Reverse([1181,0,-7086,-18896,48421]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 00:59:06 on modular [Seed = 268457948] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 1394761*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 15342371*x + 23060978374 over Rational Field function(p) ... end function (16312015259973822084249/90660490361974260025 : -123010707196967569994628098258086318/863231134032587013452533206125 : 1) 53.35619165541726260926 Total time: 13.730 seconds, Total memory usage: 5.23MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:00:08 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-22316176,0]); f := P!Reverse([601,-884,240,-48808,120052]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

P

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 00:59:47 on modular  [Seed = 487414408]
-------------------------------------

Point [ 1, 2133, 393, 1552 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1:  5963 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:00:38 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-22316176,0]);
f := P!Reverse([601,-884,240,-48808,120052]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); P Output: Magma V2.11-6 Wed Sep 22 2004 01:00:32 on modular [Seed = 420044479] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 3 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 22316176*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 15342371*x + 23060978374 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]
Univariate Polynomial Ring in x over Integer Ring

Total time: 6.030 seconds, Total memory usage: 10.64MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:02:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-22316176,0]);
f := P!Reverse([1181,0,-7086,-18896,48421]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:02:20 on modular [Seed = 1066506] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 22316176*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 15342371*x + 23060978374 over Rational Field function(p) ... end function (16312015259973822084249/90660490361974260025 : -123010707196967569994628098258086318/863231134032587013452533206125 : 1) 53.35619165541726260926 Total time: 13.730 seconds, Total memory usage: 5.14MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:04:14 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-95238081,0]); f := P!Reverse([3253,0,0,0,117108]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:03:48 on modular  [Seed = 186338793]
-------------------------------------

Point [ 1, 1542, 2897, 5814 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4596, 3753, 2939 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 95238081*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 95238081*x over Rational Field
function(p) ... end function
(-47437531124406869985349589518632880368734142084/52214953285165438755442234884\
55667390949001 : -4052824415178575477090926937455702920444619407971317519236147\
233250210/11931425687983376935181752529887053909153837378891567266686798501 : 1)
106.77625767525130129342

Total time: 14.919 seconds, Total memory usage: 5.39MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:05:07 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-35034561,0]);
f := P!Reverse([949,-1876,-36930,87212,-15191]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:04:47 on modular [Seed = 874803853] ------------------------------------- Point [ 1, 1515, 1133, 1555 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4124, 1854, 4155 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5746, 2319, 5932 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 35034561*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 35034561*x over Rational Field function(p) ... end function (195118046945330454617916851300605184003961121525404/14127423099161175658565385\ 8998201433408992009 : -27254748073994642986351323971389836751562786227849236146\ 35173965064150255690/1679169077362652984614660160538256693698089691231786582697\ 647629723 : 1) 107.113721659727247015325 Total time: 18.190 seconds, Total memory usage: 12.67MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:05:48 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-7778521,0]); f := P!Reverse([9389,6268,-26928,-3816,29380]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:05:31 on modular  [Seed = 807434621]
-------------------------------------

FourDescent(
f: 9389*x^4 + 6268*x^3 - 26928*x^2 - 3816*x + 29380
)
ReduceFD(
fd: [ [693016023334810443128724799342523482875231786962021161735...
)
StollReduce(
desc: [ [413476690479666267686073129351217573509945905421213001311...
)
Covariant(
mat1: [41347669047966626768607312935121757350994590542121300131199...,
mat2: [14361203822380342073660727189559298215439958363371872918760...
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line
335, column 37:
>>             three := [[singt1[i,j,j]/singt1[i,1,1] : j in [1..4]] : i in [2
^
Runtime error in '/': Division by zero in (possibly) real or complex division.
Maybe loss of precision?

>> F := S;
^
User error: Identifier 'S' has not been declared or assigned

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 7778521*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 85563731*x + 303720130966 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 17.059 seconds, Total memory usage: 8.05MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:06:59 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-7778521,0]); f := P!Reverse([2789,0,-16734,-44624,114349]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:06:45 on modular  [Seed = 992702984]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 7778521*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 85563731*x + 303720130966 over Rational
Field
function(p) ... end function
(234423145240075332774153/82472219166925879201 :
-216391466098977217970018586434733310/748964996583593424154320222449 : 1)
53.78277768155246718606

Total time: 14.189 seconds, Total memory usage: 5.21MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:07:43 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-46335249,0]);
f := P!Reverse([2269,0,0,0,81684]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:07:27 on modular [Seed = 657944318] ------------------------------------- Point [ 1, 1149, 4693, 1049 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2052, 2943, 4078 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3709, 324, 868 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 46335249*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 46335249*x over Rational Field function(p) ... end function (-195930641177096348284824103815084585155445356100/3071491588835255207243733537\ 1392657415071049 : 322980163657688538450715444267384195701880190246379940957717\ 41918844830/170225255825655427809799120391164312963518081514445185468435777093 : 1) 108.18970696317234114758 Total time: 15.089 seconds, Total memory usage: 11.72MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:08:27 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-15484225,0]); f := P!Reverse([239,-19,1044,-6649,15949]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:08:07 on modular  [Seed = 556886208]
-------------------------------------

Point [ 1, 5502, 3079, 2219 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 15484225*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 15484225*x over Rational Field
function(p) ... end function
(-298908799812549263923457225102755895859753754101335/8472978302362676407443043\
6365725783782229611204 : 255367577699024888900599455812510808008635361578139224\
9044942737634357047475/24663467856249877121460122423080610798968917470726733588\
422763200103608 : 1)
108.37369272661091201825

Total time: 18.600 seconds, Total memory usage: 19.00MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:09:16 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-71588521,0]);
f := P!Reverse([34021,46812,-64752,-44584,66980]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 01:08:54 on modular [Seed = 758998173] ------------------------------------- Errors: /bin/sh: line 1: 6011 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:09:45 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-71588521,0]); f := P!Reverse([8461,0,-50766,-135376,346901]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:09:31 on modular  [Seed = 3603340939]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 71588521*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 787473731*x + 8479946666534 over Rational
Field
function(p) ... end function
(-260063272460385307414871/20376466597142380729 :
373074165663247632487031304531721634/91979980963334022759283590317 : 1)
54.22061292661217635213

Total time: 14.230 seconds, Total memory usage: 5.16MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:10:14 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-55219761,0]);
f := P!Reverse([-23,12,4846302,1209603852,84929155029]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); P Output: Magma V2.11-6 Wed Sep 22 2004 01:10:07 on modular [Seed = 3519125928] ------------------------------------- FourDescent( f: -23*x^4 + 12*x^3 + 4846302*x^2 + 1209603852*x + 84929155029 ) ReduceFD( fd: [ [600837186555074661657633801503399395948956 12699969231932... ) StollReduce( desc: [ [ 2 -4 1 1] [ -4 6 1 2] [ 1 1 -12 -3] [ 1... ) Covariant( mat1: [ 2 -4 1 1] [ -4 6 1 2] [ 1 1 -12 -3] [ 1 ..., mat2: [ 2 22 -1 -2] [22 6 -3 -3] [-1 -3 2 -7] [-2 -3 -7 -6] ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line 350, column 33: >> covmat *:= 1/Sqrt(&+[Norm(c) : c in Eltseq(covmat)]); ^ Runtime error in '/': Division by zero >> F := S; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 55219761*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 55219761*x over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]
Univariate Polynomial Ring in x over Integer Ring

Total time: 7.129 seconds, Total memory usage: 6.53MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:11:28 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-55219761,0]);
f := P!Reverse([-23,12,4846302,1209603852,84929155029]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); P Output: Magma V2.11-6 Wed Sep 22 2004 01:11:15 on modular [Seed = 3637022970] ------------------------------------- FourDescent( f: -23*x^4 + 12*x^3 + 4846302*x^2 + 1209603852*x + 84929155029 ) ReduceFD( fd: [ [6080368631816266510398114804 6864339257797127198369858641... ) StollReduce( desc: [ [ 0 1 5 5] [ 1 0 -5 -10] [ 5 -5 8 4] [ 5... ) Covariant( mat1: [ 0 1 5 5] [ 1 0 -5 -10] [ 5 -5 8 4] [ 5 -..., mat2: [ 1 9 -6 5] [ 9 3 -16 1] [ -6 -16 -4 -6] [ 5 ... ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line 350, column 33: >> covmat *:= 1/Sqrt(&+[Norm(c) : c in Eltseq(covmat)]); ^ Runtime error in '/': Division by zero >> F := S; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 55219761*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 55219761*x over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]
Univariate Polynomial Ring in x over Integer Ring

Total time: 5.879 seconds, Total memory usage: 6.20MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:12:08 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-55219761,0]);
f := P!Reverse([4954,0,0,0,44586]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:11:52 on modular [Seed = 3302263818] ------------------------------------- Point [ 1, 23, 2659, 832 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 55219761*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 55219761*x over Rational Field function(p) ... end function (-377511413598186409060934779985810812112976761025/5618922415131948557107513659\ 9665713413643249 : -10961244947607224861420111802187876589139528159549402887216\ 9781827176620/42119145642080431564910898807783229635539854181295419214741562605\ 7 : 1) 108.52557507748049658857 Total time: 14.439 seconds, Total memory usage: 5.42MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:12:52 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-45981961,0]); f := P!Reverse([1205,-228,147600,305752,157924]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 01:12:31 on modular  [Seed = 3234891817]
-------------------------------------

Errors: /bin/sh: line 1:  6038 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:13:23 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-45981961,0]);
f := P!Reverse([6781,0,-40686,-108496,278021]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:13:09 on modular [Seed = 3420160888] ------------------------------------- Point [ 1, 2928, 1972, 5213 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3189, 226, 5150 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3461, 3172, 4867 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 45981961*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 505801571*x + 4365251485574 over Rational Field function(p) ... end function (1523662481444358255416089/123136055016926136025 : 45879263313362167877676587357803438/1366400000775319197909622436125 : 1) 54.38012042449717853287 Total time: 14.339 seconds, Total memory usage: 5.16MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:13:55 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-5368489,0]); f := P!Reverse([1324,-1986,-4965,5296,7613]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:13:40 on modular  [Seed = 4159159461]
-------------------------------------

Point [ 1, 153, 2097, 3076 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 658, 4364, 2608 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 5368489*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 59053379*x + 174143046182 over Rational
Field
function(p) ... end function
(7944662176487953593347146/1903712417279072106001 :
-1619046145152801325708229502736620772/83061929233173662801083321659001 : 1)
54.83181099995845642069

Total time: 14.669 seconds, Total memory usage: 16.43MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:14:30 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-85895824,0]);
f := P!Reverse([1324,-1986,-4965,5296,7613]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:14:13 on modular [Seed = 4091787392] ------------------------------------- Point [ 1, 153, 2097, 3076 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 658, 4364, 2608 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 85895824*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 59053379*x + 174143046182 over Rational Field function(p) ... end function (7944662176487953593347146/1903712417279072106001 : -1619046145152801325708229502736620772/83061929233173662801083321659001 : 1) 54.83181099995845642069 Total time: 14.740 seconds, Total memory usage: 16.43MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:15:10 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-9579025,0]); f := P!Reverse([1599,1076,4464,-14504,20484]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 01:14:47 on modular  [Seed = 4243372002]
-------------------------------------

Errors: /bin/sh: line 1:  6058 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:15:38 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9579025,0]);
f := P!Reverse([619,-619,-5571,8666,-2476]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:15:25 on modular [Seed = 4175999939] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 9579025*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 9579025*x over Rational Field function(p) ... end function (2364715294701925341526800399071567541009945049225/1247289334778893808691067164\ 227725677320164 : -363636703287928968386557336616881674844378418720741675478140\ 5469837221725/1392999027550332573930278121630129358552545472030949680674013288 : 1) 109.77604969751709518277 Total time: 12.279 seconds, Total memory usage: 14.71MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:16:15 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-7524049,0]); f := P!Reverse([-633,1055,3798,-1055,-633]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:16:01 on modular  [Seed = 3824396324]
-------------------------------------

Point [ 1, 1401, 4260, 1353 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 1401, 1747, 4654 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 7524049*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 7524049*x over Rational Field
function(p) ... end function
(4950982900159905976809722947863771141300842655625/1804784828524539626618210717\
274077813153069316 : -149859361797510879035780387150616715706296011060433963230\
549909662464675/766722392627138139669738667816657905996073129120960004662732016\
25864 : 1)
109.90526969421654257530

Total time: 13.199 seconds, Total memory usage: 10.98MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:17:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-11068929,0]);
f := P!Reverse([433,-656,-30792,134032,-130988]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:16:43 on modular [Seed = 4026508290] ------------------------------------- Point [ 1, 4184, 5775, 2586 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4396, 3143, 2537 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 11068929*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 11068929*x over Rational Field function(p) ... end function (1850673046387662283186060232052946612032884143798332/6678611134650641973977202\ 5295762624525837675409 : -79039023137433365130978350751621626889201222215805478\ 450780757983734274609410/172595407568661114408206876089484059694060777855259694\ 50762655786815673 : 1) 109.99016948899851797705 Total time: 18.129 seconds, Total memory usage: 14.51MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:17:45 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-43864129,0]); f := P!Reverse([2433,-5,981,-3418,4476]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 01:17:24 on modular  [Seed = 3925451355]
-------------------------------------

Errors: /bin/sh: line 1:  6079 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:18:04 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-43864129,0]);
f := P!Reverse([6265,8592,-37590,-8592,6265]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:17:59 on modular [Seed = 2508578756] ------------------------------------- FourDescent( f: 6265*x^4 + 8592*x^3 - 37590*x^2 - 8592*x + 6265 ) Minimise( F: [ [8356004979 16714241110140 33015084926899425 5555878838248... ) MinimiseFDAtPrime( fd_in: [ [759788640704681326926787991280 77878415069085926012673253..., prime: 179 ) MinimiseFDOnceAtPrime( fd_in: [ [3050193112007533404493132698816 6734974097150684610363535..., prime: 179 ) BoxMinimiseK1( fd_in: [ [3050193112007533404493132698816 6734974097150684610363535..., prime: 179 ) Extend3ToUnimodular( cc: [ ( 0 1 0 161), ( 1 0 0 99), ( 1 0 0 151) ] ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/utils.m", line 342, column 21: >> assert "Could not extend three rows to unimodular matri ^ Runtime error in assert: Logical expected >> F := S; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 43864129*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 43864129*x over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 4.230 seconds, Total memory usage: 7.00MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:20:20 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-43864129,0]);
f := P!Reverse([77,20,-132114,2823764,-16427711]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:20:02 on modular [Seed = 2559103564] ------------------------------------- Point [ 1, 1804, 5191, 5688 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 43864129*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 43864129*x over Rational Field function(p) ... end function (7345695215819022741501804448200688167700171268456412/7321083499804869057864448\ 3252712973743302998169 : -62820467584220372335312005390931421466663991426212097\ 9277328205973806394014950/19809022271215875684023872047605649732225144854884068\ 018386627051306947 : 1) 110.65711168152799359631 Total time: 17.579 seconds, Total memory usage: 9.19MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:21:05 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-13242321,0]); f := P!Reverse([1213,0,0,0,43668]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:20:46 on modular  [Seed = 2224344700]
-------------------------------------

Point [ 1, 321, 3013, 3550 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 13242321*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 13242321*x over Rational Field
function(p) ... end function
(-1793893405688271364276516555834218314670099215556/752148235473927554940788153\
938589942457325921 : -276878597408117963260395098125229520865598186534870210224\
5596273063767410/20627906845736772481419305474935492410498356892283993926437192\
123281 : 1)
110.67845659671796454404

Total time: 14.140 seconds, Total memory usage: 5.40MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:21:42 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-34281025,0]);
f := P!Reverse([1171,-1171,-10539,16394,-4684]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:21:29 on modular [Seed = 2156972559] ------------------------------------- Point [ 1, 4754, 4519, 2291 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4754, 1488, 3716 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 34281025*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 34281025*x over Rational Field function(p) ... end function (7271173224333835986847717587132006945004616580625/3831848609915275911146806784\ 88909360110884 : -1960679987524231745768635776354659122261798371716801558931672\ 9876857828625/237198814275549164529497284518210233774021571959814771747383848 : 1) 110.89870518535919075020 Total time: 12.660 seconds, Total memory usage: 10.20MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:22:15 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-88303609,0]); f := P!Reverse([10817,6080,-62502,103632,343657]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 01:21:54 on modular  [Seed = 2342240559]
-------------------------------------

Errors: /bin/sh: line 1:  6109 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:22:43 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-88303609,0]);
f := P!Reverse([9397,0,-56382,-150352,385277]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:22:29 on modular [Seed = 3081239284] ------------------------------------- Point [ 1, 1120, 4586, 4969 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 1895, 4772, 2364 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3045, 5618, 1845 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4849, 1982, 63 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 88303609*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 971339699*x + 11617046192822 over Rational Field function(p) ... end function (-35742269032957154728871/107884796281050390625 : 3871871896521712691123090037356952242/1120573554048160630984619140625 : 1) 55.65978220481324711954 Total time: 14.429 seconds, Total memory usage: 5.16MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:23:23 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-17098225,0]); f := P!Reverse([209,-195,135,-1950,20900]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 01:23:02 on modular  [Seed = 2980183249]
-------------------------------------

Errors: /bin/sh: line 1:  6119 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:23:31 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-18167,19240,-99012,51504,-109372]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:23:30 on modular [Seed = 3182293177] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 0.830 seconds, Total memory usage: 4.80MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:23:51 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:23:47 on modular [Seed = 3114923148] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.540 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:24:32 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17098225,0]);
f := P!Reverse([209,-195,135,-1950,20900]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 01:24:11 on modular [Seed = 2780162184] ------------------------------------- Errors: /bin/sh: line 1: 6131 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:25:03 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-17098225,0]); f := P!Reverse([-2481,3308,39696,46312,9924]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:24:49 on modular  [Seed = 2864375645]
-------------------------------------

Point [ 1, 5762, 1953, 3822 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 17098225*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 17098225*x over Rational Field
function(p) ... end function
(13237971522142569068784047240379485440556194026025/235303795743093727460721430\
0940864608149402729 : 326595302117403917194323196256699749349443521357634620869\
01618270865751900/1141414537034273908481280428125995105714239887949352026716892\
95300683 : 1)
111.42179516986232101771

Total time: 14.410 seconds, Total memory usage: 18.53MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:25:37 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-25959025,0]);
f := P!Reverse([1019,-1019,-9171,14266,-4076]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:25:24 on modular [Seed = 1497961668] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 25959025*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 25959025*x over Rational Field function(p) ... end function (12836004137155692733633917363478621794744379909225/672234548867598321937784675\ 9209160558682244 : -45987862749456380544834100765331861299058972542212642138885\ 228530378652525/174293520954432830818575249924486472892796006808590233453943404\ 72 : 1) 111.46811868393065481086 Total time: 13.949 seconds, Total memory usage: 22.77MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:26:12 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-41049649,0]); f := P!Reverse([3457,-1356,-42546,44148,-467]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

P

Output: Magma V2.11-6     Wed Sep 22 2004 01:25:55 on modular  [Seed = 1565331687]
-------------------------------------

Point [ 1, 1402, 202, 1809 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 5258, 1326, 5195 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 41049649*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 41049649*x over Rational Field
function(p) ... end function
(23875754268945413386513567410959921649652498615144988/372573277480166138776089\
6146698585436417672574241 : -75379809878733817280645841892510957432704899561611\
072387020226717542320588490/719146801779589346102022115160906236779544782422099\
4603128648651104198961 : 1)
112.18607370252978228108
Univariate Polynomial Ring in x over Integer Ring

Total time: 17.410 seconds, Total memory usage: 7.19MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:26:57 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-30261001,0]);
f := P!Reverse([4121,4720,-19926,-146496,273121]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 01:26:36 on modular [Seed = 1363221764] ------------------------------------- Errors: /bin/sh: line 1: 6152 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:27:24 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-30261001,0]); f := P!Reverse([5501,0,-33006,-88016,225541]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:27:10 on modular  [Seed = 1430591778]
-------------------------------------

Point [ 1, 2324, 2587, 5460 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 30261001*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 332871011*x + 2330520731014 over Rational
Field
function(p) ... end function
(9343161079123357026296169/979258561047071490025 :
4659383790535838518940639345328607678/30644043171430387630534272731125 : 1)
56.38213430865890529730

Total time: 13.929 seconds, Total memory usage: 5.18MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:27:57 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-20620681,0]);
f := P!Reverse([-95,-76,212496,4947144,31048052]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:27:42 on modular [Seed = 1247413853] ------------------------------------- Point [ 1, 3754, 2613, 2140 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4033, 3988, 5930 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 20620681*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 226827491*x + 1310939173894 over Rational Field function(p) ... end function (1984990277802640835856544521/153060084791621225672281 : 44427518392082649253292267260447399505362/59881534983262773670566896402454179 : 1) 56.42725344998736147772 Total time: 14.939 seconds, Total memory usage: 7.97MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:28:27 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-19114384,0]); f := P!Reverse([1093,0,-6558,-17488,44813]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:28:13 on modular  [Seed = 1314783866]
-------------------------------------

Point [ 1, 4613, 3614, 3274 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 5115, 5001, 3936 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 19114384*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 13141139*x + 18280518998 over Rational
Field
function(p) ... end function
(12493251233560917444763441/6396350846877039790681 :
-4115201667608471287859832462212724410/511562164051420879260293302467421 : 1)
56.56757198997087243697

Total time: 13.730 seconds, Total memory usage: 5.17MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:29:03 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-96766569,0]);
f := P!Reverse([1093,0,-6558,-17488,44813]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:28:49 on modular [Seed = 1112673930] ------------------------------------- Point [ 1, 4613, 3614, 3274 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5115, 5001, 3936 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 96766569*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 13141139*x + 18280518998 over Rational Field function(p) ... end function (12493251233560917444763441/6396350846877039790681 : -4115201667608471287859832462212724410/511562164051420879260293302467421 : 1) 56.56757198997087243697 Total time: 13.730 seconds, Total memory usage: 5.17MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:29:40 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-2184484,0]); f := P!Reverse([2217,-2956,-13302,14780,31777]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:29:27 on modular  [Seed = 2053781140]
-------------------------------------

Point [ 1, 2461, 2694, 1854 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3123, 4931, 722 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3637, 5786, 736 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 2184484*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 24029324*x + 45201342928 over Rational
Field
function(p) ... end function
(27638865237638600831303626/11569272938773110891009 :
47059847325829594264136367133295322488/1244397415383306410636514159915777 : 1)
56.80767169151527440362

Total time: 13.789 seconds, Total memory usage: 11.88MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:30:16 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-34951744,0]);
f := P!Reverse([2217,-2956,-13302,14780,31777]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:30:02 on modular [Seed = 2121151229] ------------------------------------- Point [ 1, 2461, 2694, 1854 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3123, 4931, 722 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3637, 5786, 736 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 34951744*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 24029324*x + 45201342928 over Rational Field function(p) ... end function (27638865237638600831303626/11569272938773110891009 : 47059847325829594264136367133295322488/1244397415383306410636514159915777 : 1) 56.80767169151527440362 Total time: 13.759 seconds, Total memory usage: 11.88MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:30:50 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-65529025,0]); f := P!Reverse([1619,-1619,-14571,22666,-6476]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:30:36 on modular  [Seed = 1919041239]
-------------------------------------

Point [ 1, 198, 5475, 1499 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3014, 1559, 248 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 65529025*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 65529025*x over Rational Field
function(p) ... end function
(266411101290079019555563790481074871345176848603225/92628053213400635061470725\
6700411030151764644 : 434666722764493354999096743146701371639304603240739766554\
4860166950617120725/28191215712741299802866964709365690105006822887811890736021\
053762728 : 1)
114.51241806835466263692

Total time: 13.710 seconds, Total memory usage: 10.11MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:31:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-65626201,0]);
f := P!Reverse([8101,0,-48606,-129616,332141]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:31:19 on modular [Seed = 1803232277] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 65626201*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 721888211*x + 7442929960214 over Rational Field function(p) ... end function (-4373320558741126449179351/602486558740473014689 : 51865952943795159725275845299778936386/14788395050440919912695183152113 : 1) 57.44302800108867046446 Total time: 14.009 seconds, Total memory usage: 5.16MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:32:09 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-42994249,0]); f := P!Reverse([1577,1328,-17181,-4482,58432]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:31:53 on modular  [Seed = 1735862391]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 42994249*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 472936739*x + 3946786069702 over Rational
Field
function(p) ... end function
(840522174356793793470600249/85898508140181721071616 :
12737058465568703003238907002316565570285/25175518964325411435013781181169664 :
1)
57.60665417602723437084

Total time: 15.660 seconds, Total memory usage: 20.01MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:32:23 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-31775769,0]);
f := P!Reverse([-20268,1848,-61920,2316,-53271]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:32:22 on modular [Seed = 453727268] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 31775769*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 349533459*x + 2507680137942 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.740 seconds, Total memory usage: 5.02MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:32:39 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-31775769,0]);
f := P!Reverse([-24175,34408,-81438,52888,-53791]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:32:37 on modular [Seed = 521097267] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 31775769*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 349533459*x + 2507680137942 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 2.490 seconds, Total memory usage: 4.74MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:33:13 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-99480676,0]);
f := P!Reverse([14961,-19948,-89766,99740,214441]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:32:58 on modular [Seed = 318987456] ------------------------------------- Point [ 1, 790, 1718, 3772 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2693, 5269, 2012 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5802, 1539, 1235 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 99480676*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 1094287436*x + 13891083673936 over Rational Field function(p) ... end function (84410057676695873420234410/4869249731262930992521 : -122862450975023191653426245481408133944/339776292695300511175214117657819 : 1) 57.70980883016325435619 Total time: 14.490 seconds, Total memory usage: 5.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:33:48 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-13942756,0]); f := P!Reverse([5601,-7468,-33606,37340,80281]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:33:34 on modular  [Seed = 386357472]
-------------------------------------

Point [ 1, 4197, 1413, 679 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 13942756*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 153370316*x + 728871512656 over Rational
Field
function(p) ... end function
(65602688812373540717309290/11431335625575110797561 :
-237335242183442888503244193860804484936/1222208961749691457055169276856691 : 1)
57.79821793171392840804

Total time: 13.929 seconds, Total memory usage: 5.34MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:34:24 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-98208100,0]);
f := P!Reverse([395,380,8040,-216480,618025]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:34:05 on modular [Seed = 203178904] ------------------------------------- Point [ 1, 4109, 1190, 2932 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5667, 2625, 1159 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 98208100*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 1080289100*x + 13625391794000 over Rational Field function(p) ... end function (14523679969426107968282165104/1432827019194306582757681 : -3306482181678911213071386839317637634965092/1715104726565097608094982498268531\ 671 : 1) 57.91275295069011264104 Total time: 18.239 seconds, Total memory usage: 28.25MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:34:55 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-10220809,0]); f := P!Reverse([2502,3892,-6255,-6950,7228]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:34:42 on modular  [Seed = 51596456]
-------------------------------------

Point [ 1, 3850, 4738, 306 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3961, 3640, 5211 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4215, 490, 2505 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 10220809*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 112428899*x + 457462969222 over Rational
Field
function(p) ... end function
(788506642332604159278041569/135938749520191850261604 :
1100504385923020130929814237799481408039/50120443571541719639727187449735192 :
1)
58.21063313001514671896

Total time: 13.810 seconds, Total memory usage: 9.14MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:35:34 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-61058596,0]);
f := P!Reverse([11721,-15628,-70326,78140,168001]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:35:19 on modular [Seed = 118966601] ------------------------------------- Point [ 1, 590, 5605, 2222 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3928, 2769, 2371 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 61058596*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 671644556*x + 6679566168016 over Rational Field function(p) ... end function (7739416930653409291837690/4296178950586821244521 : -658922248365632636134529161088824468456/281594095603338645435988014399819 : 1) 58.21314170011669375526 Total time: 14.519 seconds, Total memory usage: 5.34MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:36:07 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-90592324,0]); f := P!Reverse([17,-26,42426,986336,5454152]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:35:46 on modular  [Seed = 992703824]
-------------------------------------

Point [ 1, 233, 931, 4875 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 288, 1341, 2229 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 4173, 16, 747 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 90592324*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 996515564*x + 12071608357648 over Rational
Field
function(p) ... end function
(171228059022770607552029271741/9876405843148827221581225 :
2408129220003314904194294200880892596175211/31038333242112224096438830955964399\
125 : 1)
58.24265858652640304171

Total time: 20.760 seconds, Total memory usage: 6.69MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:36:41 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-15665764,0]);
f := P!Reverse([5937,-7916,-35622,39580,85097]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:36:27 on modular [Seed = 1060073789] ------------------------------------- Point [ 1, 98, 2247, 3839 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3509, 4132, 4140 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5557, 4504, 4448 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 15665764*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 172323404*x + 868071314768 over Rational Field function(p) ... end function (193252919284925465824578026/27249446706831571390249 : -231836387182950623901026373249399807048/4498176918013684191891824818742443 : 1) 58.42973760870366106701 Total time: 14.060 seconds, Total memory usage: 5.34MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:37:08 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-88322404,0]); f := P!Reverse([814,-1184,-22422,-3108,248048]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:36:52 on modular  [Seed = 874805785]
-------------------------------------

Point [ 1, 177, 3780, 626 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3870, 2097, 5409 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4366, 2340, 575 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 88322404*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 971546444*x + 11620755339088 over Rational
Field
function(p) ... end function
(1138569503031496383660092016/258410632984035738925849 :
-357957673953660441925423546394634711969652/13136073501066137513912687055466624\
3 : 1)
58.43627110833756432839

Total time: 15.089 seconds, Total memory usage: 6.43MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:37:40 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-46199209,0]);
f := P!Reverse([2913,3884,-93216,-147592,400052]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:37:25 on modular [Seed = 674784996] ------------------------------------- Point [ 1, 2028, 571, 3921 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2953, 5778, 563 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5986, 4670, 650 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 46199209*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 508191299*x + 4396224330022 over Rational Field function(p) ... end function (776445436026786457369444321/53709762896116913182041 : 3312160553601468185660051672527662275918/12447434589253672200458310903333411 : 1) 58.72282419915800488752 Total time: 14.439 seconds, Total memory usage: 16.74MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:38:08 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-55905529,0]); f := P!Reverse([7477,0,-44862,-119632,306557]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:37:53 on modular  [Seed = 742154948]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 55905529*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 614960819*x + 5852078964662 over Rational
Field
function(p) ... end function
(16688548895956756240372441/3645467897810329734529 :
389579360377711302720608835782109248110/220105004543514459817988966116417 : 1)
58.73732349095891436263

Total time: 14.259 seconds, Total memory usage: 5.16MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:38:40 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-6061444,0]);
f := P!Reverse([13,12,6822,182480,1026008]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:38:24 on modular [Seed = 573729963] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 6061444*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 66675884*x + 208925851792 over Rational Field function(p) ... end function (57472743242691458076482912961/14154372241220431225614400 : 3817053797989256003438170341417670724082209/53251999490929872860556035918609728\ 000 : 1) 58.83669359659547382079 Total time: 16.559 seconds, Total memory usage: 5.56MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:39:12 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-96983104,0]); f := P!Reverse([13,12,6822,182480,1026008]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:38:56 on modular  [Seed = 641099919]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 96983104*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 66675884*x + 208925851792 over Rational
Field
function(p) ... end function
(57472743242691458076482912961/14154372241220431225614400 :
3817053797989256003438170341417670724082209/53251999490929872860556035918609728\
000 : 1)
58.83669359659547382079

Total time: 16.600 seconds, Total memory usage: 5.56MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:39:48 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-79263409,0]);
f := P!Reverse([1393,577,6822,-12401,10157]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 01:39:27 on modular [Seed = 3721235595] ------------------------------------- Errors: /bin/sh: line 1: 6276 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:40:17 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-79263409,0]); f := P!Reverse([-6447,-1228,73680,100696,25788]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:40:00 on modular  [Seed = 3535963067]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 79263409*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 79263409*x over Rational Field
function(p) ... end function
(51102724579449659170700319827062678793878253334060025/286613935248259850861280\
917824494423592902985881 : 1153782607714058553798601401955348063790873759570100\
9459570005320790247495813620/15344260154354108354350760545838104975110517898411\
0868639827681323612221 : 1)
117.67422041960155354445

Total time: 17.350 seconds, Total memory usage: 15.62MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:40:46 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-63984001,0]);
f := P!Reverse([-255,-448,126936,1544368,4940244]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:40:41 on modular [Seed = 3603335126] ------------------------------------- FourDescent( f: -255*x^4 - 448*x^3 + 126936*x^2 + 1544368*x + 4940244 ) ReduceFD( fd: [ [7738572330406859313658073 13182073763343474203837816 5018... ) StollReduce( desc: [ [ 0 3 1 0] [ 3 3 1 6] [ 1 1 -5 -1] [ 0 6 -1 -7], ... ) Covariant( mat1: [ 0 3 1 0] [ 3 3 1 6] [ 1 1 -5 -1] [ 0 6 -1 -7], mat2: [ 20 -16 16 3] [-16 -17 4 -3] [ 16 4 -15 -5] [ 3 ... ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line 350, column 33: >> covmat *:= 1/Sqrt(&+[Norm(c) : c in Eltseq(covmat)]); ^ Runtime error in '/': Division by zero >> F := S; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 63984001*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 63984001*x over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 5.030 seconds, Total memory usage: 15.50MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:41:40 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-63984001,0]);
f := P!Reverse([842,0,0,0,303962]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:41:26 on modular [Seed = 3403324181] ------------------------------------- Point [ 1, 1289, 2006, 248 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 63984001*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 63984001*x over Rational Field function(p) ... end function (-31719941992926172360762043571265828845496606508754529/51549896110189748877764\ 40236450684252940692624521 : -4692379491527593019687291981249945773748745565219\ 644952813217118675116513319420/117041988468047095584403888606802303268365570995\ 09226472630992751139036069 : 1) 118.14103977765475406158 Total time: 14.890 seconds, Total memory usage: 9.01MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:42:17 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-48205249,0]); f := P!Reverse([917,-1441,-18864,57509,-41789]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:42:04 on modular  [Seed = 3285422646]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 48205249*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 48205249*x over Rational Field
function(p) ... end function
(104558835299325501589990033922674364411687811900765625/25684448668457434765296\
39747482038179567446285284 : 33314327238213511653410358793165958214253688843594\
352655976219169305871422182875/411628438588650373302705123066278378800833198094\
7745541563358164098220952 : 1)
118.18479136295680120838

Total time: 13.519 seconds, Total memory usage: 7.85MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:42:53 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-21279769,0]);
f := P!Reverse([2636,-3954,-9885,10544,15157]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:42:38 on modular [Seed = 4192839790] ------------------------------------- Point [ 1, 942, 5292, 5009 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4773, 1233, 2155 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 21279769*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 234077459*x + 1374290041558 over Rational Field function(p) ... end function (746647820528877553703863866/89756372201355673749049 : -1405739460028827157884941573829495376288/26890441717247583590732965502989843 : 1) 59.37020066233371551334 Total time: 14.439 seconds, Total memory usage: 20.33MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:43:33 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-22477081,0]); f := P!Reverse([1320,1408,-9867,3619,41646]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:43:16 on modular  [Seed = 4277055315]
-------------------------------------

Point [ 1, 4392, 3576, 3007 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 22477081*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 247247891*x + 1491893774294 over Rational
Field
function(p) ... end function
(49894654284767510936823546974/5778514172753890461174649 :
386243607891556061826661368614542582139286/138907045517867581943814254242078051\
07 : 1)
59.41186187897886128439

Total time: 17.460 seconds, Total memory usage: 14.95MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:44:10 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-25867396,0]);
f := P!Reverse([188,56,-12330,15728,312162]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:43:53 on modular [Seed = 4074939058] ------------------------------------- Point [ 1, 982, 5129, 4827 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 25867396*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 284541356*x + 1841862064784 over Rational Field function(p) ... end function (519723800191285111859197250300/58709353763318625227757121 : 58136102215711814691076208328117200221798032/4498429825111247244972739628186948\ 83169 : 1) 59.45569431351420774944 Total time: 16.940 seconds, Total memory usage: 6.89MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:44:41 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-7557001,0]); f := P!Reverse([2749,0,-16494,-43984,112709]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:44:27 on modular  [Seed = 3925457291]
-------------------------------------

Point [ 1, 3127, 5539, 3774 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3486, 2093, 3054 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 7557001*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 83127011*x + 290838740486 over Rational
Field
function(p) ... end function
(23934010803177214169603713/23467275257234323496881 :
1636079040360479162141113965800909475190/3594959491628157543060891244063721 : 1)
59.68644344423122305443

Total time: 14.199 seconds, Total memory usage: 5.21MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:45:10 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-4422609,0]);
f := P!Reverse([-83,68,119166,2395844,13553713]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:44:55 on modular [Seed = 3992829411] ------------------------------------- Point [ 1, 3118, 2287, 1337 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4024, 1940, 1651 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4929, 4156, 2543 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5751, 668, 5584 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5774, 5173, 1193 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 4422609*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 4422609*x over Rational Field function(p) ... end function (18091823229125302953979861598362235142746693830531807932/937087700477036981193\ 867967401234426837331998700681 : 7649474568169365817738342390669189442262879330\ 7311977277035708595222733996478705310/28686023940614303520695723718763674800130\ 185173855063175545667939196523473829 : 1) 119.63184174375604129636 Total time: 15.849 seconds, Total memory usage: 18.13MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:45:50 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-70761744,0]); f := P!Reverse([1402,0,0,0,12618]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:45:35 on modular  [Seed = 3790713287]
-------------------------------------

Point [ 1, 670, 1877, 2929 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 70761744*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 4422609*x over Rational Field
function(p) ... end function
(-22997329236836082999328327051237431017272160680833489/13609061074511795000709\
241491034159571229744495025 : 2583459169636267644385363593730361667991226643587\
262261600069647531422177495884/502044535830672718959716612438269113615435489776\
51080534832207961496443625 : 1)
119.63184174375604129636

Total time: 14.419 seconds, Total memory usage: 11.30MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:46:39 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-25633969,0]);
f := P!Reverse([5977,3700,864,-392,17084]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 01:46:17 on modular [Seed = 2575944041] ------------------------------------- Errors: /bin/sh: line 1: 6336 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:47:08 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-25633969,0]); f := P!Reverse([1245,913,-7470,-913,1245]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:46:55 on modular  [Seed = 2643315979]
-------------------------------------

Elliptic Curve defined by y^2 = x^3 - 25633969*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 25633969*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 13.449 seconds, Total memory usage: 15.68MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:47:31 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-25633969,0]); f := P!Reverse([61,0,0,0,1680916]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:47:29 on modular  [Seed = 2441199929]
-------------------------------------

FourDescent(
f: 61*x^4 + 1680916
)
Minimise(
F: [ [4199 874496 -617686 -2257942525396] [874496 -617686 -2257...
)
MinimiseFDAtPrime(
fd_in: [ [   -50334604196615 -10567286533036411      -281850906077 ...,
prime: 61
)
MinimiseFDOnceAtPrime(
fd_in: [ [   -295997315  -75362885174      -1066901        579622] ...,
prime: 61
)
BoxMinimiseK1(
fd_in: [ [   -295997315  -75362885174      -1066901        579622] ...,
prime: 61
)
Extend3ToUnimodular(
cc: [ ( 0  1  0 39), ( 1  0  0 45), ( 1  0  0 53) ]
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/utils.m", line 342,
column 21:
>>                     assert "Could not extend three rows to unimodular matri
^
Runtime error in assert: Logical expected

>> F := S;
^
User error: Identifier 'S' has not been declared or assigned

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 25633969*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 25633969*x over Rational Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 1.850 seconds, Total memory usage: 14.93MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:48:14 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-25633969,0]); f := P!Reverse([-22,24,198828,10060392,142340132]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:47:57 on modular  [Seed = 2508572353]
-------------------------------------

Point [ 1, 312, 3750, 3116 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 2528, 381, 1014 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 25633969*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 25633969*x over Rational Field
function(p) ... end function
(65242291784703778413839091044004227379396655995950530847/713955713384508231262\
9726742851840358400218950185169 : 438701311372187022716417240340188314976310980\
044216017083300894934185347519853262060/603263306345357997657501007160596312297\
586342579372969641557084464785974515303 : 1)
119.85493125330994246269

Total time: 16.890 seconds, Total memory usage: 17.16MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:48:58 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-64754209,0]);
f := P!Reverse([157,-273,351,-7098,106132]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:48:41 on modular [Seed = 2308561641] ------------------------------------- Point [ 1, 1829, 1431, 2083 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5513, 909, 555 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 64754209*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 64754209*x over Rational Field function(p) ... end function (-45285896890233834029102897139985076418791907304737351783/10932453344466370776\ 376623582286938853169306788311364 : -507552500203147318560558781600148341431228\ 158480521305030798798512102115138550794315/114307953355332566489459046388672228\ 0259769570479134949259003472922781729741112 : 1) 120.024030507225035080409 Total time: 17.210 seconds, Total memory usage: 15.41MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:49:42 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-45037521,0]); f := P!Reverse([1081,2040,-41616,12240,38916]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:49:23 on modular  [Seed = 2173817531]
-------------------------------------

Point [ 1, 558, 4518, 4740 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 45037521*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 45037521*x over Rational Field
function(p) ... end function
(83784994599213855113054598997160538770492386205206309596/653325166365304083176\
6178144821086189336805323590289 : 653528903170305244790907200189871517262592456\
815477094663096989274192931838797039770/528073144327223097059867803209454276981\
654988332241454478297161763640780481337 : 1)
120.15965904245948081552

Total time: 18.809 seconds, Total memory usage: 10.93MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:50:22 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-50438404,0]);
f := P!Reverse([-119,-60,474450,16361340,158001961]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:50:05 on modular [Seed = 2224346960] ------------------------------------- Point [ 1, 136, 3861, 4212 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 515, 3706, 5563 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 50438404*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 50438404*x over Rational Field function(p) ... end function (278897970750770754767907161581546701324181402171348844150/37151547727687446103\ 62939968165099266726531966320289 : -4636772713942924084582278390426850248852245\ 244315734095146086590508383036838514244920/226446371804438031191189134211085829\ 691078693116253853714915834577049227883663 : 1) 120.79754622480609782542 Total time: 16.870 seconds, Total memory usage: 11.46MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:51:00 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12538681,0]); f := P!Reverse([3541,0,-21246,-56656,145181]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:50:46 on modular  [Seed = 3098078039]
-------------------------------------

Point [ 1, 565, 557, 4459 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 2678, 3072, 3450 ] was singular mod 6007 and ignored at the #2 lift
Elliptic Curve defined by y^2 = x^3 - 12538681*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 137925491*x + 621592571894 over Rational
Field
function(p) ... end function
(167215874241103285418890609/47791989267795753942025 :
-4455391367022098737841729605309786835398/10447987915269512515071655082865125 :
1)
60.39923730477864438626

Total time: 13.939 seconds, Total memory usage: 5.18MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:51:38 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9132484,0]);
f := P!Reverse([3325,-1076,-8052,856,5859]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 01:51:17 on modular [Seed = 3165450032] ------------------------------------- Errors: /bin/sh: line 1: 6373 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:52:10 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-9132484,0]); f := P!Reverse([563,488,-3690,14432,45720]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:51:53 on modular  [Seed = 3047548437]
-------------------------------------

Point [ 1, 1875, 1020, 2856 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 9132484*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 100457324*x + 386377133072 over Rational
Field
function(p) ... end function
(-318049169559472523585592601856/38114391747242939901075801 :
-188773670589691884361545352646702928338400140/23530626487562088277612070823057\
6572451 : 1)
60.51254063960513462916

Total time: 16.879 seconds, Total memory usage: 9.50MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:52:45 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-53421481,0]);
f := P!Reverse([7309,0,-43854,-116944,299669]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:52:31 on modular [Seed = 2847538159] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 53421481*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 587636291*x + 5466406464806 over Rational Field function(p) ... end function (-242651279897209014670516991/9685849925434791293761 : -2014265000156469702816697488875477409046/953249538240350905063650486166241 : 1) 60.52741863727969473529 Total time: 14.250 seconds, Total memory usage: 5.18MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:53:24 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-10029889,0]); f := P!Reverse([302,-96,-429,37020,88339]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 01:53:03 on modular  [Seed = 2948595145]
-------------------------------------

Errors: /bin/sh: line 1:  6390 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:53:59 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-10029889,0]);
f := P!Reverse([3154,3432,-7233,-4782,6062]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 01:53:38 on modular [Seed = 2746479000] ------------------------------------- Point [ 1, 311, 538, 2184 ] was singular mod 6007 and ignored at the #3 lift Errors: /bin/sh: line 1: 6394 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:54:27 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-10029889,0]); f := P!Reverse([3154,3432,-7233,-4782,6062]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:54:17 on modular  [Seed = 2797007990]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 3 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 10029889*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 110328779*x + 444705218482 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 10.060 seconds, Total memory usage: 12.90MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:55:04 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-10582009,0]); f := P!Reverse([2813,1632,-16110,-69296,147781]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 01:54:43 on modular  [Seed = 1548488359]
-------------------------------------

Errors: /bin/sh: line 1:  6404 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:55:31 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-10582009,0]);
f := P!Reverse([3253,0,-19518,-52048,133373]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:55:17 on modular [Seed = 1396900302] ------------------------------------- Point [ 1, 3802, 5926, 261 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 10582009*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 116402099*x + 481925853878 over Rational Field function(p) ... end function (-168613415471336436947308031/53930040804376416775225 : 11308477283377482458237604061758841910422/12524088369582467981449206053222125 : 1) 61.038787295330436677431 Total time: 13.750 seconds, Total memory usage: 5.17MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:56:06 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-79798489,0]); f := P!Reverse([2353,2692,97440,791624,1382356]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 01:55:45 on modular  [Seed = 1464272366]
-------------------------------------

Errors: /bin/sh: line 1:  6415 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:56:31 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-79798489,0]);
f := P!Reverse([8933,0,-53598,-142928,366253]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:56:17 on modular [Seed = 1264262674] ------------------------------------- Point [ 1, 142, 3498, 123 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 1678, 1634, 5603 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2488, 4024, 1347 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4611, 2495, 5524 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 79798489*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 877783379*x + 9979758631318 over Rational Field function(p) ... end function (1210729545522395799776377041/81462903676705492229401 : 10825356915970238066529765146005456458790/23250903256740100645688459098479101 : 1) 61.37420878310854277515 Total time: 14.050 seconds, Total memory usage: 5.16MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:57:04 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-51108201,0]); f := P!Reverse([981,-1200,-107406,297888,1221261]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:56:47 on modular  [Seed = 1331632648]
-------------------------------------

Point [ 1, 735, 890, 3418 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 1173, 4518, 2078 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 5406, 5529, 4395 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 51108201*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 562190211*x + 5115215405286 over Rational
Field
function(p) ... end function
(4030025291102881875571363651801/269146839559072161472706281 :
1029739186813127513614483457135037389296372334/44155410512853433370373083766117\
40530571 : 1)
61.41800317663158637060

Total time: 16.989 seconds, Total memory usage: 6.06MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:57:38 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-28955161,0]);
f := P!Reverse([1165,-1488,85266,407008,443573]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 01:57:17 on modular [Seed = 1129518630] ------------------------------------- Errors: /bin/sh: line 1: 6427 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:58:05 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-28955161,0]); f := P!Reverse([5381,0,-32286,-86096,220621]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:57:51 on modular  [Seed = 2053779325]
-------------------------------------

Point [ 1, 1731, 5076, 377 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4199, 3182, 4719 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 28955161*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 318506771*x + 2181308098774 over Rational
Field
function(p) ... end function
(2002825629358604277366966969/205075535531908807990225 :
-4347709860551087678174315403639645065422/92869002641196577619393711326809625 :
1)
61.58377048050144964008

Total time: 14.099 seconds, Total memory usage: 5.25MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:58:34 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-81830116,0]);
f := P!Reverse([13569,-18092,-81414,90460,194489]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:58:19 on modular [Seed = 2121149277] ------------------------------------- Point [ 1, 2776, 2510, 5705 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3591, 437, 2910 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 81830116*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 900131276*x + 10363293210704 over Rational Field function(p) ... end function (54516675431553822750035050/107033687906424282196281 : 110206423186705703605703878151601820526008/35017144984351222581245496313415571 : 1) 61.62851072701781163232 Total time: 14.750 seconds, Total memory usage: 5.38MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 01:59:17 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-44582329,0]); f := P!Reverse([2717,1496,-17127,-8492,34958]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 01:59:01 on modular  [Seed = 1919035279]
-------------------------------------

Point [ 1, 2617, 3457, 1669 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 44582329*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 490405619*x + 4167466950262 over Rational
Field
function(p) ... end function
(521526478899860773668466277694/45699128613902824008457369 :
-73864950839177883394607625192128755348006486/308931276274596349773021160160855\
297597 : 1)
61.64374022090034088705

Total time: 16.160 seconds, Total memory usage: 13.92MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 01:59:51 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-70274689,0]);
f := P!Reverse([202,0,0,0,1391578]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 01:59:36 on modular [Seed = 2003247847] ------------------------------------- Point [ 1, 450, 5214, 2954 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4054, 3475, 4613 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4394, 3520, 39 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 70274689*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 70274689*x over Rational Field function(p) ... end function (-175261399097392868553463495422657421628561933065098081/5123711471456396576067\ 391855298087016040198745430025 : -179814062661337421408708069555402629361005398\ 71932122836560386174474620060019952572/3667558065354633081602516831168614937821\ 84115674439341959000420154913045681125 : 1) 123.33612749599205926642 Total time: 14.660 seconds, Total memory usage: 25.20MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:00:28 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-88040689,0]); f := P!Reverse([1706,0,0,0,206426]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:00:13 on modular  [Seed = 1803239134]
-------------------------------------

Point [ 1, 1408, 5286, 4972 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 2106, 819, 4489 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 5000, 970, 3991 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 88040689*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 88040689*x over Rational Field
function(p) ... end function
(-215622941079044570438500268016951353901970398626377225/6137096719468475396406\
22832893874680768070554345561 : -2672067900588208054565301142778772780097887025\
065817211274150694291563831473461980/152035305667541065266223928426108788998052\
90484702478015634648770051718094941 : 1)
123.36267361490166649673

Total time: 14.259 seconds, Total memory usage: 16.18MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:01:06 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-4652649,0]);
f := P!Reverse([405,664,-3975,2784,29482]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:00:48 on modular [Seed = 1651652138] ------------------------------------- Point [ 1, 5330, 2344, 1831 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 4652649*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 51179139*x + 140500694502 over Rational Field function(p) ... end function (597539844657832701656893283854/168070292111876161348605625 : 128593473326330123330745847762585126681306558/217889565245757243807721333775617\ 8078125 : 1) 61.71758195410016867299 Total time: 17.620 seconds, Total memory usage: 16.66MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:01:48 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-74442384,0]); f := P!Reverse([405,664,-3975,2784,29482]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:01:30 on modular  [Seed = 1719022084]
-------------------------------------

Point [ 1, 5330, 2344, 1831 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 74442384*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 51179139*x + 140500694502 over Rational
Field
function(p) ... end function
(597539844657832701656893283854/168070292111876161348605625 :
128593473326330123330745847762585126681306558/217889565245757243807721333775617\
8078125 : 1)
61.71758195410016867299

Total time: 17.640 seconds, Total memory usage: 16.67MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:02:07 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-21427641,0]);
f := P!Reverse([-12963,5760,-51822,12528,-56859]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:02:05 on modular [Seed = 436882975] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 235704051*x + 1388639702646 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.970 seconds, Total memory usage: 5.45MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:02:24 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-21427641,0]);
f := P!Reverse([-5031,4320,-56790,26544,-139679]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:02:22 on modular [Seed = 504252968] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 21427641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 235704051*x + 1388639702646 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 2.270 seconds, Total memory usage: 5.32MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:03:06 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-2627641,0]);
f := P!Reverse([1621,0,-9726,-25936,66461]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:02:52 on modular [Seed = 302139078] ------------------------------------- Point [ 1, 355, 5255, 3602 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 643, 2616, 3031 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 2627641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 28904051*x + 59631684854 over Rational Field function(p) ... end function (-926254167105038403288263351/150772415370393265230769 : 4278584872716934372663878256811003870786/58544060158322161588857220345637353 : 1) 61.81092751992849798625 Total time: 13.919 seconds, Total memory usage: 5.14MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:03:42 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-42042256,0]); f := P!Reverse([1621,0,-9726,-25936,66461]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:03:28 on modular  [Seed = 369509118]
-------------------------------------

Point [ 1, 355, 5255, 3602 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 643, 2616, 3031 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 42042256*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 28904051*x + 59631684854 over Rational
Field
function(p) ... end function
(-926254167105038403288263351/150772415370393265230769 :
4278584872716934372663878256811003870786/58544060158322161588857220345637353 :
1)
61.81092751992849798625

Total time: 13.980 seconds, Total memory usage: 5.14MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:04:16 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-22934521,0]);
f := P!Reverse([4789,0,-28734,-76624,196349]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:04:02 on modular [Seed = 220027271] ------------------------------------- Point [ 1, 3888, 5716, 5782 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 22934521*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 252279731*x + 1537667894966 over Rational Field function(p) ... end function (2684622140619943372793224729/307691228361795817842241 : -4586278828497767748236130663441749911634/170676085397434117172771443348840289 : 1) 61.86095241255383569978 Total time: 14.039 seconds, Total memory usage: 5.20MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:04:49 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-93334921,0]); f := P!Reverse([9661,0,-57966,-154576,396101]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:04:34 on modular  [Seed = 34756264]
-------------------------------------

Point [ 1, 1116, 5577, 2266 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 4350, 822, 4541 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 93334921*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 1026684131*x + 12623921404934 over
Rational Field
function(p) ... end function
(1059581265794505271403670169/88033927069350102733369 :
37034575109198313623514131131407152799794/26120116722372171716382325483676653 :
1)
61.87133087790581242870

Total time: 14.839 seconds, Total memory usage: 5.17MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:05:25 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-10118761,0]);
f := P!Reverse([3181,0,-19086,-50896,130421]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:05:11 on modular [Seed = 102125897] ------------------------------------- Point [ 1, 4668, 2364, 1105 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 10118761*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 111306371*x + 450628902374 over Rational Field function(p) ... end function (1186612161479415325653893689/281512946896911868789225 : 35456376666389615360074290011666075745262/149364558514677472740474449660219125 : 1) 61.87164455368623805497 Total time: 14.289 seconds, Total memory usage: 5.14MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:06:03 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-32982049,0]); f := P!Reverse([3934,-6028,-12285,11292,15533]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:05:42 on modular  [Seed = 992701525]
-------------------------------------

Point [ 1, 3888, 4971, 746 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1:  6499 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:06:37 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-32982049,0]);
f := P!Reverse([122,236,30675,-85670,59288]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:06:16 on modular [Seed = 1060071487] ------------------------------------- Point [ 1, 4299, 284, 4118 ] was singular mod 6007 and ignored at the #1 lift Errors: /bin/sh: line 1: 6503 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:07:12 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-32982049,0]); f := P!Reverse([3934,-6028,-12285,11292,15533]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:07:03 on modular  [Seed = 725318900]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 3 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 32982049*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 362802539*x + 2651822703698 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 8.849 seconds, Total memory usage: 6.81MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:07:50 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58844241,0]); f := P!Reverse([2410,4368,-48672,13104,21690]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:07:29 on modular  [Seed = 792688854]
-------------------------------------

Point [ 1, 1318, 5880, 234 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 1332, 4225, 381 ] was singular mod 6007 and ignored at the #1 lift

Errors: /bin/sh: line 1:  6519 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:08:21 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58844241,0]);
f := P!Reverse([2557,0,0,0,92052]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:08:06 on modular [Seed = 624259771] ------------------------------------- Point [ 1, 4038, 1870, 2798 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 58844241*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 58844241*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 15.089 seconds, Total memory usage: 11.78MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:09:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58844241,0]);
f := P!Reverse([2410,4368,-48672,13104,21690]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:08:40 on modular [Seed = 3653865065] ------------------------------------- Point [ 1, 1067, 701, 5340 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 1799, 606, 5517 ] was singular mod 6007 and ignored at the #1 lift Errors: /bin/sh: line 1: 6529 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:09:35 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-58844241,0]); f := P!Reverse([161,-257,-15075,64926,-52164]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:09:16 on modular  [Seed = 3721235337]
-------------------------------------

Point [ 1, 5279, 2640, 2549 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 58844241*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 58844241*x over Rational Field
function(p) ... end function
(1820205387736361817802673694146412392082006884714579173561/3538871101467079731\
9706309322574857986728096563902084 : -76788479503869291704522056894282289112191\
933081695404875602617953647331428155083034715/665728449281313500721757392777412\
7228163459364230249645587610089379785065443448 : 1)
124.064428413678456308844

Total time: 17.329 seconds, Total memory usage: 19.32MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:11:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-73633561,0]);
f := P!Reverse([8581,0,-51486,-137296,351821]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:10:47 on modular [Seed = 3586491370] ------------------------------------- Point [ 1, 572, 3901, 5473 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2379, 4616, 4278 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3014, 400, 4092 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5716, 5265, 4894 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 73633561*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 809969171*x + 8845894217174 over Rational Field function(p) ... end function (3323704330876287517669139449/212000300181484699923025 : 2858313727997527822287246969180241324082/97612337714692881760394956818097625 : 1) 62.062577276136202897305 Total time: 14.800 seconds, Total memory usage: 5.26MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:11:48 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-52867441,0]); f := P!Reverse([-1814,680,75324,201800,125156]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:11:28 on modular  [Seed = 3386482433]
-------------------------------------

Point [ 1, 118, 2867, 1741 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4026, 5215, 4832 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 52867441*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 52867441*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.839 seconds, Total memory usage: 23.08MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:12:18 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-52867441,0]); f := P!Reverse([825,-121,-24024,64669,-44649]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:12:03 on modular  [Seed = 3453852454]
-------------------------------------

Point [ 1, 2760, 5195, 4029 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 5228, 4868, 5894 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 52867441*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 52867441*x over Rational Field
function(p) ... end function
(567155816022254875722916536397211149640860723992936750625/48048751612876670119\
709109835854326890680447402151716 : 1064005966837234914312720901608447515830253\
1968814277279709596654987745935644631875575/10532298586335160887326011171616211\
623142307746241773191533090716583596168779736 : 1)
124.42008686390347804717

Total time: 15.250 seconds, Total memory usage: 13.25MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:12:53 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-38328481,0]);
f := P!Reverse([1458,1976,-15021,-5584,57505]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:12:36 on modular [Seed = 3251738445] ------------------------------------- Point [ 1, 1355, 790, 5068 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2063, 4599, 5135 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2510, 1180, 5947 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4044, 1728, 552 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 38328481*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 421613291*x + 3322082762194 over Rational Field function(p) ... end function (-4403764405502680198743619267682/193304168021214070356030049 : 2823253250234153542640159521186629897375193440/26875826424571341676167243646112\ 39096593 : 1) 62.25627040807519563259 Total time: 16.750 seconds, Total memory usage: 13.36MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:13:35 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-85174441,0]); f := P!Reverse([5,8,-111750,-539912,541184741]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:13:20 on modular  [Seed = 4175995296]
-------------------------------------

Point [ 1, 2672, 3029, 2870 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 85174441*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 936918851*x + 11005048823846 over Rational
Field
function(p) ... end function
(3840228874608411963026516485201/199817068681977444267709129 :
880965778229659500995684801035135532560612798/282454745296232756999803554530824\
4810117 : 1)
62.40195619815697369858

Total time: 15.080 seconds, Total memory usage: 16.00MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:14:22 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-8288641,0]);
f := P!Reverse([2046,2312,-6813,-3664,8215]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:13:54 on modular [Seed = 4243367302] ------------------------------------- Point [ 1, 504, 5873, 4539 ] was singular mod 6007 and ignored at the #3 lift Errors: /bin/sh: line 1: 6564 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:14:58 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-8288641,0]); f := P!Reverse([354,-536,-3453,-15752,67545]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:14:42 on modular  [Seed = 4058097915]
-------------------------------------

Point [ 1, 200, 5347, 1587 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 2090, 702, 132 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3109, 2339, 4346 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 5321, 1706, 4713 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 8288641*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 91175051*x + 334081964146 over Rational
Field
function(p) ... end function
(4876327022826778797721046578366/1020281624762105596152675625 :
-2821278321359393033970790195037246132588485164/3258968011389634127297684110710\
3631703125 : 1)
62.40939627225183983227

Total time: 15.990 seconds, Total memory usage: 14.61MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:15:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-26853124,0]);
f := P!Reverse([212,8,-12906,14096,282990]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:15:12 on modular [Seed = 4125469917] ------------------------------------- Point [ 1, 3779, 4125, 2127 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3848, 2008, 1080 ] was singular mod 6007 and ignored at the #3 lift Errors: /bin/sh: line 1: 6573 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:16:01 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-26853124,0]); f := P!Reverse([220,8,-13002,-13552,271506]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:15:43 on modular  [Seed = 3925454910]
-------------------------------------

Point [ 1, 357, 5339, 4949 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3619, 5169, 276 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 26853124*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 295384364*x + 1948140439952 over Rational
Field
function(p) ... end function
(8931735773301021757271883804236/1045324447080494098288452049 :
-7408578207855382819004738977876089885874419960/3379688399855827875395079779036\
8524722407 : 1)
62.44600228518309847913

Total time: 17.809 seconds, Total memory usage: 12.39MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:16:43 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-2163841,0]);
f := P!Reverse([389,-508,-3597,1456,12050]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:16:26 on modular [Seed = 3773872386] ------------------------------------- Point [ 1, 667, 4129, 4666 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 2163841*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 23802251*x + 44562141554 over Rational Field function(p) ... end function (-1997072928472936556905244774402/422257058514822729496788169 : 1966116884773485060685812394370980523121206180/86769156789012648169909486906329\ 45368197 : 1) 62.97914533973312956049 Total time: 16.780 seconds, Total memory usage: 7.27MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:17:16 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-34621456,0]); f := P!Reverse([389,-508,-3597,1456,12050]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:16:59 on modular  [Seed = 3841244519]
-------------------------------------

Point [ 1, 667, 4129, 4666 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 34621456*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 23802251*x + 44562141554 over Rational
Field
function(p) ... end function
(-1997072928472936556905244774402/422257058514822729496788169 :
1966116884773485060685812394370980523121206180/86769156789012648169909486906329\
45368197 : 1)
62.97914533973312956049

Total time: 16.629 seconds, Total memory usage: 7.27MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:17:50 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-10699441,0]);
f := P!Reverse([23,-24,11529,196246,746500]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:17:34 on modular [Seed = 2592785212] ------------------------------------- Point [ 1, 3676, 3340, 3915 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3826, 3428, 4786 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 10699441*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 117693851*x + 489970201154 over Rational Field function(p) ... end function (10788853639753049570275570363969/1975677658085018578764876100 : -8829544864129998469984520161732655653896783703/8781609742180625043394209518175\ 9673741000 : 1) 63.059664654807036754391 Total time: 15.789 seconds, Total memory usage: 8.83MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:18:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-53919649,0]); f := P!Reverse([7987,-12152,-12663,11410,12552]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:18:12 on modular  [Seed = 2660157154]
-------------------------------------

Point [ 1, 2872, 3775, 86 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1:  6598 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:20:05 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-53919649,0]);
f := P!Reverse([7987,-12152,-12663,11410,12552]);
S := FourDescent(f);
F := S;P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-53919649,0]);
f := P!Reverse([53,8,-14547,114074,2469294]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:19:34 on modular  [Seed = 2542260153]
-------------------------------------

Point [ 1, 621, 2481, 3774 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1:  6607 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:20:38 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-53919649,0]);
f := P!Reverse([53,8,-14547,114074,2469294]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:20:17 on modular [Seed = 2342245234] ------------------------------------- Point [ 1, 621, 2481, 3774 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3596, 4015, 1542 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 53919649*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 593116139*x + 5543047756498 over Rational Field function(p) ... end function (16125334425167926449640369926286/1598871048297745622120471529 : -48984773538281319304093033009826165837676198208/639322748480072643701404180245\ 86218886667 : 1) 63.110922647366571425209 Total time: 20.809 seconds, Total memory usage: 17.81MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:21:12 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-87703225,0]); f := P!Reverse([24349,-7492,-89904,44952,127364]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:20:57 on modular  [Seed = 2409617182]
-------------------------------------

Point [ 1, 571, 3743, 4036 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3135, 2118, 3373 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 87703225*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 964735475*x + 11498769829750 over Rational
Field
function(p) ... end function
(-16481611426513418184612789255/499116259917300400201369 :
955863375709394548878559599659430785459750/352616456993399577281090879761505597
: 1)
63.120359945966356463031

Total time: 15.009 seconds, Total memory usage: 14.67MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:21:44 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-8282884,0]);
f := P!Reverse([120,224,9942,-64444,91101]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:21:27 on modular [Seed = 2207505212] ------------------------------------- Point [ 1, 3815, 2133, 140 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 8282884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 91111724*x + 333733962128 over Rational Field function(p) ... end function (3941167511602567339768737431569/992699156545246757734275600 : -5816572476534403165080161112315455377162661753/3127710004826748673369754883419\ 6900904000 : 1) 63.32314677973050720538 Total time: 16.399 seconds, Total memory usage: 10.49MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:22:21 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-20921476,0]); f := P!Reverse([511,72,-9180,17060,99449]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:22:00 on modular  [Seed = 3131761130]
-------------------------------------

Errors: /bin/sh: line 1:  6626 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:22:53 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-20921476,0]);
f := P!Reverse([1517,-320,-12168,-724,29831]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:22:32 on modular [Seed = 3199133134] ------------------------------------- Errors: /bin/sh: line 1: 6630 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:23:30 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-9721924,0]); f := P!Reverse([737,-1182,-6330,11376,27184]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:23:10 on modular  [Seed = 3030708130]
-------------------------------------

Point [ 1, 95, 3983, 4548 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3814, 1536, 4637 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 9721924*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 106941164*x + 424381426448 over Rational
Field
function(p) ... end function
(10431800551358179149418475910221/1992943496198300495101396225 :
7970821469437514224203907220175282811340851731/88969772217769225996710464501794\
683594625 : 1)
63.75084187995114604063

Total time: 19.660 seconds, Total memory usage: 9.52MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:24:30 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-7006609,0]);
f := P!Reverse([842,-104,-6729,-1798,18458]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:24:14 on modular [Seed = 2847535743] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 7006609*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 77072699*x + 259650916322 over Rational Field function(p) ... end function (-11232698564050018017631213493246/1148299891759990774151260489 : 10836498643171741774147174493020177503828869554/3891194915978279060700683134320\ 0670471237 : 1) 64.039950626633668662179 Total time: 15.849 seconds, Total memory usage: 7.71MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:25:05 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-15792676,0]); f := P!Reverse([5961,-7948,-35766,39740,85441]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:24:51 on modular  [Seed = 2931750213]
-------------------------------------

Point [ 1, 677, 1435, 1430 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 15792676*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 173719436*x + 878641321936 over Rational
Field
function(p) ... end function
(60812557093229578442388279994/8400472954816966092659209 :
504591091076182213377102472892633839320168/243475690924711188106883819127450473\
23 : 1)
64.115368109208546343324

Total time: 14.000 seconds, Total memory usage: 5.34MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:25:42 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-48972004,0]);
f := P!Reverse([10497,-13996,-62982,69980,150457]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:25:27 on modular [Seed = 2780167722] ------------------------------------- Point [ 1, 462, 3248, 31 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2223, 3904, 1041 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2636, 3761, 5054 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3010, 403, 2916 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3964, 1105, 299 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5066, 2870, 5855 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 48972004*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 538692044*x + 4797885175888 over Rational Field function(p) ... end function (23779763184254118315156897514/2882600221383273707777241 : -4682514046010753403193611056723237492638136/4894142648375862116538154193575981\ 539 : 1) 64.21138787193233099515 Total time: 14.500 seconds, Total memory usage: 5.34MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:26:25 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-11874916,0]); f := P!Reverse([5169,-6892,-31014,34460,74089]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:26:11 on modular  [Seed = 1514799106]
-------------------------------------

Point [ 1, 1543, 1683, 3297 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 1783, 3922, 4717 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 5015, 6006, 2203 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 11874916*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 130624076*x + 572893447504 over Rational
Field
function(p) ... end function
(13385943851880411448870425946/5517767653162489066198609 :
-6738337864626447426975907095847655262465576/1296119705159555460087740428945486\
1273 : 1)
64.38203178605267851253

Total time: 13.750 seconds, Total memory usage: 5.34MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:26:56 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-34727449,0]);
f := P!Reverse([498,-664,6225,88976,155625]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:26:41 on modular [Seed = 1582171172] ------------------------------------- Point [ 1, 1227, 3151, 3903 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2072, 2793, 4990 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2608, 2577, 4592 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 3167, 1436, 5665 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4365, 2487, 4637 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 34727449*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 382001939*x + 2865083997398 over Rational Field function(p) ... end function (1346414847196477530743064142289/125006837418796915000168324 : 16645641414043624403554831190163461863027425/1397657154504560881882076356530407\ 458168 : 1) 64.49558668825420681969 Total time: 14.429 seconds, Total memory usage: 16.79MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:27:33 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-34727449,0]); f := P!Reverse([498,-664,6225,88976,155625]); S := FourDescent(f); F := S;P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-13653025,0]); f := P!Reverse([3159,-5404,15264,-30824,24324]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:27:11 on modular [Seed = 1380059190] ------------------------------------- Errors: /bin/sh: line 1: 6665 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:28:06 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-13653025,0]); f := P!Reverse([3159,-5404,15264,-30824,24324]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:27:44 on modular [Seed = 1447431277] ------------------------------------- Errors: /bin/sh: line 1: 6669 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:28:40 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-13653025,0]); f := P!Reverse([3159,-5404,15264,-30824,24324]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:28:19 on modular  [Seed = 1331631511]
-------------------------------------

Errors: /bin/sh: line 1:  6676 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:29:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-13653025,0]);
f := P!Reverse([739,-739,-6651,10346,-2956]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:28:49 on modular [Seed = 1129519545] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 13653025*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 13653025*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 12.740 seconds, Total memory usage: 16.66MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:30:07 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-13653025,0]);
f := P!Reverse([-694,-1096,24396,57704,15556]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:29:49 on modular [Seed = 1180048576] ------------------------------------- Point [ 1, 4291, 5683, 1042 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 13653025*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 13653025*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 17.559 seconds, Total memory usage: 18.44MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:31:07 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-13653025,0]);
f := P!Reverse([3159,-5404,15264,-30824,24324]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:30:46 on modular [Seed = 2053777207] ------------------------------------- Errors: /bin/sh: line 1: 6689 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:31:32 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-54272689,0]); f := P!Reverse([-6255,-9452,46704,81176,25020]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:31:15 on modular  [Seed = 1935879707]
-------------------------------------

Point [ 1, 1035, 224, 1143 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 54272689*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 54272689*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 17.010 seconds, Total memory usage: 8.23MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:32:07 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-54272689,0]); f := P!Reverse([77,89,6102,-41113,124033]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:31:46 on modular  [Seed = 2003249790]
-------------------------------------

Errors: /bin/sh: line 1:  6700 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:32:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-54272689,0]);
f := P!Reverse([-1711,412,45534,25660,-27443]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:32:15 on modular [Seed = 1803236959] ------------------------------------- Point [ 1, 1326, 5750, 2113 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2320, 109, 1910 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 54272689*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 54272689*x over Rational Field function(p) ... end function (902318001944825603777576342813256060120411057957836440633628/11266606970555260\ 6573115122670125778768666225997314434009 : 3361904419307854471410480786535324109656136300007611864600358623728905505120380\ 95576272710/1195885820918915488454664511538355843294200520980262405658474714762\ 968164004040546973 : 1) 129.47202181404421139632 Total time: 17.719 seconds, Total memory usage: 10.51MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:33:05 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-34257609,0]); f := P!Reverse([23860,-5736,-71856,15372,44217]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:32:47 on modular  [Seed = 1870607035]
-------------------------------------

Point [ 1, 497, 653, 1941 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 1347, 5920, 1830 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 34257609*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 376833699*x + 2807136996678 over Rational
Field
function(p) ... end function
(216184424090663615340884513379369/12213363493739727664258674049 :
1750919763909030539461945572018704187742820012790/13497487194836200444653095645\
18108733422657 : 1)
64.85762329051857477679

Total time: 17.960 seconds, Total memory usage: 5.88MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:33:37 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-45468049,0]);
f := P!Reverse([1226,0,0,0,148346]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:33:23 on modular [Seed = 1668497035] ------------------------------------- Point [ 1, 863, 23, 3070 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 45468049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 45468049*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 13.890 seconds, Total memory usage: 11.94MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:34:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-45468049,0]);
f := P!Reverse([111,-173,3951,-33010,103548]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:33:45 on modular [Seed = 1735867125] ------------------------------------- Point [ 1, 1406, 4122, 5825 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2111, 4774, 4023 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2226, 3013, 5919 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4680, 4234, 6 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4928, 3541, 3026 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 45468049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 45468049*x over Rational Field function(p) ... end function (-933118248230430502144884160904835102359179755028144955671007/1907918788318716\ 63942436024464143823190403396013413671524 : 8555322990443307685584254149734183385389593151099244790105209222213951463273284\ 22735315465/2635359255423233513352788421496142530514752299279830941157703471647\ 084398105296158232 : 1) 129.85847245253279425014 Total time: 17.030 seconds, Total memory usage: 13.29MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:34:38 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-30173049,0]); f := P!Reverse([77,136,-67110,-140744,12305405]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:34:20 on modular  [Seed = 403195311]
-------------------------------------

Point [ 1, 3069, 1868, 1355 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4363, 1872, 3175 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 4652, 5415, 5831 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 30173049*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 331903539*x + 2320367814198 over Rational
Field
function(p) ... end function
(450180300739458217424410411236321/40941087846839181077849448025 :
143262131968524410848806589529644026297871909494/828398048622081103825157148056\
3281649996125 : 1)
65.19218987389059805082

Total time: 18.579 seconds, Total memory usage: 5.93MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:35:09 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-6869641,0]);
f := P!Reverse([2621,0,-15726,-41936,107461]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:34:55 on modular [Seed = 318984007] ------------------------------------- Point [ 1, 4894, 3406, 2785 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 75566051*x + 252074606854 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.070 seconds, Total memory usage: 5.18MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:35:49 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-6869641,0]);
f := P!Reverse([10421,13852,-20592,-13224,21220]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:35:28 on modular [Seed = 386354044] ------------------------------------- Errors: /bin/sh: line 1: 6732 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:36:21 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-6869641,0]); f := P!Reverse([2621,0,-15726,-41936,107461]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:36:07 on modular  [Seed = 186341127]
-------------------------------------

Point [ 1, 4894, 3406, 2785 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 75566051*x + 252074606854 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 14.060 seconds, Total memory usage: 5.18MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:36:31 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-6869641,0]); f := P!Reverse([2621,0,-15726,-41936,107461]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:36:30 on modular  [Seed = 253711162]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 3 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 75566051*x + 252074606854 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.990 seconds, Total memory usage: 5.08MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:36:39 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-6869641,0]); f := P!Reverse([2621,0,-15726,-41936,107461]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:36:38 on modular  [Seed = 51601198]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 4 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 6869641*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 75566051*x + 252074606854 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.970 seconds, Total memory usage: 5.08MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:37:43 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-7513081,0]); f := P!Reverse([2741,0,-16446,-43856,112381]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:37:29 on modular  [Seed = 68442358]
-------------------------------------

Point [ 1, 2913, 5417, 127 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3398, 5911, 4040 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4195, 2053, 251 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4945, 3287, 4155 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 7513081*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 82643891*x + 288306970294 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 14.070 seconds, Total memory usage: 5.18MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:37:57 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-7513081,0]); f := P!Reverse([2741,0,-16446,-43856,112381]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:37:56 on modular  [Seed = 942171303]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 3 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 7513081*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 82643891*x + 288306970294 over Rational
Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.930 seconds, Total memory usage: 5.08MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:38:17 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-7513081,0]); f := P!Reverse([2741,0,-16446,-43856,112381]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:38:03 on modular  [Seed = 841117346]
-------------------------------------

Point [ 1, 1783, 4607, 5951 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 2317, 414, 4156 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 2486, 5571, 5634 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3805, 2149, 1960 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3837, 3787, 4399 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4144, 4218, 2963 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4202, 481, 5944 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 7513081*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 82643891*x + 288306970294 over Rational
Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1);; ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 14.009 seconds, Total memory usage: 5.17MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:38:57 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-7513081,0]); f := P!Reverse([2741,0,-16446,-43856,112381]); S := FourDescent(f); F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:38:36 on modular  [Seed = 908487297]
-------------------------------------

Point [ 1, 4449, 589, 4322 ] was singular mod 10007 and ignored at the #3 lift
Point [ 1, 7697, 3166, 9645 ] was singular mod 10007 and ignored at the #3 lift

Errors: /bin/sh: line 1:  6765 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:39:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-7513081,0]);
f := P!Reverse([2741,0,-16446,-43856,112381]);
S := FourDescent(f);
F := S;
pts := Points(F,9000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:39:12 on modular [Seed = 708474209] ------------------------------------- Point [ 1, 3191, 7175, 8555 ] was singular mod 9001 and ignored at the #3 lift Point [ 1, 3342, 3298, 2144 ] was singular mod 9001 and ignored at the #1 lift Point [ 1, 3900, 8699, 6930 ] was singular mod 9001 and ignored at the #3 lift Point [ 1, 4849, 2837, 6236 ] was singular mod 9001 and ignored at the #3 lift Point [ 1, 5108, 3441, 7765 ] was singular mod 9001 and ignored at the #1 lift Point [ 1, 5901, 5447, 1029 ] was singular mod 9001 and ignored at the #3 lift Point [ 1, 8760, 8030, 3511 ] was singular mod 9001 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 7513081*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 82643891*x + 288306970294 over Rational Field function(p) ... end function (23369278834477844283342719673/8927995109877538411937089 : -7999347218366885338937313670173125068858030/2667662694925329711484191435481791\ 3313 : 1) 65.38945365213672289428 Total time: 20.760 seconds, Total memory usage: 5.18MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:40:13 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-44049769,0]); f := P!Reverse([6637,0,-39822,-106192,272117]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:39:59 on modular  [Seed = 573734214]
-------------------------------------

Point [ 1, 2493, 2903, 518 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 5146, 5722, 1859 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 5707, 951, 4605 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 44049769*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 484547459*x + 4093016435942 over Rational
Field
function(p) ... end function
(-17644879161070137359242496831/2152541442542965951890625 :
-8656998348865729974529818640996304115298678/3158110215141226693276750225525390\
625 : 1)
65.49402554955396738023

Total time: 14.160 seconds, Total memory usage: 5.16MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:40:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17164449,0]);
f := P!Reverse([58,112,-1158816,88030096,-1885707638]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:40:30 on modular [Seed = 641104163] ------------------------------------- Point [ 1, 5389, 5802, 752 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 17.260 seconds, Total memory usage: 14.62MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:41:20 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17164449,0]);
f := P!Reverse([58,112,-1158816,88030096,-1885707638]);
S := FourDescent(f);
F := S;
pts := Points(F,9000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:40:59 on modular [Seed = 3670705658] ------------------------------------- Errors: /bin/sh: line 1: 6785 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:41:50 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-17164449,0]); f := P!Reverse([58,112,-1158816,88030096,-1885707638]); S := FourDescent(f); F := S; pts := Points(F,8000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:41:29 on modular  [Seed = 3552807953]
-------------------------------------

Point [ 1, 5913, 3671, 5120 ] was singular mod 8009 and ignored at the #1 lift

Errors: /bin/sh: line 1:  6792 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:42:26 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17164449,0]);
f := P!Reverse([1381,0,0,0,49716]);
S := FourDescent(f);
F := S;
pts := Points(F,7000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:42:09 on modular [Seed = 3620177997] ------------------------------------- Point [ 1, 785, 5230, 4376 ] was singular mod 7001 and ignored at the #1 lift Point [ 1, 3797, 5808, 3755 ] was singular mod 7001 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 16.839 seconds, Total memory usage: 11.71MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:43:12 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17164449,0]);
f := P!Reverse([-85,-89,8379,35118,27540]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:42:57 on modular [Seed = 3420165217] ------------------------------------- Point [ 1, 1903, 4439, 5955 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2447, 3340, 3006 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2879, 5212, 3732 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3128, 5212, 2275 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3560, 3340, 3001 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4104, 4439, 52 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.210 seconds, Total memory usage: 6.97MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:43:45 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17164449,0]);
f := P!Reverse([-85,-89,8379,35118,27540]);
S := FourDescent(f);
F := S;
pts := Points(F,8000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:43:26 on modular [Seed = 3437007513] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 18.510 seconds, Total memory usage: 6.97MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:44:27 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17164449,0]);
f := P!Reverse([1393,888,24642,-2664,12537]);
S := FourDescent(f);
F := S;
pts := Points(F,8000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:44:06 on modular [Seed = 3234897581] ------------------------------------- Errors: /bin/sh: line 1: 6811 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:44:55 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-17164449,0]); f := P!Reverse([1393,888,24642,-2664,12537]); S := FourDescent(f); F := S; pts := Points(F,7000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:44:34 on modular  [Seed = 4226524658]
-------------------------------------

Errors: /bin/sh: line 1:  6816 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:45:25 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17164449,0]);
f := P!Reverse([1393,888,24642,-2664,12537]);
S := FourDescent(f);
F := S;
pts := Points(F,6500);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:45:04 on modular [Seed = 4293894612] ------------------------------------- Errors: /bin/sh: line 1: 6820 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:45:55 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-17164449,0]); f := P!Reverse([1393,888,24642,-2664,12537]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:45:34 on modular  [Seed = 4091784486]
-------------------------------------

Errors: /bin/sh: line 1:  6824 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:46:25 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-17164449,0]);
f := P!Reverse([-85,-89,8379,35118,27540]);
S := FourDescent(f);
F := S;
pts := Points(F,8000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:46:07 on modular [Seed = 4108626432] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 17164449*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 18.399 seconds, Total memory usage: 6.97MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:55:06 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]);
f := P!Reverse([-5,0,13711111108081,0,-5641141558702829370912000]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:54:45 on modular [Seed = 3858072843] ------------------------------------- Errors: /bin/sh: line 1: 6846 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:55:39 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]); f := P!Reverse([5,0,13711111108081,0,5641141558702829370912000]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 02:55:26 on modular  [Seed = 2660171291]
-------------------------------------

FourDescent(
f: 5*x^4 + 13711111108081*x^2 + 5641141558702829370912000
)
ReduceFD(
fd: [ [-17614939462539216252685748 -29344413163936004369337853 -...
)
StollReduce(
desc: [ [ 0  1  0  0] [ 1  0  0  0] [ 0  0  1  1] [ 0  0  1 -4],  ...
)
Covariant(
mat1: [ 0  1  0  0] [ 1  0  0  0] [ 0  0  1  1] [ 0  0  1 -4],
mat2: [            3        -30832             0             0] [ ...
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line
292, column 21:
>>                     assert Dimension(ker) eq 1;
^
Runtime error in assert: Assertion failed

>> F := S;
^
User error: Identifier 'S' has not been declared or assigned

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 18154316561519*x^2 -
65627950508156300868878400*x over Rational Field
Elliptic Curve defined by y^2 + x*y = x^3 - 10967980444589832289962970*x -
13130466385106903842436793084407133100 over Rational Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 12.570 seconds, Total memory usage: 24.56MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:56:49 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]); f := P!Reverse([-7,0,13711111108081,0,-4029386827644878122080000]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:56:28 on modular  [Seed = 2458055125]
-------------------------------------

Errors: /bin/sh: line 1:  6857 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:57:23 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]);
f := P!Reverse([7,0,13711111108081,0,4029386827644878122080000]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 02:57:09 on modular [Seed = 2525427080] ------------------------------------- FourDescent( f: 7*x^4 + 13711111108081*x^2 + 4029386827644878122080000 ) ReduceFD( fd: [ [12803 -15347039 -45686190 384090] [-15347039 -78168551915... ) StollReduce( desc: [ [ 12803 384090 702286477 -... ) Covariant( mat1: [ 12803 384090 702286477 -20..., mat2: [6839115746 205173470550 1517909277183733 279766545812721] [... ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line 288, column 29: >> K := ext<R | f1>; ^ Runtime error in ext< ... >: RHS polynomial argument is not irreducible >> F := S; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 18154316561519*x^2 - 65627950508156300868878400*x over Rational Field Elliptic Curve defined by y^2 + x*y = x^3 - 10967980444589832289962970*x - 13130466385106903842436793084407133100 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 13.250 seconds, Total memory usage: 11.17MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:58:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]);
f := P!Reverse([-35,0,13711111108081,0,-805877365528975624416000]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:58:06 on modular [Seed = 2409622698] ------------------------------------- Errors: /bin/sh: line 1: 6868 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 02:59:23 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]); f := P!Reverse([35,0,13711111108081,0,805877365528975624416000]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 02:58:55 on modular  [Seed = 2207506536]
-------------------------------------

Errors: /bin/sh: line 1:  6872 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 02:59:54 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]);
f := P!Reverse([-3658,0,13711111108081,0,-7710691031578498320000]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 02:59:32 on modular [Seed = 2258035977] ------------------------------------- Errors: /bin/sh: line 1: 6877 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:00:22 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]); f := P!Reverse([3658,0,13711111108081,0,7710691031578498320000]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 03:00:06 on modular  [Seed = 3131758871]
-------------------------------------

FourDescent(
f: 3658*x^4 + 13711111108081*x^2 + 7710691031578498320000
)
ReduceFD(
fd: [ [-43608137904459761549215710410367295372411471923367821981...
)
StollReduce(
desc: [ [434443478025975945665877857113435446502 11534509755811205...
)
Covariant(
mat1: [434443478025975945665877857113435446502 1153450975581120560...,
mat2: [28298065033378678408612640857021382972855294 52612187255684...
)
In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line
288, column 29:
>>                     K := ext<R | f1>;
^
Runtime error in ext< ... >: RHS polynomial argument is not irreducible

>> F := S;
^
User error: Identifier 'S' has not been declared or assigned

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 18154316561519*x^2 -
65627950508156300868878400*x over Rational Field
Elliptic Curve defined by y^2 + x*y = x^3 - 10967980444589832289962970*x -
13130466385106903842436793084407133100 over Rational Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 16.199 seconds, Total memory usage: 25.92MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:00:57 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]); f := P!Reverse([-18290,0,13711111108081,0,-1542138206315699664000]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 03:00:36 on modular  [Seed = 3199130865]
-------------------------------------

Errors: /bin/sh: line 1:  6885 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 03:01:34 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]);
f := P!Reverse([18290,0,13711111108081,0,1542138206315699664000]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 03:01:13 on modular [Seed = 3081229781] ------------------------------------- Errors: /bin/sh: line 1: 6892 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:01:53 2004 Input: E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]); f := P!Reverse([-128030,0,13711111108081,0,-220305458045099952000]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 03:01:53 on modular  [Seed = 2881210769]
-------------------------------------

>> f := P!Reverse([-128030,0,13711111108081,0,-220305458045099952000]);
^
User error: Identifier 'P' has not been declared or assigned

>> S := FourDescent(f);
^
User error: Identifier 'f' has not been declared or assigned

>> F := S;
^
User error: Identifier 'S' has not been declared or assigned

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 = x^3 - 18154316561519*x^2 -
65627950508156300868878400*x over Rational Field

>> AssociatedEC(f);
^
User error: Identifier 'f' has not been declared or assigned

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 0.190 seconds, Total memory usage: 3.51MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:02:36 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,-18154316561519,0,-65627950508156300868878400,0]); f := P!Reverse([-128030,0,13711111108081,0,-220305458045099952000]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 03:02:15 on modular  [Seed = 2948582787]
-------------------------------------

Errors: /bin/sh: line 1:  6900 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 03:16:14 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
f := P!Reverse([-1069283275100,253352597540,-4944196555859,529370810346,-5718704313951]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 03:15:53 on modular [Seed = 1447440805] ------------------------------------- Errors: /bin/sh: line 1: 6924 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:16:37 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); f := P!Reverse([-2231755692656,3359076916776,-6807767226839,4198846145970,-3487118269775]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 03:16:34 on modular  [Seed = 1230581441]
-------------------------------------

>> F := S;
^
Runtime error in '[]': Sequence element 1 not defined

>> pts := Points(F,6000);
^
User error: Identifier 'F' has not been declared or assigned

>> X,m := Scheme(F);
^
User error: Identifier 'F' has not been declared or assigned
Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x +
1112872991819139146923702415527076900 over Rational Field
Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x +
1112872991819139146923702415527076900 over Rational Field
function(p) ... end function

>> m(pts);
^
User error: Identifier 'pts' has not been declared or assigned

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 2.919 seconds, Total memory usage: 7.20MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:17:11 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); f := P!Reverse([64733650884,104952423660,-4937900046203,-3547087319110,92587113540769]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 03:16:50 on modular  [Seed = 1297951477]
-------------------------------------

Errors: /bin/sh: line 1:  6935 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 03:17:52 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
f := P!Reverse([-59061830400,97687939680,47799108690001,-768403720918194,3403953109429569]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 03:17:31 on modular [Seed = 1196892438] ------------------------------------- Errors: /bin/sh: line 1: 6941 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:18:27 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); f := P!Reverse([-162296455100,286856399140,-5129118623639,4576040172468,-38536396778844]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 03:18:06 on modular  [Seed = 2070617359]
-------------------------------------

Errors: /bin/sh: line 1:  6945 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 03:18:51 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
f := P!Reverse([-75153051900,-46782523380,-4936811383019,-1315342877870,-81205622398775]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 03:18:41 on modular [Seed = 2137987444] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x + 1112872991819139146923702415527076900 over Rational Field Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x + 1112872991819139146923702415527076900 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 9.869 seconds, Total memory usage: 6.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 03:19:27 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
f := P!Reverse([-75153051900,-46782523380,-4936811383019,-1315342877870,-81205622398775]);
S := FourDescent(f);
F := S;
pts := Points(F,20000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 03:19:17 on modular [Seed = 1986400345] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,20000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x + 1112872991819139146923702415527076900 over Rational Field Elliptic Curve defined by y^2 + x*y = x^3 - 2029618868982900897912970*x + 1112872991819139146923702415527076900 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 10.089 seconds, Total memory usage: 6.45MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 03:20:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
f := P!Reverse([5,0,9930400468081,0,79409849685606720000000]);
S := FourDescent(f);
F := S;
pts := Points(F,20000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 03:20:26 on modular [Seed = 1803226507] ------------------------------------- Errors: /bin/sh: line 1: 6961 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:21:25 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); f := P!Reverse([7,0,9930400468081,0,56721321204004800000000]); S := FourDescent(f); F := S; pts := Points(F,20000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 03:21:04 on modular  [Seed = 1870596565]
-------------------------------------

Errors: /bin/sh: line 1:  6965 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.77 (66.63.133.77)
Time: Wed Sep 22 03:22:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]);
f := P!Reverse([35,0,9930400468081,0,11344264240800960000000]);
S := FourDescent(f);
F := S;
pts := Points(F,20000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 03:21:41 on modular [Seed = 1668483644] ------------------------------------- Errors: /bin/sh: line 1: 6969 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.77 (66.63.133.77) Time: Wed Sep 22 03:22:30 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([1,0,0,-2029618868982900897912970,1112872991819139146923702415527076900]); f := P!Reverse([35,0,9930400468081,0,11344264240800960000000]); S := FourDescent(f); F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 03:22:09 on modular  [Seed = 436892513]
-------------------------------------

Errors: /bin/sh: line 1:  6976 Killed                  nice -n 19 /usr/local/bin/magma

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:12:43 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(T^4+t+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:12:43 on modular  [Seed = 2746458354]
-------------------------------------

>> Factorization(T^4+t+2);
^
User error: Identifier 'T' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:12:51 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^4+x+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:12:51 on modular  [Seed = 2763302893]
-------------------------------------

[
<x^4 + x + 2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:12:58 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^4+x+3)

Output: Magma V2.11-6     Wed Sep 22 2004 05:12:58 on modular  [Seed = 1582193945]
-------------------------------------

[
<x + 5, 1>,
<x^3 + 2*x^2 + 4*x + 2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:13:10 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^4+2*x+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:13:10 on modular  [Seed = 1430607406]
-------------------------------------

[
<x + 2, 1>,
<x + 3, 1>,
<x^2 + 2*x + 5, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:13:16 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^4+3*x+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:13:16 on modular  [Seed = 1346392865]
-------------------------------------

[
<x + 1, 1>,
<x^3 + 6*x^2 + x + 2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:13:23 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^4+4*x+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:13:23 on modular  [Seed = 1230588455]
-------------------------------------

[
<x + 6, 1>,
<x^3 + x^2 + x + 5, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:13:32 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^4+x^2+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:13:32 on modular  [Seed = 1196901414]
-------------------------------------

[
<x^2 + 4, 2>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:13:42 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^4+x^2+1)

Output: Magma V2.11-6     Wed Sep 22 2004 05:13:42 on modular  [Seed = 1112686937]
-------------------------------------

[
<x + 2, 1>,
<x + 3, 1>,
<x + 4, 1>,
<x + 5, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:13:49 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^4+x^2+3)

Output: Magma V2.11-6     Wed Sep 22 2004 05:13:48 on modular  [Seed = 2036955752]
-------------------------------------

[
<x^4 + x^2 + 3, 1>
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:15:29 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+2)*(x^4+x^2+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^4+x+2)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 05:15:29 on modular  [Seed = 2003268763]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/134 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 134*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/134 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 134*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/134 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 134*$.2 = 0 given by a rule

Total time: 0.610 seconds, Total memory usage: 14.31MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:17:52 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+2)*(x^4+x^2+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-1)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 05:17:51 on modular  [Seed = 1769564939]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/268
Defined on 2 generators
Relations:
2*$.1 = 0 268*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/268
Defined on 2 generators
Relations:
2*$.1 = 0 268*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/268
Defined on 2 generators
Relations:
2*$.1 = 0 268*$.2 = 0 given by a rule

Total time: 0.620 seconds, Total memory usage: 14.32MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:18:31 2004

Input: Factorization(268)

Output: Magma V2.11-6     Wed Sep 22 2004 05:18:31 on modular  [Seed = 1685349982]
-------------------------------------

[ <2, 2>, <67, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:19:57 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x+1)

Output: Magma V2.11-6     Wed Sep 22 2004 05:19:57 on modular  [Seed = 521084415]
-------------------------------------

[
<x + 3, 1>,
<x + 5, 1>,
<x^3 + 4*x + 6, 1>,
<x^3 + 6*x^2 + 3*x + 6, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:20:04 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:20:04 on modular  [Seed = 436869251]
-------------------------------------

[
<x + 4, 1>,
<x^7 + 3*x^6 + 2*x^5 + 6*x^4 + 4*x^3 + 5*x^2 + x + 4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:20:10 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x+3)

Output: Magma V2.11-6     Wed Sep 22 2004 05:20:10 on modular  [Seed = 285283206]
-------------------------------------

[
<x^8 + x + 3, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:20:43 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+2)*(x^8+x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-1)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 05:20:42 on modular  [Seed = 203165371]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/9568
Defined on 2 generators
Relations:
2*$.1 = 0 9568*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/9568
Defined on 2 generators
Relations:
2*$.1 = 0 9568*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/9568
Defined on 2 generators
Relations:
2*$.1 = 0 9568*$.2 = 0 given by a rule

Total time: 0.980 seconds, Total memory usage: 14.32MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:20:52 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+2)*(x^8+x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-1)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 05:20:51 on modular  [Seed = 186321317]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/4784 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 4784*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/4784 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 4784*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/4784 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 4784*$.2 = 0 given by a rule

Total time: 0.900 seconds, Total memory usage: 14.31MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:22:08 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+2)*(x^8+x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-1)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 05:22:07 on modular  [Seed = 102105956]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/9568
Defined on 2 generators
Relations:
2*$.1 = 0 9568*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/9568
Defined on 2 generators
Relations:
2*$.1 = 0 9568*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/9568
Defined on 2 generators
Relations:
2*$.1 = 0 9568*$.2 = 0 given by a rule

Total time: 1.010 seconds, Total memory usage: 14.31MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:26:32 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x^2+3)*(x^8+x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-1)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 05:26:30 on modular  [Seed = 925315884]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/19410 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 19410*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/19410 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 19410*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/19410 +
Z
Defined on 3 generators
Relations:
2*$.1 = 0 19410*$.2 = 0 given by a rule

Total time: 1.570 seconds, Total memory usage: 16.31MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:27:29 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^5+3)

Output: Magma V2.11-6     Wed Sep 22 2004 05:27:29 on modular  [Seed = 841103086]
-------------------------------------

[
<x + 3, 1>,
<x^7 + 4*x^6 + 2*x^5 + 2*x^4 + x^3 + 4*x^2 + 2*x + 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:27:35 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^5+1)

Output: Magma V2.11-6     Wed Sep 22 2004 05:27:35 on modular  [Seed = 691613171]
-------------------------------------

[
<x^3 + 5*x + 5, 1>,
<x^5 + 2*x^3 + 3*x^2 + 4*x + 3, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:27:40 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^5+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:27:39 on modular  [Seed = 607396082]
-------------------------------------

[
<x^3 + 3*x + 5, 1>,
<x^5 + 4*x^3 + 3*x^2 + 2*x + 6, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:27:45 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^5+4)

Output: Magma V2.11-6     Wed Sep 22 2004 05:27:45 on modular  [Seed = 590555119]
-------------------------------------

[
<x^3 + 6*x + 5, 1>,
<x^5 + x^3 + 3*x^2 + x + 5, 1>
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:27:51 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^5+5)

Output: Magma V2.11-6     Wed Sep 22 2004 05:27:51 on modular  [Seed = 3738098196]
-------------------------------------

[
<x + 6, 1>,
<x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:27:57 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^5+6)

Output: Magma V2.11-6     Wed Sep 22 2004 05:27:57 on modular  [Seed = 3586511125]
-------------------------------------

[
<x + 5, 1>,
<x^7 + 2*x^6 + 4*x^5 + 2*x^4 + 4*x^3 + x^2 + 2*x + 4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:28:04 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^6+6)

Output: Magma V2.11-6     Wed Sep 22 2004 05:28:04 on modular  [Seed = 3502298153]
-------------------------------------

[
<x^2 + 2, 1>,
<x^3 + 3*x + 2, 1>,
<x^3 + 3*x + 5, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:28:09 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^6+5)

Output: Magma V2.11-6     Wed Sep 22 2004 05:28:09 on modular  [Seed = 3487550267]
-------------------------------------

[
<x + 1, 2>,
<x + 6, 2>,
<x^4 + 3*x^2 + 5, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:28:14 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^6+4)

Output: Magma V2.11-6     Wed Sep 22 2004 05:28:13 on modular  [Seed = 3403337274]
-------------------------------------

[
<x + 3, 1>,
<x + 4, 1>,
<x^2 + 4, 1>,
<x^4 + 6*x^2 + 3, 1>
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:28:19 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^6+3)

Output: Magma V2.11-6     Wed Sep 22 2004 05:28:18 on modular  [Seed = 3251750190]
-------------------------------------

[
<x^8 + x^6 + 3, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:28:48 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^8+x^6+3)*(x^8+x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-1)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 05:28:46 on modular  [Seed = 4192861546]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/618268 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 618268*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/618268 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 618268*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/618268 +
Z
Defined on 3 generators
Relations:
2*$.1 = 0 618268*$.2 = 0 given by a rule

Total time: 2.439 seconds, Total memory usage: 16.37MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:29:04 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^6+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:29:04 on modular  [Seed = 4108644425]
-------------------------------------

[
<x + 2, 1>,
<x + 5, 1>,
<x^3 + x^2 + 3*x + 5, 1>,
<x^3 + 6*x^2 + 3*x + 2, 1>
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:29:08 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^6+1)

Output: Magma V2.11-6     Wed Sep 22 2004 05:29:08 on modular  [Seed = 4091803466]
-------------------------------------

[
<x^4 + 3*x^3 + 5*x^2 + 5*x + 6, 1>,
<x^4 + 4*x^3 + 5*x^2 + 2*x + 6, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:29:14 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^7+1)

Output: Magma V2.11-6     Wed Sep 22 2004 05:29:14 on modular  [Seed = 4009683545]
-------------------------------------

[
<x + 3, 1>,
<x + 5, 1>,
<x^3 + 3*x^2 + 6, 1>,
<x^3 + 4*x^2 + x + 6, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:29:19 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^7+2)

Output: Magma V2.11-6     Wed Sep 22 2004 05:29:19 on modular  [Seed = 3858096471]
-------------------------------------

[
<x + 4, 1>,
<x^7 + 4*x^6 + 5*x^5 + x^4 + 3*x^3 + 2*x^2 + 6*x + 4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:29:24 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^8+x^7+3)

Output: Magma V2.11-6     Wed Sep 22 2004 05:29:24 on modular  [Seed = 3773883465]
-------------------------------------

[
<x^8 + x^7 + 3, 1>
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 05:29:34 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^8+x^7+3)*(x^8+x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-1)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 05:29:33 on modular  [Seed = 2660145726]
-------------------------------------

Abelian Group isomorphic to Z/1960 + Z/1960 + Z
Defined on 3 generators
Relations:
1960*$.1 = 0 1960*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/1960 + Z/1960 + Z
Defined on 3 generators
Relations:
1960*$.1 = 0 1960*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/1960 + Z/1960
+ Z
Defined on 3 generators
Relations:
1960*$.1 = 0 1960*$.2 = 0 given by a rule

Total time: 1.110 seconds, Total memory usage: 14.52MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:00:22 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^3+2)

Output: Magma V2.11-6     Wed Sep 22 2004 06:00:22 on modular  [Seed = 420025715]
-------------------------------------

[
<x^3 + 2, 1>
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:01:20 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^3+3)

Output: Magma V2.11-6     Wed Sep 22 2004 06:01:20 on modular  [Seed = 369498682]
-------------------------------------

[
<x^3 + 3, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:02:59 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^8+x^7+3)*(x^8+x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^3+3)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 06:02:58 on modular  [Seed = 236847744]
-------------------------------------

Abelian Group isomorphic to Z/1960 + Z/11760
Defined on 2 generators
Relations:
1960*$.1 = 0 11760*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/1960 + Z/11760
Defined on 2 generators
Relations:
1960*$.1 = 0 11760*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/1960 + Z/11760
Defined on 2 generators
Relations:
1960*$.1 = 0 11760*$.2 = 0 given by a rule

Total time: 1.090 seconds, Total memory usage: 14.63MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:48:11 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^8+x^7+3)*(x^4+x^2+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^3+3)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 06:48:09 on modular  [Seed = 2980161671]
-------------------------------------

Abelian Group isomorphic to Z/6 + Z/20406
Defined on 2 generators
Relations:
6*$.1 = 0 20406*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/6 + Z/20406
Defined on 2 generators
Relations:
6*$.1 = 0 20406*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/6 + Z/20406
Defined on 2 generators
Relations:
6*$.1 = 0 20406*$.2 = 0 given by a rule

Total time: 1.909 seconds, Total memory usage: 16.68MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:48:20 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^8+x^7+3)*(x^4+x^2+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^3+3)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 06:48:18 on modular  [Seed = 2898048385]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/20406 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 20406*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/20406 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 20406*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/20406 +
Z
Defined on 3 generators
Relations:
2*$.1 = 0 20406*$.2 = 0 given by a rule

Total time: 1.879 seconds, Total memory usage: 16.76MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:48:34 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^8+x^7+3)*(x^4+x+2);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^3+3)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 06:48:33 on modular  [Seed = 2813836921]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/5596 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 5596*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/5596 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 5596*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/5596 + Z
Defined on 3 generators
Relations:
2*$.1 = 0 5596*$.2 = 0 given by a rule

Total time: 1.080 seconds, Total memory usage: 14.31MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:49:16 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^6+3)

Output: Magma V2.11-6     Wed Sep 22 2004 06:49:16 on modular  [Seed = 2729622353]
-------------------------------------

[
<x^3 + 2, 1>,
<x^3 + 5, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:49:23 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^6+2)

Output: Magma V2.11-6     Wed Sep 22 2004 06:49:22 on modular  [Seed = 1548502449]
-------------------------------------

[
<x^6 + 2, 1>
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:49:40 2004

Input: R<x> := PolynomialRing(GF(7));
Factorization(x^6+4)

Output: Magma V2.11-6     Wed Sep 22 2004 06:49:40 on modular  [Seed = 1447448524]
-------------------------------------

[
<x^6 + 4, 1>
]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 06:50:07 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^6+2)*(x^6+4);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^3+3)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 06:50:06 on modular  [Seed = 1314805710]
-------------------------------------

Abelian Group isomorphic to Z/3 + Z/66 + Z/396 + Z
Defined on 4 generators
Relations:
3*$.1 = 0 66*$.2 = 0
396*$.3 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/66 + Z/396 + Z Defined on 4 generators Relations: 3*$.1 = 0
66*$.2 = 0 396*$.3 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/66 +
Z/396 + Z
Defined on 4 generators
Relations:
3*$.1 = 0 66*$.2 = 0
396*$.3 = 0 given by a rule Total time: 0.950 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 06:53:19 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+3)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 06:53:18 on modular [Seed = 1146379396] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 1.159 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:01:21 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+x+4) Output: Magma V2.11-6 Wed Sep 22 2004 07:01:21 on modular [Seed = 1986423977] ------------------------------------- [ <x^2 + x + 4, 1> ] Total time: 0.180 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:02:14 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+x+1) Output: Magma V2.11-6 Wed Sep 22 2004 07:02:14 on modular [Seed = 1853781126] ------------------------------------- [ <x + 3, 1>, <x + 5, 1> ] Total time: 0.190 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:02:20 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+x+2) Output: Magma V2.11-6 Wed Sep 22 2004 07:02:19 on modular [Seed = 1803252110] ------------------------------------- [ <x + 4, 2> ] Total time: 0.180 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:02:26 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+x+3) Output: Magma V2.11-6 Wed Sep 22 2004 07:02:26 on modular [Seed = 1685356280] ------------------------------------- [ <x^2 + x + 3, 1> ] Total time: 0.180 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:02:54 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+x+5) Output: Magma V2.11-6 Wed Sep 22 2004 07:02:54 on modular [Seed = 1634827233] ------------------------------------- [ <x + 2, 1>, <x + 6, 1> ] Total time: 0.190 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:02:59 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+x+6) Output: Magma V2.11-6 Wed Sep 22 2004 07:02:59 on modular [Seed = 436863143] ------------------------------------- [ <x^2 + x + 6, 1> ] Total time: 0.190 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:03:44 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+2*x+6) Output: Magma V2.11-6 Wed Sep 22 2004 07:03:44 on modular [Seed = 386337369] ------------------------------------- [ <x + 4, 1>, <x + 5, 1> ] Total time: 0.190 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:03:50 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+2*x+5) Output: Magma V2.11-6 Wed Sep 22 2004 07:03:49 on modular [Seed = 268438875] ------------------------------------- [ <x^2 + 2*x + 5, 1> ] Total time: 0.190 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:04:22 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+2*x+3) Output: Magma V2.11-6 Wed Sep 22 2004 07:04:22 on modular [Seed = 220008549] ------------------------------------- [ <x^2 + 2*x + 3, 1> ] Total time: 0.190 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:04:45 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+2*x+2) Output: Magma V2.11-6 Wed Sep 22 2004 07:04:45 on modular [Seed = 34742033] ------------------------------------- [ <x^2 + 2*x + 2, 1> ] Total time: 0.190 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:04:56 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+3*x+2) Output: Magma V2.11-6 Wed Sep 22 2004 07:04:56 on modular [Seed = 1060053561] ------------------------------------- [ <x + 1, 1>, <x + 2, 1> ] Total time: 0.180 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:05:02 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^2+3*x+1) Output: Magma V2.11-6 Wed Sep 22 2004 07:05:01 on modular [Seed = 942155067] ------------------------------------- [ <x^2 + 3*x + 1, 1> ] Total time: 0.200 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:07:12 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^3+2) Output: Magma V2.11-6 Wed Sep 22 2004 07:07:12 on modular [Seed = 891627659] ------------------------------------- [ <x^3 + 2, 1> ] Total time: 0.180 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:07:57 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+2)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 07:07:56 on modular [Seed = 758985087] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 1.000 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:09:30 2004 Input: R<x> := PolynomialRing(GF(7)); Factorization(x^3+x+1) Output: Magma V2.11-6 Wed Sep 22 2004 07:09:30 on modular [Seed = 607402000] ------------------------------------- [ <x^3 + x + 1, 1> ] Total time: 0.180 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 07:10:08 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+x+1)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 07:10:07 on modular [Seed = 3738092047] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 1.090 seconds, Total memory usage: 14.62MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 07:16:44 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.11-6 Wed Sep 22 2004 07:16:44 on modular [Seed = 3535981712] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 0.190 seconds, Total memory usage: 3.51MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 07:19:19 2004 Input: S:=[GF(3)|1,1,1,1,2,1,1,1,1,2]; BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 07:19:19 on modular [Seed = 3369653793] -------------------------------------$.1^4 + $.1^3 +$.1^2 + $.1 + 1 4 Total time: 0.190 seconds, Total memory usage: 3.51MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 07:20:09 2004 Input: S:=[GF(3)|1,1,1,1,1,2,1,1,1,1,1,2]; BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 07:20:09 on modular [Seed = 3251756918] ------------------------------------- 2*$.1^6 + 1
6

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Wed Sep 22 07:21:14 2004

Input: S:=[GF(3)|1,1,1,1,1,0,1,1,1,1,1,0];
BerlekampMassey(S);

Output: Magma V2.11-6     Wed Sep 22 2004 07:21:13 on modular  [Seed = 4209695629]
-------------------------------------

2*$.1^6 + 1 6 Total time: 0.190 seconds, Total memory usage: 3.51MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 07:21:23 2004 Input: S:=[GF(2)|1,1,1,1,1,0,1,1,1,1,1,0]; BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 07:21:22 on modular [Seed = 4159166107] -------------------------------------$.1^6 + 1
6

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Wed Sep 22 07:22:42 2004

Input: S:=[GF(5)|1,1,1,1,2,1,1,1,1,2];
BerlekampMassey(S);

Output: Magma V2.11-6     Wed Sep 22 2004 07:22:42 on modular  [Seed = 4041265452]
-------------------------------------

4*$.1^5 + 1 5 Total time: 0.200 seconds, Total memory usage: 3.51MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 07:22:50 2004 Input: S:=[GF(3)|1,1,1,1,2,1,1,1,1,2]; BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 07:22:50 on modular [Seed = 3908618556] -------------------------------------$.1^4 + $.1^3 +$.1^2 + $.1 + 1 4 Total time: 0.190 seconds, Total memory usage: 3.51MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 07:24:42 2004 Input: S:=[GF(5)|1,1,1,1,2,1,1,1,1,2]; BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 07:24:42 on modular [Seed = 3790716997] ------------------------------------- 4*$.1^5 + 1
5

Total time: 0.180 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Wed Sep 22 07:35:20 2004

Input: S:=[GF(7)|1,1,1,1,2,1,1,1,1,2];
BerlekampMassey(S);

Output: Magma V2.11-6     Wed Sep 22 2004 07:35:20 on modular  [Seed = 2359078570]
-------------------------------------

6*$.1^5 + 1 5 Total time: 0.180 seconds, Total memory usage: 3.51MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 07:37:30 2004 Input: S:=[GF(7)|1,1,1,1,2,1,1,1,1,2]; C<D> , L:=BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 07:37:30 on modular [Seed = 2258019362] ------------------------------------- Total time: 0.190 seconds, Total memory usage: 3.51MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 08:10:06 2004 Input: S:=[GF(7)|1,2,1,2]; C<D> , L:=BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 08:10:06 on modular [Seed = 1952734859] ------------------------------------- Total time: 0.190 seconds, Total memory usage: 3.51MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 08:10:21 2004 Input: S:=[GF(7)|1,2,1,2]; C<D> , L:=BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 08:10:21 on modular [Seed = 2070630839] ------------------------------------- Total time: 0.180 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:10:22 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+x+6)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:10:21 on modular [Seed = 2138002867] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 1.120 seconds, Total memory usage: 14.62MB '212.98.' ************** MAGMA ***************** Host 212.98.201.1 (212.98.201.1) Time: Wed Sep 22 08:10:27 2004 Input: S:=[GF(7)|1,2,1,2]; C<D>, L:=BerlekampMassey(S); Output: Magma V2.11-6 Wed Sep 22 2004 08:10:27 on modular [Seed = 1163227031] ------------------------------------- Total time: 0.190 seconds, Total memory usage: 3.51MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:10:35 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+2*x+1)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:10:34 on modular [Seed = 1213751955] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 1.000 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:10:46 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+2*x+6)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:10:45 on modular [Seed = 1331652075] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 0.940 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:11:05 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+3*x+5)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:11:03 on modular [Seed = 1464303073] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 1.139 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:11:14 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+4*x+1)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:11:13 on modular [Seed = 1514827994] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 0.960 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:11:27 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+6*x+5)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:11:26 on modular [Seed = 556862382] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 1.129 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:11:38 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+x^2+1)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:11:37 on modular [Seed = 607391420] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 0.950 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:11:51 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+x^2+3)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:11:50 on modular [Seed = 725288524] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396 Defined on 4 generators Relations: 3*$.1 = 0
3*$.2 = 0 132*$.3 = 0
396*$.4 = 0 given by a rule Total time: 1.070 seconds, Total memory usage: 14.62MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:12:23 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^6+2)*(x^6+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+x^2+x+2)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:12:22 on modular [Seed = 775816041] ------------------------------------- Abelian Group isomorphic to Z/3 + Z/66 + Z/1188 Defined on 3 generators Relations: 3*$.1 = 0
66*$.2 = 0 1188*$.3 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/66 + Z/1188
Defined on 3 generators
Relations:
3*$.1 = 0 66*$.2 = 0
1188*$.3 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/66 + Z/1188 Defined on 3 generators Relations: 3*$.1 = 0
66*$.2 = 0 1188*$.3 = 0 given by a rule

Total time: 1.000 seconds, Total memory usage: 14.62MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:13:10 2004

Input: // R<x> := PolynomialRing(GF(7));
// Factorization(x^3+x+1)
Factorization(1188)

Output: Magma V2.11-6     Wed Sep 22 2004 08:13:10 on modular  [Seed = 891623426]
-------------------------------------

[ <2, 2>, <3, 3>, <11, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:16:54 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^6+2)*(x^6+4);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^3+x^2+3*x+1)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:16:53 on modular  [Seed = 318979911]
-------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 +
Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 given by a rule

Total time: 0.960 seconds, Total memory usage: 14.62MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:17:37 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^6+2)*(x^6+4);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
f := x^3 + x^2 + 3*x + 5;
L := Factorization(f*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:17:36 on modular  [Seed = 4026516462]
-------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 +
Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 given by a rule

Total time: 1.010 seconds, Total memory usage: 14.62MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:17:59 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^6+2)*(x^6+4);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
f := x^3 + x^2 + 4*x + 6;
L := Factorization(f*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:17:58 on modular  [Seed = 3285446612]
-------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 +
Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 given by a rule

Total time: 1.090 seconds, Total memory usage: 14.62MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:18:32 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^6+2)*(x^6+4);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
f := x^3 + 3*x^2 + 4;
L := Factorization(f*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:18:31 on modular  [Seed = 3047528771]
-------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 +
Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 given by a rule

Total time: 1.030 seconds, Total memory usage: 14.62MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:18:44 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^6+2)*(x^6+4);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
f := x^3 + 3*x^2 + 6;
L := Factorization(f*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:18:43 on modular  [Seed = 3098055802]
-------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 +
Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 given by a rule

Total time: 1.090 seconds, Total memory usage: 14.62MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:19:04 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^6+2)*(x^6+4);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
f := x^3 + 4*x^2 + 6*x + 1;
L := Factorization(f*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:19:03 on modular  [Seed = 3215954793]
-------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 +
Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 given by a rule

Total time: 1.000 seconds, Total memory usage: 14.62MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:19:24 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^6+2)*(x^6+4);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
f := x^3 + 6*x^2 + 6*x + 4;
L := Factorization(f*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:19:23 on modular  [Seed = 2190650920]
-------------------------------------

Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0
Mapping from: Abelian Group isomorphic to Z/3 + Z/3 + Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 + Z/3 +
Z/132 + Z/396
Defined on 4 generators
Relations:
3*$.1 = 0 3*$.2 = 0
132*$.3 = 0 396*$.4 = 0 given by a rule

Total time: 1.010 seconds, Total memory usage: 14.62MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:42:55 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+1);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^4+x+2)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:42:55 on modular  [Seed = 2036943702]
-------------------------------------

Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
12*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/12 + Z Defined on 2 generators Relations: 12*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
12*$.1 = 0 given by a rule Total time: 0.490 seconds, Total memory usage: 13.88MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:44:01 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+x+4); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^4+x+2)*O); I := L; pl := Place(I); // SClassGroup({pl}) ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:44:00 on modular [Seed = 1079014064] ------------------------------------- Abelian Group isomorphic to Z/12 + Z Defined on 2 generators Relations: 12*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/12 + Z
Defined on 2 generators
Relations:
12*$.1 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/12 + Z Defined on 2 generators Relations: 12*$.1 = 0 given by a rule

Total time: 0.500 seconds, Total memory usage: 13.88MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:44:10 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+2*x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^4+x+2)*O);
I := L;
pl := Place(I);
// SClassGroup({pl})
ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:44:10 on modular  [Seed = 1180071100]
-------------------------------------

Abelian Group isomorphic to Z/10 + Z
Defined on 2 generators
Relations:
10*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/10 + Z Defined on 2 generators Relations: 10*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/10 + Z
Defined on 2 generators
Relations:
10*$.1 = 0 given by a rule Total time: 0.470 seconds, Total memory usage: 13.78MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 08:45:07 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-1)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 08:45:06 on modular [Seed = 1281130238] ------------------------------------- Abelian Group isomorphic to Z/20 Defined on 1 generator Relations: 20*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/20
Defined on 1 generator
Relations:
20*$.1 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/20 Defined on 1 generator Relations: 20*$.1 = 0 given by a rule

Total time: 0.500 seconds, Total memory usage: 13.78MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 08:56:13 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+2*x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization(D*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 08:56:12 on modular  [Seed = 624235049]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/20
Defined on 2 generators
Relations:
2*$.1 = 0 20*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/20
Defined on 2 generators
Relations:
2*$.1 = 0 20*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/20
Defined on 2 generators
Relations:
2*$.1 = 0 20*$.2 = 0 given by a rule

Total time: 0.490 seconds, Total memory usage: 13.88MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 09:07:56 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+2*x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-2)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 09:07:55 on modular  [Seed = 118964044]
-------------------------------------

Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 given by a rule Total time: 0.480 seconds, Total memory usage: 13.78MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:08:33 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-1)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:08:33 on modular [Seed = 285288736] ------------------------------------- Abelian Group isomorphic to Z/20 Defined on 1 generator Relations: 20*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/20
Defined on 1 generator
Relations:
20*$.1 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/20 Defined on 1 generator Relations: 20*$.1 = 0 given by a rule

Total time: 0.480 seconds, Total memory usage: 13.78MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 09:08:49 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+2*x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-2)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 09:08:48 on modular  [Seed = 369503766]
-------------------------------------

Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 given by a rule Total time: 0.490 seconds, Total memory usage: 13.78MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:32:15 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-3)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:32:15 on modular [Seed = 4277059905] ------------------------------------- Abelian Group isomorphic to Z/20 Defined on 1 generator Relations: 20*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/20
Defined on 1 generator
Relations:
20*$.1 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/20 Defined on 1 generator Relations: 20*$.1 = 0 given by a rule

Total time: 0.480 seconds, Total memory usage: 13.78MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 09:32:26 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+2*x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-4)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 09:32:25 on modular  [Seed = 3285449802]
-------------------------------------

Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 given by a rule Total time: 0.500 seconds, Total memory usage: 13.88MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:32:34 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-5)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:32:33 on modular [Seed = 3369662297] ------------------------------------- Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 given by a rule

Total time: 0.470 seconds, Total memory usage: 13.78MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 09:32:40 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+2*x+3);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x-6)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 09:32:40 on modular  [Seed = 3453874773]
-------------------------------------

Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0 given by a rule Total time: 0.500 seconds, Total memory usage: 13.88MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:34:41 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^2-3)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:34:41 on modular [Seed = 3603359943] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/20 Defined on 2 generators Relations: 2*$.1 = 0
20*$.2 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z/20 Defined on 2 generators Relations: 2*$.1 = 0
20*$.2 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/20 Defined on 2 generators Relations: 2*$.1 = 0
20*$.2 = 0 given by a rule Total time: 0.480 seconds, Total memory usage: 13.88MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:44:34 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+3)*O); I := L; pl := Place(I); SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:44:33 on modular [Seed = 2963304465] ------------------------------------- Abelian Group isomorphic to Z/30 Defined on 1 generator Relations: 30*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/30
Defined on 1 generator
Relations:
30*$.1 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/30 Defined on 1 generator Relations: 30*$.1 = 0 given by a rule

Total time: 0.500 seconds, Total memory usage: 13.88MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 09:46:33 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+2);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x+3)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 09:46:32 on modular  [Seed = 3064362478]
-------------------------------------

Abelian Group isomorphic to Z/24
Defined on 1 generator
Relations:
24*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/24 Defined on 1 generator Relations: 24*$.1 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/24
Defined on 1 generator
Relations:
24*$.1 = 0 given by a rule Total time: 0.500 seconds, Total memory usage: 13.88MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:48:59 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-2)*O); print(L); I := L; pl := Place(I); // SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:48:59 on modular [Seed = 2173780522] ------------------------------------- [ <Prime Ideal of O Generators: x + 5 alpha + 3, 1>, <Prime Ideal of O Generators: x + 5 alpha + 4, 1> ] Total time: 0.420 seconds, Total memory usage: 13.38MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:49:24 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-2)*O); print(L); I := L; print(I); pl := Place(I); // SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:49:23 on modular [Seed = 2257995013] ------------------------------------- [ <Prime Ideal of O Generators: x + 5 alpha + 3, 1>, <Prime Ideal of O Generators: x + 5 alpha + 4, 1> ] Prime Ideal of O Generators: x + 5 alpha + 3 Total time: 0.420 seconds, Total memory usage: 13.38MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:49:39 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-2)*O); print(L); I := L; print(I); pl := Place(I); // SClassGroup({pl}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:49:38 on modular [Seed = 2342209561] ------------------------------------- [ <Prime Ideal of O Generators: x + 5 alpha + 3, 1>, <Prime Ideal of O Generators: x + 5 alpha + 4, 1> ] Prime Ideal of O Generators: x + 5 alpha + 4 Total time: 0.400 seconds, Total memory usage: 13.38MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:50:40 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x-2)*O); I1 := L; I2 := L; pl1 := Place(I1); pl2 := Place(I2); SClassGroup({pl1, pl2}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:50:40 on modular [Seed = 2542228935] ------------------------------------- Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Divisor group of F Mapping from: Divisor group of F to Abelian Group of order 1 given by a rule Total time: 0.470 seconds, Total memory usage: 13.78MB '137.193' ************** MAGMA ***************** Host 137.193.61.16 (137.193.61.16) Time: Wed Sep 22 09:51:31 2004 Input: R<x> := FunctionField(GF(7)); P<y> := PolynomialRing(R); D := (x^4+2*x+3); F<alpha> := FunctionField(y^2 - D); O := MaximalOrderFinite(F); L := Factorization((x^3+3)*O); I1 := L; I2 := L; pl1 := Place(I1); pl2 := Place(I2); SClassGroup({pl1, pl2}) // ClassGroup(F) Output: Magma V2.11-6 Wed Sep 22 2004 09:51:30 on modular [Seed = 2626444958] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
3*$.1 = 0 to Divisor group of F Mapping from: Divisor group of F to Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 given by a rule

Total time: 0.500 seconds, Total memory usage: 13.78MB

'130.113'
************** MAGMA *****************
Host 130.113.128.11 (130.113.128.11)
Time: Wed Sep 22 11:32:33 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Wed Sep 22 2004 11:32:32 on modular  [Seed = 3738043565]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

'130.113'
************** MAGMA *****************
Host 130.113.128.11 (130.113.128.11)
Time: Wed Sep 22 11:32:35 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Wed Sep 22 2004 11:32:35 on modular  [Seed = 2712763345]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

'137.193'
************** MAGMA *****************
Host 137.193.61.16 (137.193.61.16)
Time: Wed Sep 22 12:35:32 2004

Input: R<x> := FunctionField(GF(7));
P<y> := PolynomialRing(R);
D := (x^4+x+2);
F<alpha> := FunctionField(y^2 - D);
O := MaximalOrderFinite(F);
L := Factorization((x^4+x+2)*O);
I := L;
pl := Place(I);
SClassGroup({pl})
// ClassGroup(F)

Output: Magma V2.11-6     Wed Sep 22 2004 12:35:31 on modular  [Seed = 1363261920]
-------------------------------------

Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
2*$.1 = 0 24*$.2 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
2*$.1 = 0 24*$.2 = 0 to Divisor group of F
Mapping from: Divisor group of F to Abelian Group isomorphic to Z/2 + Z/24
Defined on 2 generators
Relations:
2*$.1 = 0 24*$.2 = 0 given by a rule

Total time: 0.500 seconds, Total memory usage: 13.88MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:17:35 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,0,
-1241281736,-16833563535740]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:17:34 on modular  [Seed = 169511633]
-------------------------------------

[ <2, 10>, <5, 12>, <31, 9> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:18:38 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-1369116048,-19498827855440]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:18:38 on modular  [Seed = 302158473]
-------------------------------------

[ <2, 12>, <3, 7>, <13, 4>, <41, 3> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:19:17 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,1,
-957149500,11398033676903]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:19:16 on modular  [Seed = 420059736]
-------------------------------------

[ <5, 1>, <23, 10>, <29, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:20:08 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,0,
-1240752712,-16821521916944]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:20:08 on modular  [Seed = 3891750106]
-------------------------------------

[ <2, 20>, <3, 9>, <37, 2>, <43, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:20:46 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-937309179,11045170357450]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:20:46 on modular  [Seed = 3807535609]
-------------------------------------

[ <2, 11>, <3, 9>, <23, 8> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:21:31 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,1,1,
-1063413411,13347099434289]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:21:31 on modular  [Seed = 3942279460]
-------------------------------------

[ <2, 4>, <3, 5>, <5, 4>, <7, 2>, <19, 7> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:22:09 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,0,0,
-1572416986,23999231350691]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:22:09 on modular  [Seed = 4058083909]
-------------------------------------

[ <3, 6>, <5, 3>, <13, 8>, <29, 1> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:22:48 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,0,
-1392756666,-20006497323991]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:22:47 on modular  [Seed = 4243357537]
-------------------------------------

[ <2, 4>, <5, 6>, <7, 2>, <23, 9> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:23:29 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-21191782887,1187411621515645]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:23:29 on modular  [Seed = 3319089025]
-------------------------------------

[ <2, 10>, <3, 9>, <11, 2>, <19, 10> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:24:14 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,0,
-2980105574,62618225395743]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:24:13 on modular  [Seed = 3436990183]
-------------------------------------

[ <5, 5>, <7, 1>, <11, 7>, <17, 3> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:24:48 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([1,-1,1,
-4857952793,130326309109032]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:24:48 on modular  [Seed = 3403303135]
-------------------------------------

[ <3, 8>, <5, 3>, <11, 10>, <13, 1> ]

Total time: 0.180 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:25:31 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-2813028897,-57426100576936]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:25:31 on modular  [Seed = 3519107887]
-------------------------------------

[ <2, 6>, <3, 20>, <5, 8>, <7, 8> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:26:11 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,-1,0,
-8380101144,-295269028834576]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:26:10 on modular  [Seed = 3704381051]
-------------------------------------

[ <2, 18>, <7, 14>, <89, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:26:56 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,1,
-5997199966,-178762230564745]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:26:56 on modular  [Seed = 3687536974]
-------------------------------------

[ <5, 1>, <13, 9>, <83, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:27:33 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,1,1,
-15982528310,-777712916991370]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:27:33 on modular  [Seed = 2746427091]
-------------------------------------

[ <3, 1>, <13, 4>, <41, 9> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:28:10 2004

Input: Factorization(Numerator(Discriminant(EllipticCurve([0,0,0,
-8579280567,305861222251199]))));

Output: Magma V2.11-6     Wed Sep 22 2004 14:28:10 on modular  [Seed = 2931698673]
-------------------------------------

[ <2, 4>, <3, 19>, <5, 2>, <181, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'208.181'
************** MAGMA *****************
Host 208.181.90.67 (208.181.90.67)
Time: Wed Sep 22 14:28:44 2004

Input: Factorization(65160);

Output: Magma V2.11-6     Wed Sep 22 2004 14:28:44 on modular  [Seed = 3047501964]
-------------------------------------

[ <2, 3>, <3, 2>, <5, 1>, <181, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.51MB

'198.24.'
************** MAGMA *****************
Host 198.24.6.134 (198.24.6.134)
Time: Wed Sep 22 17:28:10 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Wed Sep 22 2004 17:28:09 on modular  [Seed = 2424323998]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:17:34 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:17:27 on modular [Seed = 2173862078] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.390 seconds, Total memory usage: 5.25MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:17:51 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
F := S;
pts := Points(F,10000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:17:48 on modular [Seed = 2257946530] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,10000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.399 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:18:15 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-18167,19240,-99012,51504,-109372]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:18:15 on modular [Seed = 2037020789] ------------------------------------- >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 0.860 seconds, Total memory usage: 4.79MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:18:32 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-18167,19240,-99012,51504,-109372]);
S := FourDescent(f);
#S
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:18:31 on modular [Seed = 2104392833] ------------------------------------- >> F := S; ^ User error: bad syntax >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 0.840 seconds, Total memory usage: 4.78MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:18:42 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-18167,19240,-99012,51504,-109372]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:18:42 on modular [Seed = 1902276760] ------------------------------------- 0 >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);;
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 0.820 seconds, Total memory usage: 4.79MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:19:23 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-58094884,0]);
f := P!Reverse([-5399,2012,-83910,14484,-366127]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:19:19 on modular [Seed = 1969648825] ------------------------------------- 0 >> F := S; ^ Runtime error in '[]': Sequence element 1 not defined >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 58094884*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 639043724*x + 6199188881872 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 3.509 seconds, Total memory usage: 5.35MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:21:50 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-96020401,0]);
f := P!Reverse([98,20,-14397,198490,2528324]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:21:34 on modular [Seed = 1752918061] ------------------------------------- Point [ 1, 2993, 3820, 1549 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5911, 2822, 3247 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 96020401*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 1056224411*x + 13172654731586 over Rational Field function(p) ... end function (156801535389307668570941990831761/14736631272630023345729822500 : -3169411950286153724496058998849040714061893858241/1788946388199622535982587145\ 127458339625000 : 1) 65.50886020610516879969 Total time: 16.030 seconds, Total memory usage: 17.35MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:23:00 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-82119844,0]); f := P!Reverse([3918,-1432,-21522,13736,46532]); S := FourDescent(f); F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 23:22:42 on modular  [Seed = 1820290197]
-------------------------------------

Point [ 1, 2000, 5369, 3262 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 4745, 4805, 5508 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 82119844*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 903318284*x + 10418380368592 over Rational
Field
function(p) ... end function
(73257301632340844338134331813921/8100582001897417038615353616 :
-1260456130913137850194823269306459991170253413297/7290785716674936016389418688\
46354130038336 : 1)
65.64904984592598680137

Total time: 17.910 seconds, Total memory usage: 15.25MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:23:37 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-7601049,0]);
f := P!Reverse([-171,-336,148050,2329152,9869997]);
S := FourDescent(f);
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:23:20 on modular [Seed = 1718970037] ------------------------------------- Point [ 1, 4645, 968, 3738 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5804, 2052, 453 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 7601049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 83611539*x + 293385289302 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 16.960 seconds, Total memory usage: 23.94MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:24:08 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-7601049,0]);
f := P!Reverse([-171,-336,148050,2329152,9869997]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:23:53 on modular [Seed = 1514756840] ------------------------------------- 2 Point [ 1, 585, 423, 4731 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 744, 5901, 5439 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 897, 4638, 5322 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 7601049*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 83611539*x + 293385289302 over Rational Field function(p) ... end function (74329923030690147839219409290761/850328861784690569687543449 : -637459695900272626941371074656794151915439727830/24795928773421060989127811794\ 838587888957 : 1) 65.86513965970738126998 Total time: 15.710 seconds, Total memory usage: 23.94MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:25:10 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-91642329,0]); f := P!Reverse([740,-536,-8289,-92763,349623]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:24:48 on modular  [Seed = 1548705575]
-------------------------------------

2
Point [ 1, 1127, 1056, 4005 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 1520, 1351, 1297 ] was singular mod 6007 and ignored at the #1 lift

Errors: /bin/sh: line 1: 14887 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:26:15 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-91642329,0]);
f := P!Reverse([229,-104,46545,234088,285562]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:25:54 on modular  [Seed = 1346589545]
-------------------------------------

2
Point [ 1, 138, 723, 2239 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 791, 1634, 2900 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1: 14891 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:26:51 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-91642329,0]);
f := P!Reverse([229,-104,46545,234088,285562]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:26:30 on modular  [Seed = 1413961545]
-------------------------------------

2

Errors: /bin/sh: line 1: 14895 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:28:11 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-91642329,0]);
f := P!Reverse([740,-536,-8289,-92763,349623]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:27:50 on modular  [Seed = 1213942661]
-------------------------------------

2

Errors: /bin/sh: line 1: 14899 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:28:39 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-60295225,0]);
f := P!Reverse([3677,-4628,7392,-356008,832292]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:28:18 on modular [Seed = 1281314789] ------------------------------------- Errors: /bin/sh: line 1: 14903 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:29:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-17749369,0]); f := P!Reverse([2981,-2552,-49830,24024,187429]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 23:29:32 on modular  [Seed = 1079198247]
-------------------------------------

2
Point [ 1, 3455, 5838, 1756 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 17749369*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 195243059*x + 1046893282358 over Rational
Field
function(p) ... end function
(66434058622252752140477928007609/6985224463606742518210422001 :
130891638731932128120680298726180045275196057634/583808682335607266618706848424\
281402866999 : 1)
66.16983420842190355415

Total time: 15.130 seconds, Total memory usage: 9.26MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:30:38 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9628609,0]);
f := P!Reverse([535,107,-6741,8774,-2140]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:30:25 on modular [Seed = 992491793] ------------------------------------- 4 Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 13.259 seconds, Total memory usage: 19.02MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:31:09 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9628609,0]);
f := P!Reverse([535,107,-6741,8774,-2140]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:30:56 on modular [Seed = 1059863860] ------------------------------------- 4 Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 13.320 seconds, Total memory usage: 19.02MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:31:38 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9628609,0]);
f := P!Reverse([535,107,-6741,8774,-2140]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:31:23 on modular [Seed = 857747907] ------------------------------------- 4 Point [ 1, 4321, 5330, 2682 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.839 seconds, Total memory usage: 19.03MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:33:04 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9628609,0]);
f := P!Reverse([535,107,-6741,8774,-2140]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:32:49 on modular [Seed = 925119917] ------------------------------------- 4 Point [ 1, 4321, 678, 2682 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.810 seconds, Total memory usage: 19.01MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:33:55 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9628609,0]);
f := P!Reverse([535,107,-6741,8774,-2140]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,12000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:33:34 on modular [Seed = 725102174] ------------------------------------- 4 Errors: /bin/sh: line 1: 14928 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:34:29 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-9628609,0]); f := P!Reverse([535,107,-6741,8774,-2140]); S := FourDescent(f); #S; F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 23:34:08 on modular  [Seed = 775760741]
-------------------------------------

4
Point [ 1, 6025, 277, 333 ] was singular mod 10007 and ignored at the #1 lift
Point [ 1, 6025, 9730, 9674 ] was singular mod 10007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.850 seconds, Total memory usage: 19.03MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:35:16 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-9628609,0]); f := P!Reverse([223,196,816,-18248,168452]); S := FourDescent(f); #S; F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:34:55 on modular  [Seed = 556934149]
-------------------------------------

4
Point [ 1, 7235, 1877, 6272 ] was singular mod 10007 and ignored at the #1 lift

Errors: /bin/sh: line 1: 14938 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:36:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9628609,0]);
f := P!Reverse([29,0,0,0,1328084]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:36:01 on modular [Seed = 624304383] ------------------------------------- FourDescent( f: 29*x^4 + 1328084 ) Minimise( F: [ [ 32 899 -5219246 ... ) MinimiseFDAtPrime( fd_in: [ [ -32803613287 -975581787953 -412972615 ..., prime: 29 ) MinimiseFDOnceAtPrime( fd_in: [ [ -1862235 -121726630 -32103 -44080] [ -..., prime: 29 ) BoxMinimiseK1( fd_in: [ [ -1862235 -121726630 -32103 -44080] [ -..., prime: 29 ) Extend3ToUnimodular( cc: [ ( 0 1 0 4), ( 1 0 0 0), ( 1 0 0 28) ] ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/utils.m", line 342, column 21: >> assert "Could not extend three rows to unimodular matri ^ Runtime error in assert: Logical expected >> #S; ^ User error: Identifier 'S' has not been declared or assigned >> F := S; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,10000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 9628609*x over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 1.800 seconds, Total memory usage: 13.91MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:37:36 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9628609,0]);
f := P!Reverse([-2646,-5144,15276,23000,3972]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:37:15 on modular [Seed = 420093065] ------------------------------------- 4 Errors: /bin/sh: line 1: 14946 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:39:07 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-4355569,0]); f := P!Reverse([17,-24,381,-90690,735874]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:38:46 on modular  [Seed = 318773038]
-------------------------------------

Errors: /bin/sh: line 1: 14952 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:39:41 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-4355569,0]);
f := P!Reverse([199,-364,-5445,5792,45126]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:39:22 on modular [Seed = 386142982] ------------------------------------- 2 Point [ 1, 4395, 791, 4738 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4952, 2591, 1262 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 4355569*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 47911259*x + 127261015042 over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 19.210 seconds, Total memory usage: 6.29MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:40:20 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-4355569,0]);
f := P!Reverse([199,-364,-5445,5792,45126]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:39:59 on modular [Seed = 169414398] ------------------------------------- 2 Errors: /bin/sh: line 1: 14961 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:40:53 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-4355569,0]); f := P!Reverse([199,-364,-5445,5792,45126]); S := FourDescent(f); #S; F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:40:32 on modular  [Seed = 236784325]
-------------------------------------

2
Point [ 1, 1432, 9475, 9337 ] was singular mod 10007 and ignored at the #3 lift
Point [ 1, 4207, 2813, 4610 ] was singular mod 10007 and ignored at the #3 lift

Errors: /bin/sh: line 1: 14965 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:41:34 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-69689104,0]);
f := P!Reverse([17,-24,381,-90690,735874]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:41:13 on modular [Seed = 34670240] ------------------------------------- Errors: /bin/sh: line 1: 14969 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:42:18 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-86229796,0]); f := P!Reverse([8289,776,-80196,-87952,391012]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:41:57 on modular  [Seed = 85328507]
-------------------------------------

Errors: /bin/sh: line 1: 14974 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:42:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-86229796,0]);
f := P!Reverse([13929,-18572,-83574,92860,199649]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:42:32 on modular [Seed = 4192927402] ------------------------------------- 2 Point [ 1, 233, 5813, 847 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2591, 1963, 1934 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 86229796*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 948527756*x + 11210218399184 over Rational Field function(p) ... end function (543653396998892771395227792746/32513153193892265689127089 : -29276352655677157485839331523326705183958344/185390995071379850183652684204005\ 758313 : 1) 66.35273351488972082279 Total time: 14.820 seconds, Total memory usage: 5.34MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:43:34 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-18284176,0]); f := P!Reverse([3109,348,-10608,2264,13220]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:43:13 on modular  [Seed = 4091606233]
-------------------------------------

2
Point [ 1, 3101, 1929, 924 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1: 14984 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:44:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-18284176,0]);
f := P!Reverse([1069,0,-6414,-17104,43829]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:43:48 on modular [Seed = 4158976248] ------------------------------------- 2 Point [ 1, 1424, 487, 1029 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2874, 4254, 3940 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2946, 4444, 2296 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 18284176*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 12570371*x + 17102561126 over Rational Field function(p) ... end function (-73975153990139974920200842127/27541173285562142868881521 : 25647697356660597659544931073115508448307290/1445352096157604700778580259092615\ 70569 : 1) 66.43307922758570782661 Total time: 13.429 seconds, Total memory usage: 5.17MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:44:42 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-92563641,0]); f := P!Reverse([3109,348,-10608,2264,13220]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:44:21 on modular  [Seed = 3958959109]
-------------------------------------

2
Point [ 1, 1113, 1117, 4016 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 1825, 1515, 627 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1: 14992 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:45:10 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-92563641,0]);
f := P!Reverse([1069,0,-6414,-17104,43829]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:44:56 on modular [Seed = 4009617709] ------------------------------------- 2 Point [ 1, 1424, 487, 1029 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2874, 4254, 3940 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 2946, 4444, 2296 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 92563641*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 12570371*x + 17102561126 over Rational Field function(p) ... end function (-73975153990139974920200842127/27541173285562142868881521 : 25647697356660597659544931073115508448307290/1445352096157604700778580259092615\ 70569 : 1) 66.43307922758570782661 Total time: 13.289 seconds, Total memory usage: 5.17MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:45:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-9078169,0]); f := P!Reverse([6,-7,15633,-229768,833528]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

P<

Output: Magma V2.11-6     Wed Sep 22 2004 23:45:31 on modular  [Seed = 3858162245]
-------------------------------------

2
Elliptic Curve defined by y^2 = x^3 - 9078169*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 99859859*x + 382935324758 over Rational
Field
function(p) ... end function
(159600752618309951351039789531854/43045057875893956659762511761 :
2253141997567153755670957901214975263366152271066/89306885527618784910592111991\
38317422321991 : 1)
66.49805062869140215298

>> P<;
^

Total time: 15.630 seconds, Total memory usage: 9.65MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:46:35 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-30625156,0]);
f := P!Reverse([1303,32,-15060,1204,50137]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:46:14 on modular [Seed = 3653951396] ------------------------------------- 2 Errors: /bin/sh: line 1: 15010 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:47:07 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-30625156,0]); f := P!Reverse([149,-244,-2970,-103704,602752]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:46:46 on modular  [Seed = 3721321344]
-------------------------------------

2
Point [ 1, 1238, 1326, 4583 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 1784, 3704, 4312 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 3637, 5780, 3612 ] was singular mod 6007 and ignored at the #1 lift

Errors: /bin/sh: line 1: 15014 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:47:46 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-30625156,0]);
f := P!Reverse([149,-244,-2970,-103704,602752]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,9000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:47:25 on modular [Seed = 3519207399] ------------------------------------- 2 Errors: /bin/sh: line 1: 15018 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:48:12 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-20548089,0]); f := P!Reverse([2700,1974,-11781,-5208,15693]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 23:47:54 on modular  [Seed = 3586577348]
-------------------------------------

2
Point [ 1, 875, 57, 504 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 20548089*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 226028979*x + 1304022824118 over Rational
Field
function(p) ... end function
(-34427367189445003285459107944774/8246710286439847517466621025 :
-1104427659227640474317344206877514317805892346276/7488953027137126100768722284\
05071988548625 : 1)
66.67236952828176299590

Total time: 17.629 seconds, Total memory usage: 10.66MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:49:08 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-88943761,0]);
f := P!Reverse([74,-48,-753,390066,3241450]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:48:47 on modular [Seed = 3386560301] ------------------------------------- Errors: /bin/sh: line 1: 15026 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:49:38 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-88943761,0]); f := P!Reverse([790,1432,-24741,-26432,233067]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:49:17 on modular  [Seed = 3453930251]
-------------------------------------

Errors: /bin/sh: line 1: 15030 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:50:22 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-35224225,0]);
f := P!Reverse([479,727,3801,-9242,12364]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:50:04 on modular [Seed = 3235104343] ------------------------------------- 4 Point [ 1, 5932, 3441, 5745 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 35224225*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 35224225*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 18.140 seconds, Total memory usage: 13.59MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:50:53 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-35224225,0]);
f := P!Reverse([-3561,4748,56976,66472,14244]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:50:38 on modular [Seed = 3302477233] ------------------------------------- 4 Point [ 1, 3599, 750, 3634 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 4164, 4962, 3053 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5330, 907, 5707 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 35224225*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 35224225*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.970 seconds, Total memory usage: 10.32MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:51:27 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-35224225,0]);
f := P!Reverse([-3561,4748,56976,66472,14244]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:51:06 on modular [Seed = 3182343404] ------------------------------------- 4 Point [ 1, 107, 669, 4887 ] was singular mod 10007 and ignored at the #1 lift Errors: /bin/sh: line 1: 15046 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:51:59 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-35224225,0]); f := P!Reverse([-3561,4748,56976,66472,14244]); S := FourDescent(f); #S; F := S; pts := Points(F,9000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:51:38 on modular  [Seed = 2980231296]
-------------------------------------

4
Point [ 1, 3126, 1920, 137 ] was singular mod 9001 and ignored at the #1 lift
Point [ 1, 4911, 2847, 6283 ] was singular mod 9001 and ignored at the #1 lift
Point [ 1, 5955, 8265, 6261 ] was singular mod 9001 and ignored at the #3 lift
Point [ 1, 7284, 6535, 2483 ] was singular mod 9001 and ignored at the #3 lift

Errors: /bin/sh: line 1: 15050 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:52:33 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-35224225,0]);
f := P!Reverse([-3561,4748,56976,66472,14244]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,9000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:52:12 on modular [Seed = 3047603362] ------------------------------------- 4 Point [ 1, 1717, 2466, 4892 ] was singular mod 9001 and ignored at the #3 lift Point [ 1, 3046, 736, 4370 ] was singular mod 9001 and ignored at the #3 lift Point [ 1, 7910, 2501, 7835 ] was singular mod 9001 and ignored at the #1 lift Errors: /bin/sh: line 1: 15054 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:53:11 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-35224225,0]); f := P!Reverse([-31,32,1327896,148861808,4697113684]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 23:52:51 on modular  [Seed = 2847580225]
-------------------------------------

4
Elliptic Curve defined by y^2 = x^3 - 35224225*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 35224225*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 19.780 seconds, Total memory usage: 22.41MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:53:47 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-35224225,0]); f := P!Reverse([10,0,0,0,14089690]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Wed Sep 22 2004 23:53:30 on modular  [Seed = 2746264162]
-------------------------------------

4
Point [ 1, 641, 3801, 1785 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 3129, 3522, 2490 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4006, 3595, 4300 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 5337, 2511, 1510 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 35224225*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 35224225*x over Rational Field
function(p) ... end function
(-4159309607407066794803367195625875213822359930745265572994401/322209658586093\
1763005240063462140324669692050821790204025 :
3806680488831004888640755313444261117249554421811264877177655461594347793314465\
0105452459868/18289752648390712731001474304099958818650915217901893993730630214\
0535812169844035730125 : 1)
133.77257386002608541275

Total time: 17.920 seconds, Total memory usage: 10.65MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:54:36 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-30019441,0]);
f := P!Reverse([746,136,-12021,-16200,93781]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:54:15 on modular [Seed = 2780212281] ------------------------------------- 2 Point [ 1, 18, 3799, 861 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 1071, 3256, 4385 ] was singular mod 6007 and ignored at the #3 lift Errors: /bin/sh: line 1: 15070 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:55:09 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-30019441,0]); f := P!Reverse([1654,2088,-13461,-5840,38939]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:54:48 on modular  [Seed = 2559283435]
-------------------------------------

2
Point [ 1, 2553, 723, 693 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1: 15075 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:55:34 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-98863249,0]);
f := P!Reverse([2445,1793,-14670,-1793,2445]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:55:20 on modular [Seed = 2626655439] ------------------------------------- 4 Point [ 1, 144, 2780, 308 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2136, 3517, 3750 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 2810, 3887, 3351 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4130, 1139, 5231 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 4750, 5441, 5951 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5882, 2718, 1278 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 98863249*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 98863249*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.750 seconds, Total memory usage: 9.16MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:56:11 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-98863249,0]);
f := P!Reverse([2445,1793,-14670,-1793,2445]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,8000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:55:52 on modular [Seed = 2424543395] ------------------------------------- 4 Point [ 1, 77, 6302, 3988 ] was singular mod 8009 and ignored at the #1 lift Point [ 1, 1540, 869, 6907 ] was singular mod 8009 and ignored at the #3 lift Point [ 1, 1936, 164, 7015 ] was singular mod 8009 and ignored at the #3 lift Point [ 1, 2470, 1829, 1436 ] was singular mod 8009 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 98863249*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 98863249*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 19.399 seconds, Total memory usage: 9.15MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:56:53 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-98863249,0]);
f := P!Reverse([2445,1793,-14670,-1793,2445]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:56:32 on modular [Seed = 2491915423] ------------------------------------- 4 Point [ 1, 2811, 6126, 2569 ] was singular mod 10007 and ignored at the #1 lift Point [ 1, 7154, 6977, 734 ] was singular mod 10007 and ignored at the #1 lift Errors: /bin/sh: line 1: 15087 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:57:25 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-98863249,0]); f := P!Reverse([407,492,12096,-164664,891908]); S := FourDescent(f); #S; F := S; pts := Points(F,8000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:57:04 on modular  [Seed = 2291892323]
-------------------------------------

Errors: /bin/sh: line 1: 15091 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:57:47 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-98863249,0]);
f := P!Reverse([61,0,0,0,6482836]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Wed Sep 22 2004 23:57:33 on modular [Seed = 2359264346] ------------------------------------- 4 Elliptic Curve defined by y^2 = x^3 - 98863249*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 98863249*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 14.710 seconds, Total memory usage: 8.49MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:58:20 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-98863249,0]);
f := P!Reverse([61,0,0,0,6482836]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,10000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:57:59 on modular [Seed = 2157152316] ------------------------------------- 4 Point [ 1, 4536, 3642, 2369 ] was singular mod 10007 and ignored at the #1 lift Point [ 1, 5259, 8782, 6131 ] was singular mod 10007 and ignored at the #3 lift Point [ 1, 7065, 4920, 7535 ] was singular mod 10007 and ignored at the #1 lift Errors: /bin/sh: line 1: 15099 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Wed Sep 22 23:58:59 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-98863249,0]); f := P!Reverse([-5807,-740,60876,25552,-14104]); S := FourDescent(f); #S; F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Wed Sep 22 2004 23:58:38 on modular  [Seed = 2224524305]
-------------------------------------

4
Point [ 1, 399, 2729, 6079 ] was singular mod 10007 and ignored at the #3 lift
Point [ 1, 1608, 5713, 231 ] was singular mod 10007 and ignored at the #3 lift

Errors: /bin/sh: line 1: 15103 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Wed Sep 22 23:59:44 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-3031081,0]);
f := P!Reverse([1861,496,-11070,23712,67757]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,8000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Wed Sep 22 2004 23:59:23 on modular [Seed = 2037019160] ------------------------------------- Errors: /bin/sh: line 1: 15107 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:00:23 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-3031081,0]); f := P!Reverse([1741,0,-10446,-27856,71381]); S := FourDescent(f); #S; F := S; pts := Points(F,8000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Thu Sep 23 2004 00:00:04 on modular  [Seed = 1918990668]
-------------------------------------

2
Elliptic Curve defined by y^2 = x^3 - 3031081*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 33341891*x + 73879568294 over Rational
Field
function(p) ... end function
(498655729694406253456298736649/158162502884713461222281209 :
-19744240179975894363004274786517052670714786/198909393627855060721453373653791\
5601677 : 1)
67.110193469208738292763

Total time: 18.679 seconds, Total memory usage: 5.15MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:01:06 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-48497296,0]);
f := P!Reverse([1861,496,-11070,23712,67757]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Thu Sep 23 2004 00:00:45 on modular [Seed = 1986362721] ------------------------------------- Errors: /bin/sh: line 1: 15116 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:01:33 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-48497296,0]); f := P!Reverse([1741,0,-10446,-27856,71381]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Thu Sep 23 2004 00:01:19 on modular  [Seed = 1786339743]
-------------------------------------

2
Point [ 1, 1456, 704, 5895 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 1483, 4657, 3541 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 2209, 5224, 4622 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4245, 2031, 72 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4544, 1896, 1808 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 5160, 4717, 1353 ] was singular mod 6007 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 48497296*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 33341891*x + 73879568294 over Rational
Field
function(p) ... end function
(498655729694406253456298736649/158162502884713461222281209 :
-19744240179975894363004274786517052670714786/198909393627855060721453373653791\
5601677 : 1)
67.110193469208738292763

Total time: 13.960 seconds, Total memory usage: 5.15MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:02:17 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-85803169,0]);
f := P!Reverse([-31,-16,2588856,407809040,18058149652]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:01:59 on modular [Seed = 1853711779] ------------------------------------- 4 Point [ 1, 1610, 4086, 3322 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 85803169*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 85803169*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 17.449 seconds, Total memory usage: 19.75MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:02:49 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-85803169,0]);
f := P!Reverse([314,0,0,0,1093034]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:02:34 on modular [Seed = 1718971846] ------------------------------------- 4 Point [ 1, 4110, 597, 2868 ] was singular mod 6007 and ignored at the #3 lift Point [ 1, 5395, 954, 4951 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 5952, 773, 0 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 85803169*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 85803169*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 15.269 seconds, Total memory usage: 8.69MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:03:25 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-85803169,0]);
f := P!Reverse([314,0,0,0,1093034]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,8000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:03:07 on modular [Seed = 1514754523] ------------------------------------- 4 Point [ 1, 433, 3947, 5114 ] was singular mod 8009 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 85803169*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 85803169*x over Rational Field function(p) ... end function (-3010877694330957044216640806290244110472651996031407550625/212256102157506088\ 052851922620403162929922851308826080889 : 1078842127013239108893136691492182087890198276498753393680452646565129984009933\ 65611859700/3092361637497555084596047966966680364512045759663811269699031719866\ 346706529688715213 : 1) 134.40776017696813937618 Total time: 18.600 seconds, Total memory usage: 8.70MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:04:14 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-5669161,0]); f := P!Reverse([2245,-528,-13374,43168,101933]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 00:03:53 on modular  [Seed = 1582126093]
-------------------------------------

Errors: /bin/sh: line 1: 15140 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:04:42 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-5669161,0]);
f := P!Reverse([2381,0,-14286,-38096,97621]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:04:28 on modular [Seed = 1380014180] ------------------------------------- 2 Elliptic Curve defined by y^2 = x^3 - 5669161*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 62360771*x + 188975812774 over Rational Field function(p) ... end function (-207758883735084409268825372007/22832935638070014639923689 : -6032953338307042267860092326301035165244110/1091044912885713245428537121952933\ 06613 : 1) 67.21936443734541910544 Total time: 14.140 seconds, Total memory usage: 5.15MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:05:17 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-90706576,0]); f := P!Reverse([2245,-528,-13374,43168,101933]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 00:04:56 on modular  [Seed = 1464098117]
-------------------------------------

Errors: /bin/sh: line 1: 15149 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:05:38 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-90706576,0]);
f := P!Reverse([2381,0,-14286,-38096,97621]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:05:24 on modular [Seed = 1264075189] ------------------------------------- 2 Elliptic Curve defined by y^2 = x^3 - 90706576*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 62360771*x + 188975812774 over Rational Field function(p) ... end function (-207758883735084409268825372007/22832935638070014639923689 : -6032953338307042267860092326301035165244110/1091044912885713245428537121952933\ 06613 : 1) 67.21936443734541910544 Total time: 14.080 seconds, Total memory usage: 5.15MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:06:15 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-38303721,0]); f := P!Reverse([462,276,-16335,-11352,178173]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 00:05:54 on modular  [Seed = 1331447191]
-------------------------------------

2
Point [ 1, 1953, 2708, 3317 ] was singular mod 6007 and ignored at the #1 lift

Errors: /bin/sh: line 1: 15157 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:06:44 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-38303721,0]);
f := P!Reverse([4759,2745,-16380,-4887,16731]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:06:28 on modular [Seed = 1129335293] ------------------------------------- 2 Point [ 1, 2214, 1010, 4134 ] was singular mod 6007 and ignored at the #3 lift Elliptic Curve defined by y^2 = x^3 - 38303721*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 421340931*x + 3318864209766 over Rational Field function(p) ... end function (-633133179825881608523523794768790/29042915413285752242201856961 : 7247150912854370408068791131798860544287167721956/49494884480624211417142393102\ 53210833115041 : 1) 67.24919675052625223088 Total time: 16.660 seconds, Total memory usage: 5.92MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:07:29 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-57138481,0]); f := P!Reverse([55,8,-15255,-114442,2500164]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 00:07:08 on modular  [Seed = 1196707281]
-------------------------------------

2

Errors: /bin/sh: line 1: 15165 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:08:02 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-57138481,0]);
f := P!Reverse([161,-212,-20037,26464,759450]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Thu Sep 23 2004 00:07:41 on modular [Seed = 992491084] ------------------------------------- Errors: /bin/sh: line 1: 15169 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:08:29 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-71995225,0]); f := P!Reverse([221,88,-23622,-1266040,13997453]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 00:08:08 on modular  [Seed = 1026437231]
-------------------------------------

2
Point [ 1, 573, 1502, 5972 ] was singular mod 6007 and ignored at the #3 lift

Errors: /bin/sh: line 1: 15175 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:08:55 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-71995225,0]);
f := P!Reverse([22061,-6788,-81456,40728,115396]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:08:40 on modular [Seed = 824327171] ------------------------------------- 2 Point [ 1, 1456, 3043, 5456 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 1895, 902, 829 ] was singular mod 6007 and ignored at the #1 lift Point [ 1, 3370, 4840, 1956 ] was singular mod 6007 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 71995225*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 791947475*x + 8552312777750 over Rational Field function(p) ... end function (-1237918005925112454515272153055/49418290745910886818595201 : -1236665298502230401930564286081576067370357650/3474014127788024286929082506547\ 88532801 : 1) 67.54223186788796340351 Total time: 14.929 seconds, Total memory usage: 14.67MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:09:25 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12159169,0]); f := P!Reverse([317,0,0,0,153428]); S := FourDescent(f); #S; F := S; pts := Points(F,6000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Thu Sep 23 2004 00:09:10 on modular  [Seed = 891697193]
-------------------------------------

4
Point [ 1, 303, 360, 1989 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 1265, 966, 3137 ] was singular mod 6007 and ignored at the #3 lift
Point [ 1, 4596, 4940, 590 ] was singular mod 6007 and ignored at the #1 lift
Point [ 1, 5334, 1728, 4650 ] was singular mod 6007 and ignored at the #3 lift
Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 14.439 seconds, Total memory usage: 6.60MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:10:00 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12159169,0]); f := P!Reverse([317,0,0,0,153428]); S := FourDescent(f); #S; F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 00:09:39 on modular  [Seed = 691676368]
-------------------------------------

4

Errors: /bin/sh: line 1: 15187 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:10:28 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-12159169,0]);
f := P!Reverse([317,0,0,0,153428]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,9000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:10:07 on modular [Seed = 573648839] ------------------------------------- 4 Point [ 1, 1661, 3680, 3054 ] was singular mod 9001 and ignored at the #1 lift Point [ 1, 3449, 3960, 4365 ] was singular mod 9001 and ignored at the #1 lift Point [ 1, 4913, 5132, 3482 ] was singular mod 9001 and ignored at the #1 lift Point [ 1, 7637, 7613, 7329 ] was singular mod 9001 and ignored at the #1 lift Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 20.629 seconds, Total memory usage: 6.61MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:11:03 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-12159169,0]);
f := P!Reverse([273,-512,-27306,125024,-108063]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:10:44 on modular [Seed = 641018776] ------------------------------------- 4 Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field function(p) ... end function >> m(pts); ^ Runtime error in '[]': Sequence element 1 not defined >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 18.600 seconds, Total memory usage: 13.82MB

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:11:32 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-12159169,0]);
f := P!Reverse([273,-512,-27306,125024,-108063]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,9000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Thu Sep 23 2004 00:11:11 on modular [Seed = 436803519] ------------------------------------- 4 Errors: /bin/sh: line 1: 15200 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:12:02 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12159169,0]); f := P!Reverse([-7,-9,5379,22686,-82516]); S := FourDescent(f); #S; F := S; pts := Points(F,8000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Thu Sep 23 2004 00:11:45 on modular  [Seed = 504173157]
-------------------------------------

4
Point [ 1, 1827, 6761, 552 ] was singular mod 8009 and ignored at the #1 lift
Point [ 1, 1827, 1248, 7457 ] was singular mod 8009 and ignored at the #1 lift
Point [ 1, 2359, 3801, 1892 ] was singular mod 8009 and ignored at the #1 lift
Point [ 1, 2359, 4208, 6117 ] was singular mod 8009 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 17.379 seconds, Total memory usage: 8.79MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:12:42 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12159169,0]); f := P!Reverse([-7,-9,5379,22686,-82516]); S := FourDescent(f); #S; F := S; pts := Points(F,9000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Thu Sep 23 2004 00:12:24 on modular  [Seed = 302063168]
-------------------------------------

4
Point [ 1, 7496, 4740, 1017 ] was singular mod 9001 and ignored at the #1 lift
Point [ 1, 7496, 4261, 7984 ] was singular mod 9001 and ignored at the #1 lift
Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 18.730 seconds, Total memory usage: 8.80MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:13:23 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12159169,0]); f := P!Reverse([-7,-9,5379,22686,-82516]); S := FourDescent(f); #S; F := S; pts := Points(F,10000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: Magma V2.11-6     Thu Sep 23 2004 00:13:02 on modular  [Seed = 369433122]
-------------------------------------

4
Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field
Elliptic Curve defined by y^2 = x^3 - 12159169*x over Rational Field
function(p) ... end function

>> m(pts);
^
Runtime error in '[]': Sequence element 1 not defined

>> Height($1); ^ Runtime error in 'Height': Bad argument types Argument types given: CrvEll[FldRat] Total time: 20.800 seconds, Total memory usage: 8.80MB '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:14:00 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12159169,0]); f := P!Reverse([1807,544,8502,-21248,21983]); S := FourDescent(f); #S; F := S; pts := Points(F,9000); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 00:13:39 on modular  [Seed = 169412099]
-------------------------------------

Errors: /bin/sh: line 1: 15216 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:14:31 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-12159169,0]);
f := P!Reverse([1807,544,8502,-21248,21983]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,8000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.11-6 Thu Sep 23 2004 00:14:10 on modular [Seed = 236782310] ------------------------------------- Errors: /bin/sh: line 1: 15220 Killed nice -n 19 /usr/local/bin/magma '66.63.1' ************** MAGMA ***************** Host 66.63.133.107 (66.63.133.107) Time: Thu Sep 23 00:15:02 2004 Input: P<x> := PolynomialRing(Integers()); E := EllipticCurve([0,0,0,-12159169,0]); f := P!Reverse([1807,544,8502,-21248,21983]); S := FourDescent(f); #S; F := S; pts := Points(F,7500); X,m := Scheme(F); E; AssociatedEC(f); m(pts); Height($1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 00:14:41 on modular  [Seed = 51384267]
-------------------------------------

Errors: /bin/sh: line 1: 15225 Killed                  nice -n 19 /usr/local/bin/magma

'66.63.1'
************** MAGMA *****************
Host 66.63.133.107 (66.63.133.107)
Time: Thu Sep 23 00:15:27 2004

Input: P<x> := PolynomialRing(Integers());
E := EllipticCurve([0,0,0,-9369721,0]);
f := P!Reverse([1885,3552,-4398,-103984,168869]);
S := FourDescent(f);
#S;
F := S;
pts := Points(F,6000);
X,m := Scheme(F);
E;
AssociatedEC(f);
m(pts);
Height($1); Output: Magma V2.11-6 Thu Sep 23 2004 00:15:10 on modular [Seed = 118754227] ------------------------------------- FourDescent( f: 1885*x^4 + 3552*x^3 - 4398*x^2 - 103984*x + 168869 ) ReduceFD( fd: [ [-41617750135290013888369064449317792069583530954379765719... ) StollReduce( desc: [ [243062764338950785921771106850275170385223816905625221138... ) Covariant( mat1: [24306276433895078592177110685027517038522381690562522113803..., mat2: [50031863926273400701283480423456954482152989951564970704139... ) In file "/usr/local/magma/package/Geometry/CrvEll/FourDesc/stoll_reduce.m", line 335, column 37: >> three := [[singt1[i,j,j]/singt1[i,1,1] : j in [1..4]] : i in [2 ^ Runtime error in '/': Division by zero in (possibly) real or complex division. Maybe loss of precision? >> #S; ^ User error: Identifier 'S' has not been declared or assigned >> F := S; ^ User error: Identifier 'S' has not been declared or assigned >> pts := Points(F,6000); ^ User error: Identifier 'F' has not been declared or assigned >> X,m := Scheme(F); ^ User error: Identifier 'F' has not been declared or assigned Elliptic Curve defined by y^2 = x^3 - 9369721*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 103066931*x + 401530023734 over Rational Field function(p) ... end function >> m(pts); ^ User error: Identifier 'pts' has not been declared or assigned >> Height($1);
^
Runtime error in 'Height': Bad argument types
Argument types given: CrvEll[FldRat]

Total time: 17.010 seconds, Total memory usage: 10.26MB

'128.250'
************** MAGMA *****************
Host 128.250.6.244 (128.250.6.244)
Time: Thu Sep 23 02:35:51 2004

Input: o:=895345667699102774401586145216665244372227956180030408652275210172990575775371852357246810190225812091543697403297233568718790859558624218928807565245152029112371308407805340970689509185898662074880855074503956909360142366409664141753404
7684374716819073679317475038905629385884563472619584;
Factorization(o);

Output: Magma V2.11-6     Thu Sep 23 2004 02:35:51 on modular  [Seed = 2359272241]
-------------------------------------

>> 7684374716819073679317475038905629385884563472619584;
^

>> Factorization(o);;
^
User error: Identifier 'o' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.51MB

'128.250'
************** MAGMA *****************
Host 128.250.6.244 (128.250.6.244)
Time: Thu Sep 23 02:36:45 2004

Input: o:=8953456676991027744015861452166652443722279561800304086522752101729905757753718523572468101902258120915436974032972335687187908595586242189288075652451520291123713084078053409706895091858986620748808550745039569093601423664096641417534047684374716819073679317475038905629385884563472619584;
Factorization(o);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.11-6     Thu Sep 23 2004 02:36:24 on modular  [Seed = 2173873683]
-------------------------------------

Errors: /bin/sh: line 1: 15355 Killed                  nice -n 19 /usr/local/bin/magma

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:13:46 2004

Input: S:= [GF(7)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);

Output: Magma V2.11-6     Thu Sep 23 2004 04:13:46 on modular  [Seed = 1230671246]
-------------------------------------

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:14:57 2004

Input: S:= [GF(7)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;

Output: Magma V2.11-6     Thu Sep 23 2004 04:14:57 on modular  [Seed = 1180008762]
-------------------------------------

6*D^5 + 1

Total time: 0.180 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:15:37 2004

Input: S:= [GF(7)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:15:37 on modular  [Seed = 1026488937]
-------------------------------------

6*D^5 + 1
5

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:16:17 2004

Input: S:= [GF(11)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:16:17 on modular  [Seed = 942407444]
-------------------------------------

10*D^5 + 1
5

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:16:25 2004

Input: S:= [GF(13)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:16:25 on modular  [Seed = 925167635]
-------------------------------------

12*D^5 + 1
5

Total time: 0.190 seconds, Total memory usage: 3.56MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:16:34 2004

Input: S:= [GF(17)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:16:34 on modular  [Seed = 841086253]
-------------------------------------

16*D^5 + 1
5

Total time: 0.200 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:16:43 2004

Input: S:= [GF(8)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:16:42 on modular  [Seed = 691727934]
-------------------------------------

D^4 + D^3 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:16:59 2004

Input: S:= [GF(9)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:16:59 on modular  [Seed = 607642402]
-------------------------------------

D^4 + D^3 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.56MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:17:10 2004

Input: S:= [GF(23)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:17:10 on modular  [Seed = 487512806]
-------------------------------------

22*D^5 + 1
5

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:17:19 2004

Input: S:= [GF(29)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:17:18 on modular  [Seed = 403431403]
-------------------------------------

28*D^5 + 1
5

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:17:28 2004

Input: S:= [GF(31)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:17:28 on modular  [Seed = 386191602]
-------------------------------------

30*D^5 + 1
5

Total time: 0.180 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:18:33 2004

Input: S:= [GF(31)| 1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:18:32 on modular  [Seed = 302110135]
-------------------------------------

30*D^4 + 30*D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:18:42 2004

Input: S:= [GF(3)| 1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:18:42 on modular  [Seed = 152751766]
-------------------------------------

2*D^4 + 2*D + 1
4

Total time: 0.180 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:18:59 2004

Input: S:= [GF(3)| 1,1,1,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:18:59 on modular  [Seed = 68666250]
-------------------------------------

2*D + 1
1

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:19:13 2004

Input: S:= [GF(3)| 1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:19:13 on modular  [Seed = 51430783]
-------------------------------------

2*D^4 + 2*D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:19:43 2004

Input: S:= [GF(3)| 1,1,1,1,2,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:19:43 on modular  [Seed = 4276959388]
-------------------------------------

2*D^4 + D^2 + D + 1
4

Total time: 0.180 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:20:03 2004

Input: S:= [GF(3)| 1,1,1,1,2,1,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:20:03 on modular  [Seed = 4158927289]
-------------------------------------

2*D^4 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:20:12 2004

Input: S:= [GF(3)| 1,1,1,1,2,1,1,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:20:12 on modular  [Seed = 4074845363]
-------------------------------------

D^4 + D^3 + D^2 + D + 1
4

Total time: 0.180 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:21:42 2004

Input: S:= [GF(3)| 1,1,1,1,2,1,1,1,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:21:42 on modular  [Seed = 3925487362]
-------------------------------------

D^4 + D^3 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:21:49 2004

Input: S:= [GF(3)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:21:48 on modular  [Seed = 3841401349]
-------------------------------------

D^4 + D^3 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:22:53 2004

Input: S:= [GF(3)| 1,1,1,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:22:53 on modular  [Seed = 3807454274]
-------------------------------------

2*D + 1
1

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:23:24 2004

Input: S:= [GF(3)| 1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:23:23 on modular  [Seed = 3687325021]
-------------------------------------

2*D^4 + 2*D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:24:15 2004

Input: S:= [GF(3)| 1,1,1,1,2,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:24:15 on modular  [Seed = 3519158403]
-------------------------------------

2*D^4 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:24:43 2004

Input: S:= [GF(3)| 1,1,1,1,2,1,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:24:43 on modular  [Seed = 3437168122]
-------------------------------------

2*D^4 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:25:14 2004

Input: S:= [GF(3)| 1,1,1,1,2,1,1,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:25:14 on modular  [Seed = 3403219933]
-------------------------------------

D^4 + D^3 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:26:00 2004

Input: S:= [GF(3)| 1,1,1,1,2,1,1,1,1];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:25:59 on modular  [Seed = 3251767339]
-------------------------------------

D^4 + D^3 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 04:26:38 2004

Input: S:= [GF(3)| 1,1,1,1,2,1,1,1,1,2];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 04:26:38 on modular  [Seed = 3114954874]
-------------------------------------

D^4 + D^3 + D^2 + D + 1
4

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 08:51:59 2004

Input: S:= [GF(11)| 1,2,3,4,5,6,7,9,8,10];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 08:51:59 on modular  [Seed = 3182311980]
-------------------------------------

9*D^6 + D^5 + 4*D^4 + 8*D^3 + 6*D^2 + 3*D + 1
6

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 08:52:17 2004

Input: S:= [GF(11)| 1,2,3,4,5,6,7];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 08:52:16 on modular  [Seed = 3064279240]
-------------------------------------

D^2 + 9*D + 1
2

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 08:52:27 2004

Input: S:= [GF(11)| 1,2,3,4,5,6,7,9,8];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 08:52:27 on modular  [Seed = 3013621190]
-------------------------------------

9*D^6 + D^5 + 5*D^3 + 2*D^2 + 3*D + 1
6

Total time: 0.190 seconds, Total memory usage: 3.51MB

'212.98.'
************** MAGMA *****************
Host 212.98.201.1 (212.98.201.1)
Time: Thu Sep 23 08:52:37 2004

Input: S:= [GF(11)| 1,2,3,4,5,6,7,9,8,10];
C<D>, L := BerlekampMassey(S);
C;
L;

Output: Magma V2.11-6     Thu Sep 23 2004 08:52:37 on modular  [Seed = 2898209479]
-------------------------------------

9*D^6 + D^5 + 4*D^4 + 8*D^3 + 6*D^2 + 3*D + 1
6

Total time: 0.190 seconds, Total memory usage: 3.51MB

'132.229'
************** MAGMA *****************
Host 132.229.228.228 (132.229.228.228)
Time: Thu Sep 23 10:25:42 2004

Input: P<x>:=PolynomialRing(Rationals());
N<u>:=NumberField(4*x^3-156*x^2+57*x-4);
E:=EllipticCurve([0,4*u-156,0,4*(4*u^2-156*u+57),0]);
twoE := MultiplicationByMMap(E, 2);
muE := CasselsMap(twoE);
SE, toSE := SelmerGroup(twoE);
rkEQ := RankBound(E);
PseudoMordellWeilGroup(E);

Output: Magma V2.11-6     Thu Sep 23 2004 10:25:29 on modular  [Seed = 1786378163]
-------------------------------------

false
Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to CrvEll: E given by a rule [no inverse]

Total time: 12.720 seconds, Total memory usage: 8.30MB

'132.229'
************** MAGMA *****************
Host 132.229.228.228 (132.229.228.228)
Time: Thu Sep 23 10:26:23 2004

Input: P<x>:=PolynomialRing(Rationals());
N<u>:=NumberField(4*x^3-156*x^2+57*x-4);
E:=EllipticCurve([0,4*u-156,0,4*(4*u^2-156*u+57),0]);
twoE := MultiplicationByMMap(E, 2);
muE := CasselsMap(twoE);
SE, toSE := SelmerGroup(twoE);
RankBound(E);
PseudoMordellWeilGroup(E);

Output: Magma V2.11-6     Thu Sep 23 2004 10:26:09 on modular  [Seed = 1870459758]
-------------------------------------

2
false
Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to CrvEll: E given by a rule [no inverse]

Total time: 13.339 seconds, Total memory usage: 8.54MB

'132.229'
************** MAGMA *****************
Host 132.229.228.228 (132.229.228.228)
Time: Thu Sep 23 10:28:29 2004

Input: P<x>:=PolynomialRing(Rationals());
N<u>:=NumberField(4*x^3-156*x^2+57*x-4);
E:=EllipticCurve([0,4*(-4*u^2+157*u-39),0,4*(4*u^2-92*u+25),0]);
twoE := MultiplicationByMMap(E, 2);
muE := CasselsMap(twoE);
SE, toSE := SelmerGroup(twoE);
RankBound(E);
PseudoMordellWeilGroup(E);

Output: Magma V2.11-6     Thu Sep 23 2004 10:28:26 on modular  [Seed = 2053760752]
-------------------------------------

SelmerGroup(
phi: Elliptic curve isogeny from: Elliptic Curve defined by y^2 =...
)
TwoSelmWorkOdd(
F: $.1^3 + (-16*u^2 + 628*u - 156)*$.1^2 + (16*u^2 - 368*u + 10...
)
pSelmerGroup(
A: Univariate Quotient Polynomial Algebra in theta over Number ...,
p: 2,
S: { Prime Ideal Two element generators: [2, 0, 0] [0, 0, 1], P...
)
pSelmerGroup(
p: 2,
S: { Prime Ideal of O Two element generators: [3, 0, 0, 0, 0, 0...
)
In file "/usr/local/magma/package/Ring/FldNum/order.m", line 128, column 22:
>>   C, mC := ClassGroup(O: Proof := "Current");
^
Runtime error in 'ClassGroup': precision error -- increase precision (and
bounds)
1
true
Abelian Group isomorphic to Z/2 + Z
Defined on 2 generators
Relations:
2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 to CrvEll: E given by a rule [no inverse]

Total time: 3.319 seconds, Total memory usage: 7.83MB

'132.229'
************** MAGMA *****************
Host 132.229.228.228 (132.229.228.228)
Time: Thu Sep 23 10:29:01 2004

Input: P<x>:=PolynomialRing(Rationals());
N<u>:=NumberField(4*x^3-156*x^2+57*x-4);
E:=EllipticCurve([0,4*(-4*u^2+157*u-39),0,4*(4*u^2-92*u+25),0]);
RankBound(E);
PseudoMordellWeilGroup(E);

Output: Magma V2.11-6     Thu Sep 23 2004 10:28:59 on modular  [Seed = 2342000416]
-------------------------------------

1
true
Abelian Group isomorphic to Z/2 + Z
Defined on 2 generators
Relations:
2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z Defined on 2 generators Relations: 2*$.1 = 0 to CrvEll: E given by a rule [no inverse]

Total time: 2.149 seconds, Total memory usage: 7.06MB

'217.57.'
************** MAGMA *****************
Host 217.57.196.233 (217.57.196.233)
Time: Thu Sep 23 11:27:27 2004

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-6     Thu Sep 23 2004 11:27:26 on modular  [Seed = 3603266696]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.51MB

'129.93.'
************** MAGMA *****************
Host 129.93.181.78 (129.93.181.78)
Time: Thu Sep 23 16:54:54 2004

Input: 2 +3

Output: Magma V2.11-6     Thu Sep 23 2004 16:54:54 on modular  [Seed = 624385084]
-------------------------------------

5

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:11:59 2004

Input: n:=228618946967762521;
x:=90208952368431523;

n1:=GCD(x-1, n); n1;
n2:=GCD(x^2+x+1, n); n2;
Factorization(n);

Output: Magma V2.11-6     Thu Sep 23 2004 22:11:56 on modular  [Seed = 470736702]
-------------------------------------

933376471
244937551
[ <244937551, 1>, <933376471, 1> ]

Total time: 0.250 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:13:11 2004

Input: p:=1234621183;

IsPrime(p);

a:=3; b:=2; n:=p-1; x:=0;

f:=[* 2, 3, 83, 383, 6473 *];
m:=[* *];
for i in f do
printf �x mod %o�, i;
as:=Modexp(a, Integers()!(n/i), p);
bs:=Modexp(b, Integers()!(n/i), p);

for j in [0..i-1] do
if (Modexp(as, j, p) eq bs) then
printf � = %on�, j;
// Gauss� Algorithm
one, n_inv, k:=XGCD(Integers()!(n/i), i);
x+:=j*(Integers()!(n/i))*n_inv mod n;
Append(~m, j);
end if;
end for;
end for;
printf �:. log3(2)=%on�, x;

Output: Magma V2.11-6     Thu Sep 23 2004 22:13:11 on modular  [Seed = 420207328]
-------------------------------------

true

>>         printf ^�x mod %o^�, i;
^
User error: Unknown character (ASCII value 147)

>>         as:=Modexp(a, Integers()!(n/i), p);
^
User error: Identifier 'i' has not been declared or assigned

>>         bs:=Modexp(b, Integers()!(n/i), p);
^
User error: Identifier 'i' has not been declared or assigned

>>                         printf ^� = %on^�, j;
^
User error: Unknown character (ASCII value 147)

>>                         one, n_inv, k:=XGCD(Integers()!(n/i), i);
^
User error: Identifier 'i' has not been declared or assigned

>>                         x+:=j*(Integers()!(n/i))*n_inv mod n;
^
User error: Identifier 'j' has not been declared or assigned

>>                         Append(~m, j);
^
User error: Identifier 'j' has not been declared or assigned

>>                 end if;
^

>>         end for;
^

>> end for;
^

>> printf ^�:. log3(2)=%on^�, x;
^
User error: Unknown character (ASCII value 147)

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:15:08 2004

Input: p:=1234621183;

IsPrime(p);

a:=3; b:=2; n:=p-1; x:=0;

f:=[* 2, 3, 83, 383, 6473 *];
m:=[* *];
for i in f do
printf "x mod %o", i;
as:=Modexp(a, Integers()!(n/i), p);
bs:=Modexp(b, Integers()!(n/i), p);

for j in [0..i-1] do
if (Modexp(as, j, p) eq bs) then
printf " = %on", j;
// Gauss� Algorithm
one, n_inv, k:=XGCD(Integers()!(n/i), i);
x+:=j*(Integers()!(n/i))*n_inv mod n;
Append(~m, j);
end if;
end for;
end for;
printf ":. log3(2)=%on", x;

Output: Magma V2.11-6     Thu Sep 23 2004 22:15:08 on modular  [Seed = 775744588]
-------------------------------------

true
x mod 2 = 0nx mod 3 = 0nx mod 83 = 56nx mod 383 = 215nx mod 6473 = 5635n:.
log3(2)=1624256106n
Total time: 0.210 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:16:58 2004

Input: Modexp(3, 1624256106, 1234621183);

Output: Magma V2.11-6     Thu Sep 23 2004 22:16:58 on modular  [Seed = 641000690]
-------------------------------------

2

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:19:01 2004

Input: g:=1; lp:=0; ltt:=0; n:=65536; p:=65537;
as:=Modexp(a, Integers()!(n/2), p);

for j in [0..15] do

g:=g*Modexp(a, Integers()!(n/2), p);
// find inverse of g
one, g_inv, k:=XGCD(g, p);
bs:=Modexp(b*g_inv, Integers()!(n/2^(j+1)), p);
// �exhaustive search� of two things! &#61514;
if (as eq bs) then ltt+:=2^j; lp:=1; else lp:=0; end if;

end for;

printf ":. log3(2)=%on", ltt;

Output: Magma V2.11-6     Thu Sep 23 2004 22:19:01 on modular  [Seed = 557048954]
-------------------------------------

>> as:=Modexp(a, Integers()!(n/2), p);
^
User error: Identifier 'a' has not been declared or assigned

>>         g:=g*Modexp(a, Integers()!(n/2), p);
^
User error: Identifier 'a' has not been declared or assigned
:. log3(2)=0n
Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:19:55 2004

Input: a:=3; b:=2;

g:=1; lp:=0; ltt:=0; n:=65536; p:=65537;
as:=Modexp(a, Integers()!(n/2), p);

for j in [0..15] do

g:=g*Modexp(a, Integers()!(n/2), p);
// find inverse of g
one, g_inv, k:=XGCD(g, p);
bs:=Modexp(b*g_inv, Integers()!(n/2^(j+1)), p);
// �exhaustive search� of two things! &#61514;
if (as eq bs) then ltt+:=2^j; lp:=1; else lp:=0; end if;

end for;

printf ":. log3(2)=%on", ltt;

Output: Magma V2.11-6     Thu Sep 23 2004 22:19:54 on modular  [Seed = 992607807]
-------------------------------------

:. log3(2)=2048n
Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:21:10 2004

Input: Modexp(3, 2048, 65537);

Output: Magma V2.11-6     Thu Sep 23 2004 22:21:09 on modular  [Seed = 857863912]
-------------------------------------

65529

Total time: 0.200 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:21:52 2004

Input: p:=1234621183;

IsPrime(p);

a:=3; b:=2; n:=p-1; x:=0;

f:=[* 2, 3, 83, 383, 6473 *];
m:=[* *];
for i in f do
printf �x mod %o�, i;
as:=Modexp(a, Integers()!(n/i), p);
bs:=Modexp(b, Integers()!(n/i), p);

for j in [0..i-1] do
if (Modexp(as, j, p) eq bs) then
printf � = %on�, j;
// Gauss� Algorithm
one, n_inv, k:=XGCD(Integers()!(n/i), i);
x+:=j*(Integers()!(n/i))*n_inv mod n;
Append(~m, j);
end if;
end for;
end for;
printf �:. log3(2)=%on�, x;

Modexp(3, 1624256106, 1234621183);

g:=1; lp:=0; ltt:=0; n:=65536; p:=65537;
as:=Modexp(a, Integers()!(n/2), p);

for j in [0..15] do

g:=g*Modexp(a, Integers()!(n/2), p);
// find inverse of g
one, g_inv, k:=XGCD(g, p);
bs:=Modexp(b*g_inv, Integers()!(n/2^(j+1)), p);
// �exhaustive search� of two things! &#61514;
if (as eq bs) then ltt+:=2^j; lp:=1; else lp:=0; end if;

end for;

printf �:. log3(2)=%on�, ltt;

Output: Magma V2.11-6     Thu Sep 23 2004 22:21:51 on modular  [Seed = 3437103421]
-------------------------------------

true

>>         printf ^�x mod %o^�, i;
^
User error: Unknown character (ASCII value 147)

>>         as:=Modexp(a, Integers()!(n/i), p);
^
User error: Identifier 'i' has not been declared or assigned

>>         bs:=Modexp(b, Integers()!(n/i), p);
^
User error: Identifier 'i' has not been declared or assigned

>>                         printf ^� = %on^�, j;
^
User error: Unknown character (ASCII value 147)

>>                         one, n_inv, k:=XGCD(Integers()!(n/i), i);
^
User error: Identifier 'i' has not been declared or assigned

>>                         x+:=j*(Integers()!(n/i))*n_inv mod n;
^
User error: Identifier 'j' has not been declared or assigned

>>                         Append(~m, j);
^
User error: Identifier 'j' has not been declared or assigned

>>                 end if;
^

>>         end for;
^

>> end for;
^

>> printf ^�:. log3(2)=%on^�, x;
^
User error: Unknown character (ASCII value 147)
2

>> printf ^�:. log3(2)=%on^�, ltt;
^
User error: Unknown character (ASCII value 147)

Total time: 0.180 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:22:28 2004

Input: p:=1234621183;

IsPrime(p);

a:=3; b:=2; n:=p-1; x:=0;

f:=[* 2, 3, 83, 383, 6473 *];
m:=[* *];
for i in f do
printf "x mod %o", i;
as:=Modexp(a, Integers()!(n/i), p);
bs:=Modexp(b, Integers()!(n/i), p);

for j in [0..i-1] do
if (Modexp(as, j, p) eq bs) then
printf " = %on", j;
// Gauss� Algorithm
one, n_inv, k:=XGCD(Integers()!(n/i), i);
x+:=j*(Integers()!(n/i))*n_inv mod n;
Append(~m, j);
end if;
end for;
end for;
printf ":. log3(2)=%on", x;

Modexp(3, 1624256106, 1234621183);

g:=1; lp:=0; ltt:=0; n:=65536; p:=65537;
as:=Modexp(a, Integers()!(n/2), p);

for j in [0..15] do

g:=g*Modexp(a, Integers()!(n/2), p);
// find inverse of g
one, g_inv, k:=XGCD(g, p);
bs:=Modexp(b*g_inv, Integers()!(n/2^(j+1)), p);
// �exhaustive search� of two things! &#61514;
if (as eq bs) then ltt+:=2^j; lp:=1; else lp:=0; end if;

end for;

printf ":. log3(2)=%on", ltt;

Output: Magma V2.11-6     Thu Sep 23 2004 22:22:28 on modular  [Seed = 3386575971]
-------------------------------------

true
x mod 2 = 0nx mod 3 = 0nx mod 83 = 56nx mod 383 = 215nx mod 6473 = 5635n:.
log3(2)=1624256106n2
:. log3(2)=2048n
Total time: 0.220 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:24:25 2004

Input: p:=1234621183;

IsPrime(p);

a:=3; b:=2; n:=p-1; x:=0;

f:=[* 2, 3, 83, 383, 6473 *];
m:=[* *];
for i in f do
printf "x mod %o", i;
as:=Modexp(a, Integers()!(n/i), p);
bs:=Modexp(b, Integers()!(n/i), p);

for j in [0..i-1] do
if (Modexp(as, j, p) eq bs) then
printf " = %on", j;
// Gauss� Algorithm
one, n_inv, k:=XGCD(Integers()!(n/i), i);
x+:=j*(Integers()!(n/i))*n_inv mod n;
Append(~m, j);
end if;
end for;
end for;
printf ":. log3(2)=%on", x;

Modexp(3, 1624256106, 1234621183);

g:=1; lp:=0; ltt:=0; n:=65536; p:=65537;
as:=Modexp(a, Integers()!(n/2), p);

for j in [0..15] do

g:=g*Modexp(a, Integers()!(lp*2^(j-1)), p);
// find inverse of g
one, g_inv, k:=XGCD(g, p);
bs:=Modexp(b*g_inv, Integers()!(n/2^(j+1)), p);
// �exhaustive search� of two things! &#61514;
if (as eq bs) then ltt+:=2^j; lp:=1; else lp:=0; end if;

end for;

printf ":. log3(2)=%on", ltt;

Output: Magma V2.11-6     Thu Sep 23 2004 22:24:24 on modular  [Seed = 3754761160]
-------------------------------------

true
x mod 2 = 0nx mod 3 = 0nx mod 83 = 56nx mod 383 = 215nx mod 6473 = 5635n:.
log3(2)=1624256106n2
:. log3(2)=55296n
Total time: 0.220 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:24:43 2004

Input: Modexp(3, 55296, 65537);

Output: Magma V2.11-6     Thu Sep 23 2004 22:24:43 on modular  [Seed = 3653967356]
-------------------------------------

2

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:28:58 2004

Input: Modexp(3, 55296, 65537);Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; x:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Output: Magma V2.11-6     Thu Sep 23 2004 22:28:58 on modular  [Seed = 3519223541]
-------------------------------------

2

>> Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:
^
x^2 + 7*x + 9
1
x^2 + 3*x + 8
1

>>         a:=Terms(z);
^
User error: Identifier 'z' has not been declared or assigned

>> i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist
^
Runtime error in '[]': Value for index (0) should be in the range [1..0]

>> printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers(
^
Runtime error in '[]': Value for index (0) should be in the range [1..0]

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:29:22 2004

Input: Modexp(3, 55296, 65537);Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; x:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Output: Magma V2.11-6     Thu Sep 23 2004 22:29:22 on modular  [Seed = 3925552677]
-------------------------------------

2
x^2 + 7*x + 9
1
x^2 + 3*x + 8
1

>>         a:=Terms(z);
^
User error: Identifier 'z' has not been declared or assigned

>> i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist
^
Runtime error in '[]': Value for index (0) should be in the range [1..0]

>> printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers(
^
Runtime error in '[]': Value for index (0) should be in the range [1..0]

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:29:40 2004

Input: Modexp(3, 55296, 65537);Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Output: Magma V2.11-6     Thu Sep 23 2004 22:29:40 on modular  [Seed = 3824231481]
-------------------------------------

2
x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n
Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:31:07 2004

Input: Modexp(3,5/2,10);

Output: Magma V2.11-6     Thu Sep 23 2004 22:31:07 on modular  [Seed = 4260313688]
-------------------------------------

>> Modexp(3,5/2,10);;
^
Runtime error in 'Modexp': Bad argument types
Argument types given: RngIntElt, FldRatElt, RngIntElt

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:31:40 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Output: Magma V2.11-6     Thu Sep 23 2004 22:31:39 on modular  [Seed = 4142149811]
-------------------------------------

>> Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:
^
x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n
Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:31:57 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Output: Magma V2.11-6     Thu Sep 23 2004 22:31:57 on modular  [Seed = 4091622816]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n
Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:34:10 2004

Input: 365461299940 mod 61;
697060 mod 61;
504363576777 mod 61;
961993 mod 61;

Output: Magma V2.11-6     Thu Sep 23 2004 22:34:09 on modular  [Seed = 2342079844]
-------------------------------------

29
13
0
23

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:34:34 2004

Input: 365461299940 mod 61;
697060 mod 61;
504363576777 mod 61;
961993 mod 61;
(29-13)/23

Output: Magma V2.11-6     Thu Sep 23 2004 22:34:34 on modular  [Seed = 2241282929]
-------------------------------------

29
13
0
23
16/23

Total time: 0.180 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:36:46 2004

Input: 365461299940 mod 61;
697060 mod 61;
504363576777 mod 61;
961993 mod 61;
(29-13)/23
one, n_inv, k:=XGCD(23, 61);

Output: Magma V2.11-6     Thu Sep 23 2004 22:36:45 on modular  [Seed = 2643416302]
-------------------------------------

29
13
0
23

>> one, n_inv, k:=XGCD(23, 61);;
^

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:37:03 2004

Input: 365461299940 mod 61;
697060 mod 61;
504363576777 mod 61;
961993 mod 61;
(29-13)/23;
one, n_inv, k:=XGCD(23, 61);

Output: Magma V2.11-6     Thu Sep 23 2004 22:37:03 on modular  [Seed = 2525257623]
-------------------------------------

29
13
0
23
16/23

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:37:12 2004

Input: 365461299940 mod 61;
697060 mod 61;
504363576777 mod 61;
961993 mod 61;
(29-13)/23;
one, n_inv, k:=XGCD(23, 61); n_inv;

Output: Magma V2.11-6     Thu Sep 23 2004 22:37:12 on modular  [Seed = 2474728069]
-------------------------------------

29
13
0
23
16/23
8

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:37:23 2004

Input: 365461299940 mod 61;
697060 mod 61;
504363576777 mod 61;
961993 mod 61;
(29-13)/23;
one, n_inv, k:=XGCD(23, 61); n_inv;
8*23 mod 61;

Output: Magma V2.11-6     Thu Sep 23 2004 22:37:23 on modular  [Seed = 2898158977]
-------------------------------------

29
13
0
23
16/23
8
1

Total time: 0.180 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:37:44 2004

Input: 365461299940 mod 61;
697060 mod 61;
504363576777 mod 61;
961993 mod 61;
(29-13)/23;
one, n_inv, k:=XGCD(23, 61); n_inv;
n_inv*16 mod 61;

Output: Magma V2.11-6     Thu Sep 23 2004 22:37:43 on modular  [Seed = 2847629456]
-------------------------------------

29
13
0
23
16/23
8
6

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:38:49 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:38:49 on modular  [Seed = 3215816264]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n6*x^2 + 6

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:39:10 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:39:10 on modular  [Seed = 3098177848]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n6*x^2 + 6

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:39:19 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:39:18 on modular  [Seed = 3047652397]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n6*x^2 + 6

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:39:30 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:39:30 on modular  [Seed = 1363384546]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n6*x^2 + 6

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:39:38 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);

Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:39:38 on modular  [Seed = 1464180460]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n6*x^2 + 6

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:40:03 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:40:03 on modular  [Seed = 1514705416]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
6*x^2 + 6

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:40:17 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
printf "n";
xx,yy;
Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:40:17 on modular  [Seed = 1095993601]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945nn7*x + 3
x^2 + 2
6*x^2 + 6

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:41:12 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:41:12 on modular  [Seed = 1230733648]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
6*x^2 + 6

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:41:48 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;
Modexp(xx, 8, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:41:48 on modular  [Seed = 1281262705]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
6*x^2 + 6

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:42:05 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;
Modexp(xx, 51, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:42:04 on modular  [Seed = 1935784798]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
3*x^2 + 3*x + 8

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:43:09 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;

for i in [0..61] do
i;Modexp(xx, i, x^3-x+1);
end for;

Output: Magma V2.11-6     Thu Sep 23 2004 22:43:09 on modular  [Seed = 1986313882]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
0
1
1
7*x + 3
2
10*x^2 + 3*x + 9
3
12*x^2 + 12*x + 9
4
3*x^2 + x + 8
5
3*x^2 + 2*x + 3
6
10*x^2 + 9*x + 1
7
2*x^2 + 11
8
6*x^2 + 6
9
5*x^2 + 6*x + 2
10
5*x^2 + 2*x + 10
11
3*x^2 + 7*x + 8
12
6*x^2 + 7*x + 3
13
2*x^2 + 6*x + 6
14
9*x^2 + 9*x + 4
15
12*x^2 + x + 1
16
4*x^2 + 3*x + 10
17
7*x^2 + 3*x + 2
18
3*x^2 + 7*x + 9
19
6*x^2 + x + 6
20
12*x^2 + 9*x + 2
21
8*x^2 + 8*x
22
2*x^2 + 2*x + 9
23
7*x^2 + 5*x
24
4*x^2 + 12*x + 3
25
5*x^2 + 7*x + 7
26
12*x^2 + x + 12
27
4*x^2 + 2*x + 4
28
10*x + 10
29
5*x^2 + 9*x + 4
30
12*x + 3
31
6*x^2 + 5*x + 9
32
x^2 + 3*x + 11
33
11*x^2 + 2*x
34
8*x^2 + 5*x + 1
35
7*x^2 + 12
36
8*x^2 + 3*x
37
6*x^2 + 9
38
5*x^2 + x + 11
39
9*x^2 + 11*x + 11
40
4*x + 9
41
2*x^2 + 10*x + 1
42
11*x^2 + 12*x + 2
43
10*x + 7
44
5*x^2 + x + 8
45
9*x^2 + 3*x + 2
46
9*x^2 + 8*x + 8
47
5*x^2
48
2*x^2 + 9*x + 4
49
4*x^2 + 4*x + 11
50
x^2 + 5
51
3*x^2 + 3*x + 8
52
4*x^2 + 8*x + 3
53
3*x^2 + 8*x + 7
54
3*x
55
8*x^2 + 9*x
56
9*x^2 + 5*x + 9
57
10*x^2 + 11*x + 3
58
3*x^2 + 7*x + 4
59
6*x^2 + 5*x + 4
60
x^2 + 7*x + 9
61
7

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:44:37 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;

for i in [0..61] do
i;Modexp(xx, i, x^3-x+1);
end for;

x^2+2 mod x^3-x+1;

Output: Magma V2.11-6     Thu Sep 23 2004 22:44:37 on modular  [Seed = 1651550502]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
0
1
1
7*x + 3
2
10*x^2 + 3*x + 9
3
12*x^2 + 12*x + 9
4
3*x^2 + x + 8
5
3*x^2 + 2*x + 3
6
10*x^2 + 9*x + 1
7
2*x^2 + 11
8
6*x^2 + 6
9
5*x^2 + 6*x + 2
10
5*x^2 + 2*x + 10
11
3*x^2 + 7*x + 8
12
6*x^2 + 7*x + 3
13
2*x^2 + 6*x + 6
14
9*x^2 + 9*x + 4
15
12*x^2 + x + 1
16
4*x^2 + 3*x + 10
17
7*x^2 + 3*x + 2
18
3*x^2 + 7*x + 9
19
6*x^2 + x + 6
20
12*x^2 + 9*x + 2
21
8*x^2 + 8*x
22
2*x^2 + 2*x + 9
23
7*x^2 + 5*x
24
4*x^2 + 12*x + 3
25
5*x^2 + 7*x + 7
26
12*x^2 + x + 12
27
4*x^2 + 2*x + 4
28
10*x + 10
29
5*x^2 + 9*x + 4
30
12*x + 3
31
6*x^2 + 5*x + 9
32
x^2 + 3*x + 11
33
11*x^2 + 2*x
34
8*x^2 + 5*x + 1
35
7*x^2 + 12
36
8*x^2 + 3*x
37
6*x^2 + 9
38
5*x^2 + x + 11
39
9*x^2 + 11*x + 11
40
4*x + 9
41
2*x^2 + 10*x + 1
42
11*x^2 + 12*x + 2
43
10*x + 7
44
5*x^2 + x + 8
45
9*x^2 + 3*x + 2
46
9*x^2 + 8*x + 8
47
5*x^2
48
2*x^2 + 9*x + 4
49
4*x^2 + 4*x + 11
50
x^2 + 5
51
3*x^2 + 3*x + 8
52
4*x^2 + 8*x + 3
53
3*x^2 + 8*x + 7
54
3*x
55
8*x^2 + 9*x
56
9*x^2 + 5*x + 9
57
10*x^2 + 11*x + 3
58
3*x^2 + 7*x + 4
59
6*x^2 + 5*x + 4
60
x^2 + 7*x + 9
61
7
x^2 + 12*x + 3

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:45:11 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;

for i in [0..61] do
i;Modexp(xx, i, x^3-x+1);
end for;

(x^2+2) mod (x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:45:11 on modular  [Seed = 1769710095]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
0
1
1
7*x + 3
2
10*x^2 + 3*x + 9
3
12*x^2 + 12*x + 9
4
3*x^2 + x + 8
5
3*x^2 + 2*x + 3
6
10*x^2 + 9*x + 1
7
2*x^2 + 11
8
6*x^2 + 6
9
5*x^2 + 6*x + 2
10
5*x^2 + 2*x + 10
11
3*x^2 + 7*x + 8
12
6*x^2 + 7*x + 3
13
2*x^2 + 6*x + 6
14
9*x^2 + 9*x + 4
15
12*x^2 + x + 1
16
4*x^2 + 3*x + 10
17
7*x^2 + 3*x + 2
18
3*x^2 + 7*x + 9
19
6*x^2 + x + 6
20
12*x^2 + 9*x + 2
21
8*x^2 + 8*x
22
2*x^2 + 2*x + 9
23
7*x^2 + 5*x
24
4*x^2 + 12*x + 3
25
5*x^2 + 7*x + 7
26
12*x^2 + x + 12
27
4*x^2 + 2*x + 4
28
10*x + 10
29
5*x^2 + 9*x + 4
30
12*x + 3
31
6*x^2 + 5*x + 9
32
x^2 + 3*x + 11
33
11*x^2 + 2*x
34
8*x^2 + 5*x + 1
35
7*x^2 + 12
36
8*x^2 + 3*x
37
6*x^2 + 9
38
5*x^2 + x + 11
39
9*x^2 + 11*x + 11
40
4*x + 9
41
2*x^2 + 10*x + 1
42
11*x^2 + 12*x + 2
43
10*x + 7
44
5*x^2 + x + 8
45
9*x^2 + 3*x + 2
46
9*x^2 + 8*x + 8
47
5*x^2
48
2*x^2 + 9*x + 4
49
4*x^2 + 4*x + 11
50
x^2 + 5
51
3*x^2 + 3*x + 8
52
4*x^2 + 8*x + 3
53
3*x^2 + 8*x + 7
54
3*x
55
8*x^2 + 9*x
56
9*x^2 + 5*x + 9
57
10*x^2 + 11*x + 3
58
3*x^2 + 7*x + 4
59
6*x^2 + 5*x + 4
60
x^2 + 7*x + 9
61
7
x^2 + 2

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:46:54 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;
51;Modexp(xx, 51, x^3-x+1);

for i in [0..61] do
i;Modexp(xx, i, x^3-x+1);
end for;

(x^2+2) mod (x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:46:54 on modular  [Seed = 1820239779]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
51
3*x^2 + 3*x + 8
0
1
1
7*x + 3
2
10*x^2 + 3*x + 9
3
12*x^2 + 12*x + 9
4
3*x^2 + x + 8
5
3*x^2 + 2*x + 3
6
10*x^2 + 9*x + 1
7
2*x^2 + 11
8
6*x^2 + 6
9
5*x^2 + 6*x + 2
10
5*x^2 + 2*x + 10
11
3*x^2 + 7*x + 8
12
6*x^2 + 7*x + 3
13
2*x^2 + 6*x + 6
14
9*x^2 + 9*x + 4
15
12*x^2 + x + 1
16
4*x^2 + 3*x + 10
17
7*x^2 + 3*x + 2
18
3*x^2 + 7*x + 9
19
6*x^2 + x + 6
20
12*x^2 + 9*x + 2
21
8*x^2 + 8*x
22
2*x^2 + 2*x + 9
23
7*x^2 + 5*x
24
4*x^2 + 12*x + 3
25
5*x^2 + 7*x + 7
26
12*x^2 + x + 12
27
4*x^2 + 2*x + 4
28
10*x + 10
29
5*x^2 + 9*x + 4
30
12*x + 3
31
6*x^2 + 5*x + 9
32
x^2 + 3*x + 11
33
11*x^2 + 2*x
34
8*x^2 + 5*x + 1
35
7*x^2 + 12
36
8*x^2 + 3*x
37
6*x^2 + 9
38
5*x^2 + x + 11
39
9*x^2 + 11*x + 11
40
4*x + 9
41
2*x^2 + 10*x + 1
42
11*x^2 + 12*x + 2
43
10*x + 7
44
5*x^2 + x + 8
45
9*x^2 + 3*x + 2
46
9*x^2 + 8*x + 8
47
5*x^2
48
2*x^2 + 9*x + 4
49
4*x^2 + 4*x + 11
50
x^2 + 5
51
3*x^2 + 3*x + 8
52
4*x^2 + 8*x + 3
53
3*x^2 + 8*x + 7
54
3*x
55
8*x^2 + 9*x
56
9*x^2 + 5*x + 9
57
10*x^2 + 11*x + 3
58
3*x^2 + 7*x + 4
59
6*x^2 + 5*x + 4
60
x^2 + 7*x + 9
61
7
x^2 + 2

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:48:15 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;
61;Modexp(xx, 51, x^3-x+1);

for i in [0..61] do
printf "%o: %on", i, Modexp(xx, i, x^3-x+1);
end for;

(x^2+2) mod (x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:48:14 on modular  [Seed = 335994795]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
61
3*x^2 + 3*x + 8
0: 1n1: 7*x + 3n2: 10*x^2 + 3*x + 9n3: 12*x^2 + 12*x + 9n4: 3*x^2 + x + 8n5:
3*x^2 + 2*x + 3n6: 10*x^2 + 9*x + 1n7: 2*x^2 + 11n8: 6*x^2 + 6n9: 5*x^2 + 6*x +
2n10: 5*x^2 + 2*x + 10n11: 3*x^2 + 7*x + 8n12: 6*x^2 + 7*x + 3n13: 2*x^2 + 6*x +
6n14: 9*x^2 + 9*x + 4n15: 12*x^2 + x + 1n16: 4*x^2 + 3*x + 10n17: 7*x^2 + 3*x +
2n18: 3*x^2 + 7*x + 9n19: 6*x^2 + x + 6n20: 12*x^2 + 9*x + 2n21: 8*x^2 + 8*xn22:
2*x^2 + 2*x + 9n23: 7*x^2 + 5*xn24: 4*x^2 + 12*x + 3n25: 5*x^2 + 7*x + 7n26:
12*x^2 + x + 12n27: 4*x^2 + 2*x + 4n28: 10*x + 10n29: 5*x^2 + 9*x + 4n30: 12*x +
3n31: 6*x^2 + 5*x + 9n32: x^2 + 3*x + 11n33: 11*x^2 + 2*xn34: 8*x^2 + 5*x +
1n35: 7*x^2 + 12n36: 8*x^2 + 3*xn37: 6*x^2 + 9n38: 5*x^2 + x + 11n39: 9*x^2 +
11*x + 11n40: 4*x + 9n41: 2*x^2 + 10*x + 1n42: 11*x^2 + 12*x + 2n43: 10*x +
7n44: 5*x^2 + x + 8n45: 9*x^2 + 3*x + 2n46: 9*x^2 + 8*x + 8n47: 5*x^2n48: 2*x^2
+ 9*x + 4n49: 4*x^2 + 4*x + 11n50: x^2 + 5n51: 3*x^2 + 3*x + 8n52: 4*x^2 + 8*x +
3n53: 3*x^2 + 8*x + 7n54: 3*xn55: 8*x^2 + 9*xn56: 9*x^2 + 5*x + 9n57: 10*x^2 +
11*x + 3n58: 3*x^2 + 7*x + 4n59: 6*x^2 + 5*x + 4n60: x^2 + 7*x + 9n61: 7nx^2 + 2

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:48:30 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;
61;Modexp(xx, 51, x^3-x+1);

for i in [0..61] do
printf "%o: %o", i, Modexp(xx, i, x^3-x+1);
" ";
end for;

(x^2+2) mod (x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:48:30 on modular  [Seed = 453628084]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
61
3*x^2 + 3*x + 8
0: 1
1: 7*x + 3
2: 10*x^2 + 3*x + 9
3: 12*x^2 + 12*x + 9
4: 3*x^2 + x + 8
5: 3*x^2 + 2*x + 3
6: 10*x^2 + 9*x + 1
7: 2*x^2 + 11
8: 6*x^2 + 6
9: 5*x^2 + 6*x + 2
10: 5*x^2 + 2*x + 10
11: 3*x^2 + 7*x + 8
12: 6*x^2 + 7*x + 3
13: 2*x^2 + 6*x + 6
14: 9*x^2 + 9*x + 4
15: 12*x^2 + x + 1
16: 4*x^2 + 3*x + 10
17: 7*x^2 + 3*x + 2
18: 3*x^2 + 7*x + 9
19: 6*x^2 + x + 6
20: 12*x^2 + 9*x + 2
21: 8*x^2 + 8*x
22: 2*x^2 + 2*x + 9
23: 7*x^2 + 5*x
24: 4*x^2 + 12*x + 3
25: 5*x^2 + 7*x + 7
26: 12*x^2 + x + 12
27: 4*x^2 + 2*x + 4
28: 10*x + 10
29: 5*x^2 + 9*x + 4
30: 12*x + 3
31: 6*x^2 + 5*x + 9
32: x^2 + 3*x + 11
33: 11*x^2 + 2*x
34: 8*x^2 + 5*x + 1
35: 7*x^2 + 12
36: 8*x^2 + 3*x
37: 6*x^2 + 9
38: 5*x^2 + x + 11
39: 9*x^2 + 11*x + 11
40: 4*x + 9
41: 2*x^2 + 10*x + 1
42: 11*x^2 + 12*x + 2
43: 10*x + 7
44: 5*x^2 + x + 8
45: 9*x^2 + 3*x + 2
46: 9*x^2 + 8*x + 8
47: 5*x^2
48: 2*x^2 + 9*x + 4
49: 4*x^2 + 4*x + 11
50: x^2 + 5
51: 3*x^2 + 3*x + 8
52: 4*x^2 + 8*x + 3
53: 3*x^2 + 8*x + 7
54: 3*x
55: 8*x^2 + 9*x
56: 9*x^2 + 5*x + 9
57: 10*x^2 + 11*x + 3
58: 3*x^2 + 7*x + 4
59: 6*x^2 + 5*x + 4
60: x^2 + 7*x + 9
61: 7
x^2 + 2

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:49:49 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

//Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %on", (nlist[i]-nlist[Integers()!(i/2)])/(mlist[Integers()!(i/2)]-mlist[i]);
xx,yy;
-30783851 mod 61;
22305945 mod 61;
o, n, k:=XGCD(14,61);
n*43 mod 61;
ANS:=Modexp(xx, 51, x^3-x+1);
for i in [0..12] do
ANS*i;
end for;

for i in [0..61] do
printf "%o: %o", i, Modexp(xx, i, x^3-x+1);
" ";
end for;

(x^2+2) mod (x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:49:49 on modular  [Seed = 18074397]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = -30783851/22305945n7*x + 3
x^2 + 2
43
14
51
0
3*x^2 + 3*x + 8
6*x^2 + 6*x + 3
9*x^2 + 9*x + 11
12*x^2 + 12*x + 6
2*x^2 + 2*x + 1
5*x^2 + 5*x + 9
8*x^2 + 8*x + 4
11*x^2 + 11*x + 12
x^2 + x + 7
4*x^2 + 4*x + 2
7*x^2 + 7*x + 10
10*x^2 + 10*x + 5
0: 1
1: 7*x + 3
2: 10*x^2 + 3*x + 9
3: 12*x^2 + 12*x + 9
4: 3*x^2 + x + 8
5: 3*x^2 + 2*x + 3
6: 10*x^2 + 9*x + 1
7: 2*x^2 + 11
8: 6*x^2 + 6
9: 5*x^2 + 6*x + 2
10: 5*x^2 + 2*x + 10
11: 3*x^2 + 7*x + 8
12: 6*x^2 + 7*x + 3
13: 2*x^2 + 6*x + 6
14: 9*x^2 + 9*x + 4
15: 12*x^2 + x + 1
16: 4*x^2 + 3*x + 10
17: 7*x^2 + 3*x + 2
18: 3*x^2 + 7*x + 9
19: 6*x^2 + x + 6
20: 12*x^2 + 9*x + 2
21: 8*x^2 + 8*x
22: 2*x^2 + 2*x + 9
23: 7*x^2 + 5*x
24: 4*x^2 + 12*x + 3
25: 5*x^2 + 7*x + 7
26: 12*x^2 + x + 12
27: 4*x^2 + 2*x + 4
28: 10*x + 10
29: 5*x^2 + 9*x + 4
30: 12*x + 3
31: 6*x^2 + 5*x + 9
32: x^2 + 3*x + 11
33: 11*x^2 + 2*x
34: 8*x^2 + 5*x + 1
35: 7*x^2 + 12
36: 8*x^2 + 3*x
37: 6*x^2 + 9
38: 5*x^2 + x + 11
39: 9*x^2 + 11*x + 11
40: 4*x + 9
41: 2*x^2 + 10*x + 1
42: 11*x^2 + 12*x + 2
43: 10*x + 7
44: 5*x^2 + x + 8
45: 9*x^2 + 3*x + 2
46: 9*x^2 + 8*x + 8
47: 5*x^2
48: 2*x^2 + 9*x + 4
49: 4*x^2 + 4*x + 11
50: x^2 + 5
51: 3*x^2 + 3*x + 8
52: 4*x^2 + 8*x + 3
53: 3*x^2 + 8*x + 7
54: 3*x
55: 8*x^2 + 9*x
56: 9*x^2 + 5*x + 9
57: 10*x^2 + 11*x + 3
58: 3*x^2 + 7*x + 4
59: 6*x^2 + 5*x + 4
60: x^2 + 7*x + 9
61: 7
x^2 + 2

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:51:29 2004

Input: ?ModDiv

Output: Magma V2.11-6     Thu Sep 23 2004 22:51:29 on modular  [Seed = 152814569]
-------------------------------------

No references for word "ModDiv"

Total time: 0.190 seconds, Total memory usage: 3.51MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:52:12 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; x:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)] mod 61*13), (mlist[Integers()!(i/2)]-mlist[i] mod 61*13);

Output: Magma V2.11-6     Thu Sep 23 2004 22:52:12 on modular  [Seed = 203343489]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1

>>         a:=Terms(z);
^
User error: Identifier 'z' has not been declared or assigned

>> i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist
^
Runtime error in '[]': Value for index (0) should be in the range [1..0]

>> printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)] mod 61*13),
^
Runtime error in '[]': Value for index (0) should be in the range [1..0]

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:52:26 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)] mod 61*13), (mlist[Integers()!(i/2)]-mlist[i] mod 61*13);

Output: Magma V2.11-6     Thu Sep 23 2004 22:52:26 on modular  [Seed = 857864584]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 504363576478 / 696683 n
Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:52:52 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod 61*13, (mlist[Integers()!(i/2)]-mlist[i]) mod 61*13;

Output: Magma V2.11-6     Thu Sep 23 2004 22:52:52 on modular  [Seed = 908393315]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 494 / 585 n
Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:53:32 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod 61*13, (mlist[Integers()!(i/2)]-mlist[i]) mod 61*13;
o,n,k:=XGCD(585,61*13);
ans:=n*494 mod 61*13; ans;
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:53:31 on modular  [Seed = 540208474]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 494 / 585 n689
6*x^2 + x + 5

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:54:39 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod (61*13), (mlist[Integers()!(i/2)]-mlist[i]) mod (61*13);
o,n,k:=XGCD(585,(61*13));
ans:=n*494 mod (61*13); ans;
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:54:39 on modular  [Seed = 641002264]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 587 / 472 n663
12*x^2 + 6*x + 2

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:55:19 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod (61*13), (mlist[Integers()!(i/2)]-mlist[i]) mod (61*13);
o,n,k:=XGCD(472,(61*13));
ans:=n*587 mod (61*13); ans;
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:55:19 on modular  [Seed = 759161067]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 587 / 472 n722
6*x^2 + 6*x + 3

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:56:09 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod (61*13), (mlist[Integers()!(i/2)]-mlist[i]) mod (61*13);
o,n,k:=XGCD(472,(61*13));
ans:=(n*587) mod (61*13); ans;
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:56:08 on modular  [Seed = 3586594893]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 587 / 472 n722
6*x^2 + 6*x + 3

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:56:55 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod (61*13), (mlist[Integers()!(i/2)]-mlist[i]) mod (61*13);
oo,nn,kk:=XGCD(472,(61*13));
ans:=(nn*587) mod (61*13); ans;
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:56:55 on modular  [Seed = 3637122430]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 587 / 472 n722
6*x^2 + 6*x + 3

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:59:15 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod (61*12), (mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
oo,nn,kk:=XGCD(472,(61*12));
ans:=(nn*587) mod (61*12); ans;
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:59:14 on modular  [Seed = 3234991123]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 404 / 228 n692
3*x^2 + 3*x

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 22:59:29 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod (61*12), (mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
oo,nn,kk:=XGCD(228,(61*12));
ans:=(nn*404) mod (61*12); ans;
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 22:59:29 on modular  [Seed = 3352627975]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 404 / 228 n124
9*x^2 + 4*x + 12

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:00:01 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod (61*12), (mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
oo,nn,kk:=XGCD(228,(61*12));
//ans:=(nn*404) mod (61*12); ans;
ans:=(61*12);
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 23:00:01 on modular  [Seed = 3437101100]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 404 / 228 n1

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:00:43 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
printf "logx(y) = %o / %o n", (nlist[i]-nlist[Integers()!(i/2)]) mod (61*12), (mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
oo,nn,kk:=XGCD(228,(61*12));
ans:=(nn*404) mod (61*12); ans;
//ans:=(61*12);
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 23:00:43 on modular  [Seed = 4091625337]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 404 / 228 n124
9*x^2 + 4*x + 12

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:03:59 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
lt:= (nlist[i]-nlist[Integers()!(i/2)]) mod (61*12);
lb:= (mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
printf "logx(y) = %o / %o n", lt, lb;
oo,nn,kk:=XGCD(228,(61*12));
ans:=(nn*404) mod (61*12); ans;
//ans:=(61*12);
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 23:03:58 on modular  [Seed = 4226364468]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993n
>> lt:= (nlist[i]-nlist[Integers()!(i/2)]) mod (61*12);
^

>> printf "logx(y) = %o / %o n", lt, lb;
^
124
9*x^2 + 4*x + 12

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:04:24 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
lt:=(nlist[i]-nlist[Integers()!(i/2)]) mod (61*12);
lb:=(mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
printf "logx(y) = %o / %o n", lt, lb;
oo,nn,kk:=XGCD(228,(61*12));
ans:=(nn*404) mod (61*12); ans;
//ans:=(61*12);
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 23:04:24 on modular  [Seed = 4276891927]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993n
>> lt:=(nlist[i]-nlist[Integers()!(i/2)]) mod (61*12);
^

>> printf "logx(y) = %o / %o n", lt, lb;
^
124
9*x^2 + 4*x + 12

Total time: 0.190 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:04:59 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
llt:=(nlist[i]-nlist[Integers()!(i/2)]) mod (61*12);
llb:=(mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
printf "logx(y) = %o / %o n", lt, lb;
oo,nn,kk:=XGCD(228,(61*12));
ans:=(nn*404) mod (61*12); ans;
//ans:=(61*12);
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 23:04:59 on modular  [Seed = 3841338222]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993n
>> printf "logx(y) = %o / %o n", lt, lb;
^
124
9*x^2 + 4*x + 12

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:05:13 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
llt:=(nlist[i]-nlist[Integers()!(i/2)]) mod (61*12);
llb:=(mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
printf "logx(y) = %o / %o n", llt, llb;
oo,nn,kk:=XGCD(228,(61*12));
ans:=(nn*404) mod (61*12); ans;
//ans:=(61*12);
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 23:05:13 on modular  [Seed = 3976078164]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 404 / 228 n124
9*x^2 + 4*x + 12

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:05:53 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

while (q eq 0) do

i+:=1;
a:=Terms(z);

if (a lt 5) then

z:=yy*z mod (x^3-x+1);
Append(~zlist, z);
Append(~nlist, n);
m:=m+1;
Append(~mlist, m);

elif (a lt 9) then
z:=z^2 mod (x^3-x+1);
Append(~zlist, z);
n:=2*n;
Append(~nlist, n);
m:=2*m;
Append(~mlist, m);

else

z:=xx*z mod (x^3-x+1);
Append(~zlist, z);
n:=n+1;
Append(~nlist, n);
Append(~mlist, m);

end if;

if ((i mod 2) eq 0) then
if (zlist[i] eq zlist[Integers()!(i/2)]) then
q:=1;
end if;
end if;

end while;

printf "x = %o, y = %oni = %ona[i] = %o, a[i/2] = %onb[i] = %o, b[i/2] = %on", xx, yy, i, mlist[i], mlist[Integers()!(i/2)], nlist[i], nlist[Integers()!(i/2)];
llt:=(nlist[i]-nlist[Integers()!(i/2)]) mod (61*12);
llb:=(mlist[Integers()!(i/2)]-mlist[i]) mod (61*12);
printf "logx(y) = %o / %o n", llt, llb;
oo,nn,kk:=XGCD(llb,(61*12));
ans:=(nn*llt) mod (61*12); ans;
//ans:=(61*12);
Modexp(xx, ans, x^3-x+1);

Output: Magma V2.11-6     Thu Sep 23 2004 23:05:53 on modular  [Seed = 2474728915]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
x = 7*x + 3, y = x^2 + 2ni = 124na[i] = 365461299940, a[i/2] = 697060nb[i] =
504363576777, b[i/2] = 961993nlogx(y) = 404 / 228 n124
9*x^2 + 4*x + 12

Total time: 0.200 seconds, Total memory usage: 3.56MB

'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:06:41 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

// Demonstrate that the order of &#61556;+6 and &#61556;+10 is 61:

Modexp(x+6, 60, x^3-x+1);
Modexp(x+6, 61, x^3-x+1);

Modexp(x+10, 60, x^3-x+1);
Modexp(x+10, 61, x^3-x+1);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

for i in [0..(61*12)] do
Modexp(xx, i, x^3-x+1);
end for;

Output: Magma V2.11-6     Thu Sep 23 2004 23:06:41 on modular  [Seed = 2525255814]
-------------------------------------

x^2 + 7*x + 9
1
x^2 + 3*x + 8
1
1
7*x + 3
10*x^2 + 3*x + 9
12*x^2 + 12*x + 9
3*x^2 + x + 8
3*x^2 + 2*x + 3
10*x^2 + 9*x + 1
2*x^2 + 11
6*x^2 + 6
5*x^2 + 6*x + 2
5*x^2 + 2*x + 10
3*x^2 + 7*x + 8
6*x^2 + 7*x + 3
2*x^2 + 6*x + 6
9*x^2 + 9*x + 4
12*x^2 + x + 1
4*x^2 + 3*x + 10
7*x^2 + 3*x + 2
3*x^2 + 7*x + 9
6*x^2 + x + 6
12*x^2 + 9*x + 2
8*x^2 + 8*x
2*x^2 + 2*x + 9
7*x^2 + 5*x
4*x^2 + 12*x + 3
5*x^2 + 7*x + 7
12*x^2 + x + 12
4*x^2 + 2*x + 4
10*x + 10
5*x^2 + 9*x + 4
12*x + 3
6*x^2 + 5*x + 9
x^2 + 3*x + 11
11*x^2 + 2*x
8*x^2 + 5*x + 1
7*x^2 + 12
8*x^2 + 3*x
6*x^2 + 9
5*x^2 + x + 11
9*x^2 + 11*x + 11
4*x + 9
2*x^2 + 10*x + 1
11*x^2 + 12*x + 2
10*x + 7
5*x^2 + x + 8
9*x^2 + 3*x + 2
9*x^2 + 8*x + 8
5*x^2
2*x^2 + 9*x + 4
4*x^2 + 4*x + 11
x^2 + 5
3*x^2 + 3*x + 8
4*x^2 + 8*x + 3
3*x^2 + 8*x + 7
3*x
8*x^2 + 9*x
9*x^2 + 5*x + 9
10*x^2 + 11*x + 3
3*x^2 + 7*x + 4
6*x^2 + 5*x + 4
x^2 + 7*x + 9
7
10*x + 8
5*x^2 + 8*x + 11
6*x^2 + 6*x + 11
8*x^2 + 7*x + 4
8*x^2 + x + 8
5*x^2 + 11*x + 7
x^2 + 12
3*x^2 + 3
9*x^2 + 3*x + 1
9*x^2 + x + 5
8*x^2 + 10*x + 4
3*x^2 + 10*x + 8
x^2 + 3*x + 3
11*x^2 + 11*x + 2
6*x^2 + 7*x + 7
2*x^2 + 8*x + 5
10*x^2 + 8*x + 1
8*x^2 + 10*x + 11
3*x^2 + 7*x + 3
6*x^2 + 11*x + 1
4*x^2 + 4*x
x^2 + x + 11
10*x^2 + 9*x
2*x^2 + 6*x + 8
9*x^2 + 10*x + 10
6*x^2 + 7*x + 6
2*x^2 + x + 2
5*x + 5
9*x^2 + 11*x + 2
6*x + 8
3*x^2 + 9*x + 11
7*x^2 + 8*x + 12
12*x^2 + x
4*x^2 + 9*x + 7
10*x^2 + 6
4*x^2 + 8*x
3*x^2 + 11
9*x^2 + 7*x + 12
11*x^2 + 12*x + 12
2*x + 11
x^2 + 5*x + 7
12*x^2 + 6*x + 1
5*x + 10
9*x^2 + 7*x + 4
11*x^2 + 8*x + 1
11*x^2 + 4*x + 4
9*x^2
x^2 + 11*x + 2
2*x^2 + 2*x + 12
7*x^2 + 9
8*x^2 + 8*x + 4
2*x^2 + 4*x + 8
8*x^2 + 4*x + 10
8*x
4*x^2 + 11*x
11*x^2 + 9*x + 11
5*x^2 + 12*x + 8
8*x^2 + 10*x + 2
3*x^2 + 9*x + 2
7*x^2 + 10*x + 11
10
5*x + 4
9*x^2 + 4*x + 12
3*x^2 + 3*x + 12
4*x^2 + 10*x + 2
4*x^2 + 7*x + 4
9*x^2 + 12*x + 10
7*x^2 + 6
8*x^2 + 8
11*x^2 + 8*x + 7
11*x^2 + 7*x + 9
4*x^2 + 5*x + 2
8*x^2 + 5*x + 4
7*x^2 + 8*x + 8
12*x^2 + 12*x + 1
3*x^2 + 10*x + 10
x^2 + 4*x + 9
5*x^2 + 4*x + 7
4*x^2 + 5*x + 12
8*x^2 + 10*x + 8
3*x^2 + 12*x + 7
2*x^2 + 2*x
7*x^2 + 7*x + 12
5*x^2 + 11*x
x^2 + 3*x + 4
11*x^2 + 5*x + 5
3*x^2 + 10*x + 3
x^2 + 7*x + 1
9*x + 9
11*x^2 + 12*x + 1
3*x + 4
8*x^2 + 11*x + 12
10*x^2 + 4*x + 6
6*x^2 + 7*x
2*x^2 + 11*x + 10
5*x^2 + 3
2*x^2 + 4*x
8*x^2 + 12
11*x^2 + 10*x + 6
12*x^2 + 6*x + 6
x + 12
7*x^2 + 9*x + 10
6*x^2 + 3*x + 7
9*x + 5
11*x^2 + 10*x + 2
12*x^2 + 4*x + 7
12*x^2 + 2*x + 2
11*x^2
7*x^2 + 12*x + 1
x^2 + x + 6
10*x^2 + 11
4*x^2 + 4*x + 2
x^2 + 2*x + 4
4*x^2 + 2*x + 5
4*x
2*x^2 + 12*x
12*x^2 + 11*x + 12
9*x^2 + 6*x + 4
4*x^2 + 5*x + 1
8*x^2 + 11*x + 1
10*x^2 + 5*x + 12
5
9*x + 2
11*x^2 + 2*x + 6
8*x^2 + 8*x + 6
2*x^2 + 5*x + 1
2*x^2 + 10*x + 2
11*x^2 + 6*x + 5
10*x^2 + 3
4*x^2 + 4
12*x^2 + 4*x + 10
12*x^2 + 10*x + 11
2*x^2 + 9*x + 1
4*x^2 + 9*x + 2
10*x^2 + 4*x + 4
6*x^2 + 6*x + 7
8*x^2 + 5*x + 5
7*x^2 + 2*x + 11
9*x^2 + 2*x + 10
2*x^2 + 9*x + 6
4*x^2 + 5*x + 4
8*x^2 + 6*x + 10
x^2 + x
10*x^2 + 10*x + 6
9*x^2 + 12*x
7*x^2 + 8*x + 2
12*x^2 + 9*x + 9
8*x^2 + 5*x + 8
7*x^2 + 10*x + 7
11*x + 11
12*x^2 + 6*x + 7
8*x + 2
4*x^2 + 12*x + 6
5*x^2 + 2*x + 3
3*x^2 + 10*x
x^2 + 12*x + 5
9*x^2 + 8
x^2 + 2*x
4*x^2 + 6
12*x^2 + 5*x + 3
6*x^2 + 3*x + 3
7*x + 6
10*x^2 + 11*x + 5
3*x^2 + 8*x + 10
11*x + 9
12*x^2 + 5*x + 1
6*x^2 + 2*x + 10
6*x^2 + x + 1
12*x^2
10*x^2 + 6*x + 7
7*x^2 + 7*x + 3
5*x^2 + 12
2*x^2 + 2*x + 1
7*x^2 + x + 2
2*x^2 + x + 9
2*x
x^2 + 6*x
6*x^2 + 12*x + 6
11*x^2 + 3*x + 2
2*x^2 + 9*x + 7
4*x^2 + 12*x + 7
5*x^2 + 9*x + 6
9
11*x + 1
12*x^2 + x + 3
4*x^2 + 4*x + 3
x^2 + 9*x + 7
x^2 + 5*x + 1
12*x^2 + 3*x + 9
5*x^2 + 8
2*x^2 + 2
6*x^2 + 2*x + 5
6*x^2 + 5*x + 12
x^2 + 11*x + 7
2*x^2 + 11*x + 1
5*x^2 + 2*x + 2
3*x^2 + 3*x + 10
4*x^2 + 9*x + 9
10*x^2 + x + 12
11*x^2 + x + 5
x^2 + 11*x + 3
2*x^2 + 9*x + 2
4*x^2 + 3*x + 5
7*x^2 + 7*x
5*x^2 + 5*x + 3
11*x^2 + 6*x
10*x^2 + 4*x + 1
6*x^2 + 11*x + 11
4*x^2 + 9*x + 4
10*x^2 + 5*x + 10
12*x + 12
6*x^2 + 3*x + 10
4*x + 1
2*x^2 + 6*x + 3
9*x^2 + x + 8
8*x^2 + 5*x
7*x^2 + 6*x + 9
11*x^2 + 4
7*x^2 + x
2*x^2 + 3
6*x^2 + 9*x + 8
3*x^2 + 8*x + 8
10*x + 3
5*x^2 + 12*x + 9
8*x^2 + 4*x + 5
12*x + 11
6*x^2 + 9*x + 7
3*x^2 + x + 5
3*x^2 + 7*x + 7
6*x^2
5*x^2 + 3*x + 10
10*x^2 + 10*x + 8
9*x^2 + 6
x^2 + x + 7
10*x^2 + 7*x + 1
x^2 + 7*x + 11
x
7*x^2 + 3*x
3*x^2 + 6*x + 3
12*x^2 + 8*x + 1
x^2 + 11*x + 10
2*x^2 + 6*x + 10
9*x^2 + 11*x + 3
11
12*x + 7
6*x^2 + 7*x + 8
2*x^2 + 2*x + 8
7*x^2 + 11*x + 10
7*x^2 + 9*x + 7
6*x^2 + 8*x + 11
9*x^2 + 4
x^2 + 1
3*x^2 + x + 9
3*x^2 + 9*x + 6
7*x^2 + 12*x + 10
x^2 + 12*x + 7
9*x^2 + x + 1
8*x^2 + 8*x + 5
2*x^2 + 11*x + 11
5*x^2 + 7*x + 6
12*x^2 + 7*x + 9
7*x^2 + 12*x + 8
x^2 + 11*x + 1
2*x^2 + 8*x + 9
10*x^2 + 10*x
9*x^2 + 9*x + 8
12*x^2 + 3*x
5*x^2 + 2*x + 7
3*x^2 + 12*x + 12
2*x^2 + 11*x + 2
5*x^2 + 9*x + 5
6*x + 6
3*x^2 + 8*x + 5
2*x + 7
x^2 + 3*x + 8
11*x^2 + 7*x + 4
4*x^2 + 9*x
10*x^2 + 3*x + 11
12*x^2 + 2
10*x^2 + 7*x
x^2 + 8
3*x^2 + 11*x + 4
8*x^2 + 4*x + 4
5*x + 8
9*x^2 + 6*x + 11
4*x^2 + 2*x + 9
6*x + 12
3*x^2 + 11*x + 10
8*x^2 + 7*x + 9
8*x^2 + 10*x + 10
3*x^2
9*x^2 + 8*x + 5
5*x^2 + 5*x + 4
11*x^2 + 3
7*x^2 + 7*x + 10
5*x^2 + 10*x + 7
7*x^2 + 10*x + 12
7*x
10*x^2 + 8*x
8*x^2 + 3*x + 8
6*x^2 + 4*x + 7
7*x^2 + 12*x + 5
x^2 + 3*x + 5
11*x^2 + 12*x + 8
12
6*x + 10
3*x^2 + 10*x + 4
x^2 + x + 4
10*x^2 + 12*x + 5
10*x^2 + 11*x + 10
3*x^2 + 4*x + 12
11*x^2 + 2
7*x^2 + 7
8*x^2 + 7*x + 11
8*x^2 + 11*x + 3
10*x^2 + 6*x + 5
7*x^2 + 6*x + 10
11*x^2 + 7*x + 7
4*x^2 + 4*x + 9
x^2 + 12*x + 12
9*x^2 + 10*x + 3
6*x^2 + 10*x + 11
10*x^2 + 6*x + 4
7*x^2 + 12*x + 7
x^2 + 4*x + 11
5*x^2 + 5*x
11*x^2 + 11*x + 4
6*x^2 + 8*x
9*x^2 + x + 10
8*x^2 + 6*x + 6
x^2 + 12*x + 1
9*x^2 + 11*x + 9
3*x + 3
8*x^2 + 4*x + 9
x + 10
7*x^2 + 8*x + 4
12*x^2 + 10*x + 2
2*x^2 + 11*x
5*x^2 + 8*x + 12
6*x^2 + 1
5*x^2 + 10*x
7*x^2 + 4
8*x^2 + 12*x + 2
4*x^2 + 2*x + 2
9*x + 4
11*x^2 + 3*x + 12
2*x^2 + x + 11
3*x + 6
8*x^2 + 12*x + 5
4*x^2 + 10*x + 11
4*x^2 + 5*x + 5
8*x^2
11*x^2 + 4*x + 9
9*x^2 + 9*x + 2
12*x^2 + 8
10*x^2 + 10*x + 5
9*x^2 + 5*x + 10
10*x^2 + 5*x + 6
10*x
5*x^2 + 4*x
4*x^2 + 8*x + 4
3*x^2 + 2*x + 10
10*x^2 + 6*x + 9
7*x^2 + 8*x + 9
12*x^2 + 6*x + 4
6
3*x + 5
8*x^2 + 5*x + 2
7*x^2 + 7*x + 2
5*x^2 + 6*x + 9
5*x^2 + 12*x + 5
8*x^2 + 2*x + 6
12*x^2 + 1
10*x^2 + 10
4*x^2 + 10*x + 12
4*x^2 + 12*x + 8
5*x^2 + 3*x + 9
10*x^2 + 3*x + 5
12*x^2 + 10*x + 10
2*x^2 + 2*x + 11
7*x^2 + 6*x + 6
11*x^2 + 5*x + 8
3*x^2 + 5*x + 12
5*x^2 + 3*x + 2
10*x^2 + 6*x + 10
7*x^2 + 2*x + 12
9*x^2 + 9*x
12*x^2 + 12*x + 2
3*x^2 + 4*x
11*x^2 + 7*x + 5
4*x^2 + 3*x + 3
7*x^2 + 6*x + 7
11*x^2 + 12*x + 11
8*x + 8
4*x^2 + 2*x + 11
7*x + 5
10*x^2 + 4*x + 2
6*x^2 + 5*x + 1
x^2 + 12*x
9*x^2 + 4*x + 6
3*x^2 + 7
9*x^2 + 5*x
10*x^2 + 2
4*x^2 + 6*x + 1
2*x^2 + x + 1
11*x + 2
12*x^2 + 8*x + 6
x^2 + 7*x + 12
8*x + 3
4*x^2 + 6*x + 9
2*x^2 + 5*x + 12
2*x^2 + 9*x + 9
4*x^2
12*x^2 + 2*x + 11
11*x^2 + 11*x + 1
6*x^2 + 4
5*x^2 + 5*x + 9
11*x^2 + 9*x + 5
5*x^2 + 9*x + 3
5*x
9*x^2 + 2*x
2*x^2 + 4*x + 2
8*x^2 + x + 5
5*x^2 + 3*x + 11
10*x^2 + 4*x + 11
6*x^2 + 3*x + 2
3
8*x + 9
4*x^2 + 9*x + 1
10*x^2 + 10*x + 1
9*x^2 + 3*x + 11
9*x^2 + 6*x + 9
4*x^2 + x + 3
6*x^2 + 7
5*x^2 + 5
2*x^2 + 5*x + 6
2*x^2 + 6*x + 4
9*x^2 + 8*x + 11
5*x^2 + 8*x + 9
6*x^2 + 5*x + 5
x^2 + x + 12
10*x^2 + 3*x + 3
12*x^2 + 9*x + 4
8*x^2 + 9*x + 6
9*x^2 + 8*x + 1
5*x^2 + 3*x + 5
10*x^2 + x + 6
11*x^2 + 11*x
6*x^2 + 6*x + 1
8*x^2 + 2*x
12*x^2 + 10*x + 9
2*x^2 + 8*x + 8
10*x^2 + 3*x + 10
12*x^2 + 6*x + 12
4*x + 4
2*x^2 + x + 12
10*x + 9
5*x^2 + 2*x + 1
3*x^2 + 9*x + 7
7*x^2 + 6*x
11*x^2 + 2*x + 3
8*x^2 + 10
11*x^2 + 9*x
5*x^2 + 1
2*x^2 + 3*x + 7
x^2 + 7*x + 7
12*x + 1
6*x^2 + 4*x + 3
7*x^2 + 10*x + 6
4*x + 8
2*x^2 + 3*x + 11
x^2 + 9*x + 6
x^2 + 11*x + 11
2*x^2
6*x^2 + x + 12
12*x^2 + 12*x + 7
3*x^2 + 2
9*x^2 + 9*x + 11
12*x^2 + 11*x + 9
9*x^2 + 11*x + 8
9*x
11*x^2 + x
x^2 + 2*x + 1
4*x^2 + 7*x + 9
9*x^2 + 8*x + 12
5*x^2 + 2*x + 12
3*x^2 + 8*x + 1
8
4*x + 11
2*x^2 + 11*x + 7
5*x^2 + 5*x + 7
11*x^2 + 8*x + 12
11*x^2 + 3*x + 11
2*x^2 + 7*x + 8
3*x^2 + 10
9*x^2 + 9
x^2 + 9*x + 3
x^2 + 3*x + 2
11*x^2 + 4*x + 12
9*x^2 + 4*x + 11
3*x^2 + 9*x + 9
7*x^2 + 7*x + 6
5*x^2 + 8*x + 8
6*x^2 + 11*x + 2
4*x^2 + 11*x + 3
11*x^2 + 4*x + 7
9*x^2 + 8*x + 9
5*x^2 + 7*x + 3
12*x^2 + 12*x
3*x^2 + 3*x + 7
4*x^2 + x
6*x^2 + 5*x + 11
x^2 + 4*x + 4
5*x^2 + 8*x + 5
6*x^2 + 3*x + 6
2*x + 2
x^2 + 7*x + 6
5*x + 11
9*x^2 + x + 7
8*x^2 + 11*x + 10
10*x^2 + 3*x
12*x^2 + x + 8
4*x^2 + 5
12*x^2 + 11*x
9*x^2 + 7
x^2 + 8*x + 10
7*x^2 + 10*x + 10
6*x + 7
3*x^2 + 2*x + 8
10*x^2 + 5*x + 3
2*x + 4
x^2 + 8*x + 12
7*x^2 + 11*x + 3
7*x^2 + 12*x + 12
x^2
3*x^2 + 7*x + 6
6*x^2 + 6*x + 10
8*x^2 + 1
11*x^2 + 11*x + 12
6*x^2 + 12*x + 11
11*x^2 + 12*x + 4
11*x
12*x^2 + 7*x
7*x^2 + x + 7
2*x^2 + 10*x + 11
11*x^2 + 4*x + 6
9*x^2 + x + 6
8*x^2 + 4*x + 7
4
2*x + 12
x^2 + 12*x + 10
9*x^2 + 9*x + 10
12*x^2 + 4*x + 6
12*x^2 + 8*x + 12
x^2 + 10*x + 4
8*x^2 + 5
11*x^2 + 11
7*x^2 + 11*x + 8
7*x^2 + 8*x + 1
12*x^2 + 2*x + 6
11*x^2 + 2*x + 12
8*x^2 + 11*x + 11
10*x^2 + 10*x + 3
9*x^2 + 4*x + 4
3*x^2 + 12*x + 1
2*x^2 + 12*x + 8
12*x^2 + 2*x + 10
11*x^2 + 4*x + 11
9*x^2 + 10*x + 8
6*x^2 + 6*x
8*x^2 + 8*x + 10
2*x^2 + 7*x
3*x^2 + 9*x + 12
7*x^2 + 2*x + 2
9*x^2 + 4*x + 9
3*x^2 + 8*x + 3
x + 1
7*x^2 + 10*x + 3
9*x + 12
11*x^2 + 7*x + 10
4*x^2 + 12*x + 5
5*x^2 + 8*x
6*x^2 + 7*x + 4
2*x^2 + 9
6*x^2 + 12*x
11*x^2 + 10
7*x^2 + 4*x + 5
10*x^2 + 5*x + 5
3*x + 10
8*x^2 + x + 4
5*x^2 + 9*x + 8
x + 2
7*x^2 + 4*x + 6
10*x^2 + 12*x + 8
10*x^2 + 6*x + 6
7*x^2
8*x^2 + 10*x + 3
3*x^2 + 3*x + 5
4*x^2 + 7
12*x^2 + 12*x + 6
3*x^2 + 6*x + 12
12*x^2 + 6*x + 2
12*x
6*x^2 + 10*x
10*x^2 + 7*x + 10
x^2 + 5*x + 12
12*x^2 + 2*x + 3
11*x^2 + 7*x + 3
4*x^2 + 2*x + 10
2
x + 6
7*x^2 + 6*x + 5
11*x^2 + 11*x + 5
6*x^2 + 2*x + 3
6*x^2 + 4*x + 6
7*x^2 + 5*x + 2
4*x^2 + 9
12*x^2 + 12
10*x^2 + 12*x + 4
10*x^2 + 4*x + 7
6*x^2 + x + 3
12*x^2 + x + 6
4*x^2 + 12*x + 12
5*x^2 + 5*x + 8
11*x^2 + 2*x + 2
8*x^2 + 6*x + 7
x^
** WARNING: Output too long, hence truncated.
'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:07:18 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

for i in [0..(61*12)] do
printf "%o: %o   ",i,Modexp(xx, i, x^3-x+1);
end for;

Output: Magma V2.11-6     Thu Sep 23 2004 23:07:18 on modular  [Seed = 2643415978]
-------------------------------------

0: 1   1: 7*x + 3   2: 10*x^2 + 3*x + 9   3: 12*x^2 + 12*x + 9   4: 3*x^2 + x +
8   5: 3*x^2 + 2*x + 3   6: 10*x^2 + 9*x + 1   7: 2*x^2 + 11   8: 6*x^2 + 6   9:
5*x^2 + 6*x + 2   10: 5*x^2 + 2*x + 10   11: 3*x^2 + 7*x + 8   12: 6*x^2 + 7*x +
3   13: 2*x^2 + 6*x + 6   14: 9*x^2 + 9*x + 4   15: 12*x^2 + x + 1   16: 4*x^2 +
3*x + 10   17: 7*x^2 + 3*x + 2   18: 3*x^2 + 7*x + 9   19: 6*x^2 + x + 6   20:
12*x^2 + 9*x + 2   21: 8*x^2 + 8*x   22: 2*x^2 + 2*x + 9   23: 7*x^2 + 5*x   24:
4*x^2 + 12*x + 3   25: 5*x^2 + 7*x + 7   26: 12*x^2 + x + 12   27: 4*x^2 + 2*x +
4   28: 10*x + 10   29: 5*x^2 + 9*x + 4   30: 12*x + 3   31: 6*x^2 + 5*x + 9
32: x^2 + 3*x + 11   33: 11*x^2 + 2*x   34: 8*x^2 + 5*x + 1   35: 7*x^2 + 12
36: 8*x^2 + 3*x   37: 6*x^2 + 9   38: 5*x^2 + x + 11   39: 9*x^2 + 11*x + 11
40: 4*x + 9   41: 2*x^2 + 10*x + 1   42: 11*x^2 + 12*x + 2   43: 10*x + 7   44:
5*x^2 + x + 8   45: 9*x^2 + 3*x + 2   46: 9*x^2 + 8*x + 8   47: 5*x^2   48:
2*x^2 + 9*x + 4   49: 4*x^2 + 4*x + 11   50: x^2 + 5   51: 3*x^2 + 3*x + 8   52:
4*x^2 + 8*x + 3   53: 3*x^2 + 8*x + 7   54: 3*x   55: 8*x^2 + 9*x   56: 9*x^2 +
5*x + 9   57: 10*x^2 + 11*x + 3   58: 3*x^2 + 7*x + 4   59: 6*x^2 + 5*x + 4
60: x^2 + 7*x + 9   61: 7   62: 10*x + 8   63: 5*x^2 + 8*x + 11   64: 6*x^2 +
6*x + 11   65: 8*x^2 + 7*x + 4   66: 8*x^2 + x + 8   67: 5*x^2 + 11*x + 7   68:
x^2 + 12   69: 3*x^2 + 3   70: 9*x^2 + 3*x + 1   71: 9*x^2 + x + 5   72: 8*x^2 +
10*x + 4   73: 3*x^2 + 10*x + 8   74: x^2 + 3*x + 3   75: 11*x^2 + 11*x + 2
76: 6*x^2 + 7*x + 7   77: 2*x^2 + 8*x + 5   78: 10*x^2 + 8*x + 1   79: 8*x^2 +
10*x + 11   80: 3*x^2 + 7*x + 3   81: 6*x^2 + 11*x + 1   82: 4*x^2 + 4*x   83:
x^2 + x + 11   84: 10*x^2 + 9*x   85: 2*x^2 + 6*x + 8   86: 9*x^2 + 10*x + 10
87: 6*x^2 + 7*x + 6   88: 2*x^2 + x + 2   89: 5*x + 5   90: 9*x^2 + 11*x + 2
91: 6*x + 8   92: 3*x^2 + 9*x + 11   93: 7*x^2 + 8*x + 12   94: 12*x^2 + x   95:
4*x^2 + 9*x + 7   96: 10*x^2 + 6   97: 4*x^2 + 8*x   98: 3*x^2 + 11   99: 9*x^2
+ 7*x + 12   100: 11*x^2 + 12*x + 12   101: 2*x + 11   102: x^2 + 5*x + 7   103:
12*x^2 + 6*x + 1   104: 5*x + 10   105: 9*x^2 + 7*x + 4   106: 11*x^2 + 8*x + 1
107: 11*x^2 + 4*x + 4   108: 9*x^2   109: x^2 + 11*x + 2   110: 2*x^2 + 2*x + 12
111: 7*x^2 + 9   112: 8*x^2 + 8*x + 4   113: 2*x^2 + 4*x + 8   114: 8*x^2 + 4*x
+ 10   115: 8*x   116: 4*x^2 + 11*x   117: 11*x^2 + 9*x + 11   118: 5*x^2 + 12*x
+ 8   119: 8*x^2 + 10*x + 2   120: 3*x^2 + 9*x + 2   121: 7*x^2 + 10*x + 11
122: 10   123: 5*x + 4   124: 9*x^2 + 4*x + 12   125: 3*x^2 + 3*x + 12   126:
4*x^2 + 10*x + 2   127: 4*x^2 + 7*x + 4   128: 9*x^2 + 12*x + 10   129: 7*x^2 +
6   130: 8*x^2 + 8   131: 11*x^2 + 8*x + 7   132: 11*x^2 + 7*x + 9   133: 4*x^2
+ 5*x + 2   134: 8*x^2 + 5*x + 4   135: 7*x^2 + 8*x + 8   136: 12*x^2 + 12*x + 1
137: 3*x^2 + 10*x + 10   138: x^2 + 4*x + 9   139: 5*x^2 + 4*x + 7   140: 4*x^2
+ 5*x + 12   141: 8*x^2 + 10*x + 8   142: 3*x^2 + 12*x + 7   143: 2*x^2 + 2*x
144: 7*x^2 + 7*x + 12   145: 5*x^2 + 11*x   146: x^2 + 3*x + 4   147: 11*x^2 +
5*x + 5   148: 3*x^2 + 10*x + 3   149: x^2 + 7*x + 1   150: 9*x + 9   151:
11*x^2 + 12*x + 1   152: 3*x + 4   153: 8*x^2 + 11*x + 12   154: 10*x^2 + 4*x +
6   155: 6*x^2 + 7*x   156: 2*x^2 + 11*x + 10   157: 5*x^2 + 3   158: 2*x^2 +
4*x   159: 8*x^2 + 12   160: 11*x^2 + 10*x + 6   161: 12*x^2 + 6*x + 6   162: x
+ 12   163: 7*x^2 + 9*x + 10   164: 6*x^2 + 3*x + 7   165: 9*x + 5   166: 11*x^2
+ 10*x + 2   167: 12*x^2 + 4*x + 7   168: 12*x^2 + 2*x + 2   169: 11*x^2   170:
7*x^2 + 12*x + 1   171: x^2 + x + 6   172: 10*x^2 + 11   173: 4*x^2 + 4*x + 2
174: x^2 + 2*x + 4   175: 4*x^2 + 2*x + 5   176: 4*x   177: 2*x^2 + 12*x   178:
12*x^2 + 11*x + 12   179: 9*x^2 + 6*x + 4   180: 4*x^2 + 5*x + 1   181: 8*x^2 +
11*x + 1   182: 10*x^2 + 5*x + 12   183: 5   184: 9*x + 2   185: 11*x^2 + 2*x +
6   186: 8*x^2 + 8*x + 6   187: 2*x^2 + 5*x + 1   188: 2*x^2 + 10*x + 2   189:
11*x^2 + 6*x + 5   190: 10*x^2 + 3   191: 4*x^2 + 4   192: 12*x^2 + 4*x + 10
193: 12*x^2 + 10*x + 11   194: 2*x^2 + 9*x + 1   195: 4*x^2 + 9*x + 2   196:
10*x^2 + 4*x + 4   197: 6*x^2 + 6*x + 7   198: 8*x^2 + 5*x + 5   199: 7*x^2 +
2*x + 11   200: 9*x^2 + 2*x + 10   201: 2*x^2 + 9*x + 6   202: 4*x^2 + 5*x + 4
203: 8*x^2 + 6*x + 10   204: x^2 + x   205: 10*x^2 + 10*x + 6   206: 9*x^2 +
12*x   207: 7*x^2 + 8*x + 2   208: 12*x^2 + 9*x + 9   209: 8*x^2 + 5*x + 8
210: 7*x^2 + 10*x + 7   211: 11*x + 11   212: 12*x^2 + 6*x + 7   213: 8*x + 2
214: 4*x^2 + 12*x + 6   215: 5*x^2 + 2*x + 3   216: 3*x^2 + 10*x   217: x^2 +
12*x + 5   218: 9*x^2 + 8   219: x^2 + 2*x   220: 4*x^2 + 6   221: 12*x^2 + 5*x
+ 3   222: 6*x^2 + 3*x + 3   223: 7*x + 6   224: 10*x^2 + 11*x + 5   225: 3*x^2
+ 8*x + 10   226: 11*x + 9   227: 12*x^2 + 5*x + 1   228: 6*x^2 + 2*x + 10
229: 6*x^2 + x + 1   230: 12*x^2   231: 10*x^2 + 6*x + 7   232: 7*x^2 + 7*x + 3
233: 5*x^2 + 12   234: 2*x^2 + 2*x + 1   235: 7*x^2 + x + 2   236: 2*x^2 + x + 9
237: 2*x   238: x^2 + 6*x   239: 6*x^2 + 12*x + 6   240: 11*x^2 + 3*x + 2   241:
2*x^2 + 9*x + 7   242: 4*x^2 + 12*x + 7   243: 5*x^2 + 9*x + 6   244: 9   245:
11*x + 1   246: 12*x^2 + x + 3   247: 4*x^2 + 4*x + 3   248: x^2 + 9*x + 7
249: x^2 + 5*x + 1   250: 12*x^2 + 3*x + 9   251: 5*x^2 + 8   252: 2*x^2 + 2
253: 6*x^2 + 2*x + 5   254: 6*x^2 + 5*x + 12   255: x^2 + 11*x + 7   256: 2*x^2
+ 11*x + 1   257: 5*x^2 + 2*x + 2   258: 3*x^2 + 3*x + 10   259: 4*x^2 + 9*x + 9
260: 10*x^2 + x + 12   261: 11*x^2 + x + 5   262: x^2 + 11*x + 3   263: 2*x^2 +
9*x + 2   264: 4*x^2 + 3*x + 5   265: 7*x^2 + 7*x   266: 5*x^2 + 5*x + 3   267:
11*x^2 + 6*x   268: 10*x^2 + 4*x + 1   269: 6*x^2 + 11*x + 11   270: 4*x^2 + 9*x
+ 4   271: 10*x^2 + 5*x + 10   272: 12*x + 12   273: 6*x^2 + 3*x + 10   274: 4*x
+ 1   275: 2*x^2 + 6*x + 3   276: 9*x^2 + x + 8   277: 8*x^2 + 5*x   278: 7*x^2
+ 6*x + 9   279: 11*x^2 + 4   280: 7*x^2 + x   281: 2*x^2 + 3   282: 6*x^2 + 9*x
+ 8   283: 3*x^2 + 8*x + 8   284: 10*x + 3   285: 5*x^2 + 12*x + 9   286: 8*x^2
+ 4*x + 5   287: 12*x + 11   288: 6*x^2 + 9*x + 7   289: 3*x^2 + x + 5   290:
3*x^2 + 7*x + 7   291: 6*x^2   292: 5*x^2 + 3*x + 10   293: 10*x^2 + 10*x + 8
294: 9*x^2 + 6   295: x^2 + x + 7   296: 10*x^2 + 7*x + 1   297: x^2 + 7*x + 11
298: x   299: 7*x^2 + 3*x   300: 3*x^2 + 6*x + 3   301: 12*x^2 + 8*x + 1   302:
x^2 + 11*x + 10   303: 2*x^2 + 6*x + 10   304: 9*x^2 + 11*x + 3   305: 11   306:
12*x + 7   307: 6*x^2 + 7*x + 8   308: 2*x^2 + 2*x + 8   309: 7*x^2 + 11*x + 10
310: 7*x^2 + 9*x + 7   311: 6*x^2 + 8*x + 11   312: 9*x^2 + 4   313: x^2 + 1
314: 3*x^2 + x + 9   315: 3*x^2 + 9*x + 6   316: 7*x^2 + 12*x + 10   317: x^2 +
12*x + 7   318: 9*x^2 + x + 1   319: 8*x^2 + 8*x + 5   320: 2*x^2 + 11*x + 11
321: 5*x^2 + 7*x + 6   322: 12*x^2 + 7*x + 9   323: 7*x^2 + 12*x + 8   324: x^2
+ 11*x + 1   325: 2*x^2 + 8*x + 9   326: 10*x^2 + 10*x   327: 9*x^2 + 9*x + 8
328: 12*x^2 + 3*x   329: 5*x^2 + 2*x + 7   330: 3*x^2 + 12*x + 12   331: 2*x^2 +
11*x + 2   332: 5*x^2 + 9*x + 5   333: 6*x + 6   334: 3*x^2 + 8*x + 5   335: 2*x
+ 7   336: x^2 + 3*x + 8   337: 11*x^2 + 7*x + 4   338: 4*x^2 + 9*x   339:
10*x^2 + 3*x + 11   340: 12*x^2 + 2   341: 10*x^2 + 7*x   342: x^2 + 8   343:
3*x^2 + 11*x + 4   344: 8*x^2 + 4*x + 4   345: 5*x + 8   346: 9*x^2 + 6*x + 11
347: 4*x^2 + 2*x + 9   348: 6*x + 12   349: 3*x^2 + 11*x + 10   350: 8*x^2 + 7*x
+ 9   351: 8*x^2 + 10*x + 10   352: 3*x^2   353: 9*x^2 + 8*x + 5   354: 5*x^2 +
5*x + 4   355: 11*x^2 + 3   356: 7*x^2 + 7*x + 10   357: 5*x^2 + 10*x + 7   358:
7*x^2 + 10*x + 12   359: 7*x   360: 10*x^2 + 8*x   361: 8*x^2 + 3*x + 8   362:
6*x^2 + 4*x + 7   363: 7*x^2 + 12*x + 5   364: x^2 + 3*x + 5   365: 11*x^2 +
12*x + 8   366: 12   367: 6*x + 10   368: 3*x^2 + 10*x + 4   369: x^2 + x + 4
370: 10*x^2 + 12*x + 5   371: 10*x^2 + 11*x + 10   372: 3*x^2 + 4*x + 12   373:
11*x^2 + 2   374: 7*x^2 + 7   375: 8*x^2 + 7*x + 11   376: 8*x^2 + 11*x + 3
377: 10*x^2 + 6*x + 5   378: 7*x^2 + 6*x + 10   379: 11*x^2 + 7*x + 7   380:
4*x^2 + 4*x + 9   381: x^2 + 12*x + 12   382: 9*x^2 + 10*x + 3   383: 6*x^2 +
10*x + 11   384: 10*x^2 + 6*x + 4   385: 7*x^2 + 12*x + 7   386: x^2 + 4*x + 11
387: 5*x^2 + 5*x   388: 11*x^2 + 11*x + 4   389: 6*x^2 + 8*x   390: 9*x^2 + x +
10   391: 8*x^2 + 6*x + 6   392: x^2 + 12*x + 1   393: 9*x^2 + 11*x + 9   394:
3*x + 3   395: 8*x^2 + 4*x + 9   396: x + 10   397: 7*x^2 + 8*x + 4   398:
12*x^2 + 10*x + 2   399: 2*x^2 + 11*x   400: 5*x^2 + 8*x + 12   401: 6*x^2 + 1
402: 5*x^2 + 10*x   403: 7*x^2 + 4   404: 8*x^2 + 12*x + 2   405: 4*x^2 + 2*x +
2   406: 9*x + 4   407: 11*x^2 + 3*x + 12   408: 2*x^2 + x + 11   409: 3*x + 6
410: 8*x^2 + 12*x + 5   411: 4*x^2 + 10*x + 11   412: 4*x^2 + 5*x + 5   413:
8*x^2   414: 11*x^2 + 4*x + 9   415: 9*x^2 + 9*x + 2   416: 12*x^2 + 8   417:
10*x^2 + 10*x + 5   418: 9*x^2 + 5*x + 10   419: 10*x^2 + 5*x + 6   420: 10*x
421: 5*x^2 + 4*x   422: 4*x^2 + 8*x + 4   423: 3*x^2 + 2*x + 10   424: 10*x^2 +
6*x + 9   425: 7*x^2 + 8*x + 9   426: 12*x^2 + 6*x + 4   427: 6   428: 3*x + 5
429: 8*x^2 + 5*x + 2   430: 7*x^2 + 7*x + 2   431: 5*x^2 + 6*x + 9   432: 5*x^2
+ 12*x + 5   433: 8*x^2 + 2*x + 6   434: 12*x^2 + 1   435: 10*x^2 + 10   436:
4*x^2 + 10*x + 12   437: 4*x^2 + 12*x + 8   438: 5*x^2 + 3*x + 9   439: 10*x^2 +
3*x + 5   440: 12*x^2 + 10*x + 10   441: 2*x^2 + 2*x + 11   442: 7*x^2 + 6*x + 6
443: 11*x^2 + 5*x + 8   444: 3*x^2 + 5*x + 12   445: 5*x^2 + 3*x + 2   446:
10*x^2 + 6*x + 10   447: 7*x^2 + 2*x + 12   448: 9*x^2 + 9*x   449: 12*x^2 +
12*x + 2   450: 3*x^2 + 4*x   451: 11*x^2 + 7*x + 5   452: 4*x^2 + 3*x + 3
453: 7*x^2 + 6*x + 7   454: 11*x^2 + 12*x + 11   455: 8*x + 8   456: 4*x^2 + 2*x
+ 11   457: 7*x + 5   458: 10*x^2 + 4*x + 2   459: 6*x^2 + 5*x + 1   460: x^2 +
12*x   461: 9*x^2 + 4*x + 6   462: 3*x^2 + 7   463: 9*x^2 + 5*x   464: 10*x^2 +
2   465: 4*x^2 +
** WARNING: Output too long, hence truncated.
'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:07:40 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

for i in [0..(61*12)] do
printf "%o:%o*",i,Modexp(xx, i, x^3-x+1);
end for;

Output: Magma V2.11-6     Thu Sep 23 2004 23:07:40 on modular  [Seed = 2157072045]
-------------------------------------

0:1*1:7*x + 3*2:10*x^2 + 3*x + 9*3:12*x^2 + 12*x + 9*4:3*x^2 + x + 8*5:3*x^2 +
2*x + 3*6:10*x^2 + 9*x + 1*7:2*x^2 + 11*8:6*x^2 + 6*9:5*x^2 + 6*x + 2*10:5*x^2 +
2*x + 10*11:3*x^2 + 7*x + 8*12:6*x^2 + 7*x + 3*13:2*x^2 + 6*x + 6*14:9*x^2 + 9*x
+ 4*15:12*x^2 + x + 1*16:4*x^2 + 3*x + 10*17:7*x^2 + 3*x + 2*18:3*x^2 + 7*x +
9*19:6*x^2 + x + 6*20:12*x^2 + 9*x + 2*21:8*x^2 + 8*x*22:2*x^2 + 2*x +
9*23:7*x^2 + 5*x*24:4*x^2 + 12*x + 3*25:5*x^2 + 7*x + 7*26:12*x^2 + x +
12*27:4*x^2 + 2*x + 4*28:10*x + 10*29:5*x^2 + 9*x + 4*30:12*x + 3*31:6*x^2 + 5*x
+ 9*32:x^2 + 3*x + 11*33:11*x^2 + 2*x*34:8*x^2 + 5*x + 1*35:7*x^2 + 12*36:8*x^2
+ 3*x*37:6*x^2 + 9*38:5*x^2 + x + 11*39:9*x^2 + 11*x + 11*40:4*x + 9*41:2*x^2 +
10*x + 1*42:11*x^2 + 12*x + 2*43:10*x + 7*44:5*x^2 + x + 8*45:9*x^2 + 3*x +
2*46:9*x^2 + 8*x + 8*47:5*x^2*48:2*x^2 + 9*x + 4*49:4*x^2 + 4*x + 11*50:x^2 +
5*51:3*x^2 + 3*x + 8*52:4*x^2 + 8*x + 3*53:3*x^2 + 8*x + 7*54:3*x*55:8*x^2 +
9*x*56:9*x^2 + 5*x + 9*57:10*x^2 + 11*x + 3*58:3*x^2 + 7*x + 4*59:6*x^2 + 5*x +
4*60:x^2 + 7*x + 9*61:7*62:10*x + 8*63:5*x^2 + 8*x + 11*64:6*x^2 + 6*x +
11*65:8*x^2 + 7*x + 4*66:8*x^2 + x + 8*67:5*x^2 + 11*x + 7*68:x^2 + 12*69:3*x^2
+ 3*70:9*x^2 + 3*x + 1*71:9*x^2 + x + 5*72:8*x^2 + 10*x + 4*73:3*x^2 + 10*x +
8*74:x^2 + 3*x + 3*75:11*x^2 + 11*x + 2*76:6*x^2 + 7*x + 7*77:2*x^2 + 8*x +
5*78:10*x^2 + 8*x + 1*79:8*x^2 + 10*x + 11*80:3*x^2 + 7*x + 3*81:6*x^2 + 11*x +
1*82:4*x^2 + 4*x*83:x^2 + x + 11*84:10*x^2 + 9*x*85:2*x^2 + 6*x + 8*86:9*x^2 +
10*x + 10*87:6*x^2 + 7*x + 6*88:2*x^2 + x + 2*89:5*x + 5*90:9*x^2 + 11*x +
2*91:6*x + 8*92:3*x^2 + 9*x + 11*93:7*x^2 + 8*x + 12*94:12*x^2 + x*95:4*x^2 +
9*x + 7*96:10*x^2 + 6*97:4*x^2 + 8*x*98:3*x^2 + 11*99:9*x^2 + 7*x +
12*100:11*x^2 + 12*x + 12*101:2*x + 11*102:x^2 + 5*x + 7*103:12*x^2 + 6*x +
1*104:5*x + 10*105:9*x^2 + 7*x + 4*106:11*x^2 + 8*x + 1*107:11*x^2 + 4*x +
4*108:9*x^2*109:x^2 + 11*x + 2*110:2*x^2 + 2*x + 12*111:7*x^2 + 9*112:8*x^2 +
8*x + 4*113:2*x^2 + 4*x + 8*114:8*x^2 + 4*x + 10*115:8*x*116:4*x^2 +
11*x*117:11*x^2 + 9*x + 11*118:5*x^2 + 12*x + 8*119:8*x^2 + 10*x + 2*120:3*x^2 +
9*x + 2*121:7*x^2 + 10*x + 11*122:10*123:5*x + 4*124:9*x^2 + 4*x + 12*125:3*x^2
+ 3*x + 12*126:4*x^2 + 10*x + 2*127:4*x^2 + 7*x + 4*128:9*x^2 + 12*x +
10*129:7*x^2 + 6*130:8*x^2 + 8*131:11*x^2 + 8*x + 7*132:11*x^2 + 7*x +
9*133:4*x^2 + 5*x + 2*134:8*x^2 + 5*x + 4*135:7*x^2 + 8*x + 8*136:12*x^2 + 12*x
+ 1*137:3*x^2 + 10*x + 10*138:x^2 + 4*x + 9*139:5*x^2 + 4*x + 7*140:4*x^2 + 5*x
+ 12*141:8*x^2 + 10*x + 8*142:3*x^2 + 12*x + 7*143:2*x^2 + 2*x*144:7*x^2 + 7*x +
12*145:5*x^2 + 11*x*146:x^2 + 3*x + 4*147:11*x^2 + 5*x + 5*148:3*x^2 + 10*x +
3*149:x^2 + 7*x + 1*150:9*x + 9*151:11*x^2 + 12*x + 1*152:3*x + 4*153:8*x^2 +
11*x + 12*154:10*x^2 + 4*x + 6*155:6*x^2 + 7*x*156:2*x^2 + 11*x + 10*157:5*x^2 +
3*158:2*x^2 + 4*x*159:8*x^2 + 12*160:11*x^2 + 10*x + 6*161:12*x^2 + 6*x +
6*162:x + 12*163:7*x^2 + 9*x + 10*164:6*x^2 + 3*x + 7*165:9*x + 5*166:11*x^2 +
10*x + 2*167:12*x^2 + 4*x + 7*168:12*x^2 + 2*x + 2*169:11*x^2*170:7*x^2 + 12*x +
1*171:x^2 + x + 6*172:10*x^2 + 11*173:4*x^2 + 4*x + 2*174:x^2 + 2*x +
4*175:4*x^2 + 2*x + 5*176:4*x*177:2*x^2 + 12*x*178:12*x^2 + 11*x + 12*179:9*x^2
+ 6*x + 4*180:4*x^2 + 5*x + 1*181:8*x^2 + 11*x + 1*182:10*x^2 + 5*x +
12*183:5*184:9*x + 2*185:11*x^2 + 2*x + 6*186:8*x^2 + 8*x + 6*187:2*x^2 + 5*x +
1*188:2*x^2 + 10*x + 2*189:11*x^2 + 6*x + 5*190:10*x^2 + 3*191:4*x^2 +
4*192:12*x^2 + 4*x + 10*193:12*x^2 + 10*x + 11*194:2*x^2 + 9*x + 1*195:4*x^2 +
9*x + 2*196:10*x^2 + 4*x + 4*197:6*x^2 + 6*x + 7*198:8*x^2 + 5*x + 5*199:7*x^2 +
2*x + 11*200:9*x^2 + 2*x + 10*201:2*x^2 + 9*x + 6*202:4*x^2 + 5*x + 4*203:8*x^2
+ 6*x + 10*204:x^2 + x*205:10*x^2 + 10*x + 6*206:9*x^2 + 12*x*207:7*x^2 + 8*x +
2*208:12*x^2 + 9*x + 9*209:8*x^2 + 5*x + 8*210:7*x^2 + 10*x + 7*211:11*x +
11*212:12*x^2 + 6*x + 7*213:8*x + 2*214:4*x^2 + 12*x + 6*215:5*x^2 + 2*x +
3*216:3*x^2 + 10*x*217:x^2 + 12*x + 5*218:9*x^2 + 8*219:x^2 + 2*x*220:4*x^2 +
6*221:12*x^2 + 5*x + 3*222:6*x^2 + 3*x + 3*223:7*x + 6*224:10*x^2 + 11*x +
5*225:3*x^2 + 8*x + 10*226:11*x + 9*227:12*x^2 + 5*x + 1*228:6*x^2 + 2*x +
10*229:6*x^2 + x + 1*230:12*x^2*231:10*x^2 + 6*x + 7*232:7*x^2 + 7*x +
3*233:5*x^2 + 12*234:2*x^2 + 2*x + 1*235:7*x^2 + x + 2*236:2*x^2 + x +
9*237:2*x*238:x^2 + 6*x*239:6*x^2 + 12*x + 6*240:11*x^2 + 3*x + 2*241:2*x^2 +
9*x + 7*242:4*x^2 + 12*x + 7*243:5*x^2 + 9*x + 6*244:9*245:11*x + 1*246:12*x^2 +
x + 3*247:4*x^2 + 4*x + 3*248:x^2 + 9*x + 7*249:x^2 + 5*x + 1*250:12*x^2 + 3*x +
9*251:5*x^2 + 8*252:2*x^2 + 2*253:6*x^2 + 2*x + 5*254:6*x^2 + 5*x + 12*255:x^2 +
11*x + 7*256:2*x^2 + 11*x + 1*257:5*x^2 + 2*x + 2*258:3*x^2 + 3*x + 10*259:4*x^2
+ 9*x + 9*260:10*x^2 + x + 12*261:11*x^2 + x + 5*262:x^2 + 11*x + 3*263:2*x^2 +
9*x + 2*264:4*x^2 + 3*x + 5*265:7*x^2 + 7*x*266:5*x^2 + 5*x + 3*267:11*x^2 +
6*x*268:10*x^2 + 4*x + 1*269:6*x^2 + 11*x + 11*270:4*x^2 + 9*x + 4*271:10*x^2 +
5*x + 10*272:12*x + 12*273:6*x^2 + 3*x + 10*274:4*x + 1*275:2*x^2 + 6*x +
3*276:9*x^2 + x + 8*277:8*x^2 + 5*x*278:7*x^2 + 6*x + 9*279:11*x^2 + 4*280:7*x^2
+ x*281:2*x^2 + 3*282:6*x^2 + 9*x + 8*283:3*x^2 + 8*x + 8*284:10*x + 3*285:5*x^2
+ 12*x + 9*286:8*x^2 + 4*x + 5*287:12*x + 11*288:6*x^2 + 9*x + 7*289:3*x^2 + x +
5*290:3*x^2 + 7*x + 7*291:6*x^2*292:5*x^2 + 3*x + 10*293:10*x^2 + 10*x +
8*294:9*x^2 + 6*295:x^2 + x + 7*296:10*x^2 + 7*x + 1*297:x^2 + 7*x +
11*298:x*299:7*x^2 + 3*x*300:3*x^2 + 6*x + 3*301:12*x^2 + 8*x + 1*302:x^2 + 11*x
+ 10*303:2*x^2 + 6*x + 10*304:9*x^2 + 11*x + 3*305:11*306:12*x + 7*307:6*x^2 +
7*x + 8*308:2*x^2 + 2*x + 8*309:7*x^2 + 11*x + 10*310:7*x^2 + 9*x + 7*311:6*x^2
+ 8*x + 11*312:9*x^2 + 4*313:x^2 + 1*314:3*x^2 + x + 9*315:3*x^2 + 9*x +
6*316:7*x^2 + 12*x + 10*317:x^2 + 12*x + 7*318:9*x^2 + x + 1*319:8*x^2 + 8*x +
5*320:2*x^2 + 11*x + 11*321:5*x^2 + 7*x + 6*322:12*x^2 + 7*x + 9*323:7*x^2 +
12*x + 8*324:x^2 + 11*x + 1*325:2*x^2 + 8*x + 9*326:10*x^2 + 10*x*327:9*x^2 +
9*x + 8*328:12*x^2 + 3*x*329:5*x^2 + 2*x + 7*330:3*x^2 + 12*x + 12*331:2*x^2 +
11*x + 2*332:5*x^2 + 9*x + 5*333:6*x + 6*334:3*x^2 + 8*x + 5*335:2*x + 7*336:x^2
+ 3*x + 8*337:11*x^2 + 7*x + 4*338:4*x^2 + 9*x*339:10*x^2 + 3*x + 11*340:12*x^2
+ 2*341:10*x^2 + 7*x*342:x^2 + 8*343:3*x^2 + 11*x + 4*344:8*x^2 + 4*x +
4*345:5*x + 8*346:9*x^2 + 6*x + 11*347:4*x^2 + 2*x + 9*348:6*x + 12*349:3*x^2 +
11*x + 10*350:8*x^2 + 7*x + 9*351:8*x^2 + 10*x + 10*352:3*x^2*353:9*x^2 + 8*x +
5*354:5*x^2 + 5*x + 4*355:11*x^2 + 3*356:7*x^2 + 7*x + 10*357:5*x^2 + 10*x +
7*358:7*x^2 + 10*x + 12*359:7*x*360:10*x^2 + 8*x*361:8*x^2 + 3*x + 8*362:6*x^2 +
4*x + 7*363:7*x^2 + 12*x + 5*364:x^2 + 3*x + 5*365:11*x^2 + 12*x +
8*366:12*367:6*x + 10*368:3*x^2 + 10*x + 4*369:x^2 + x + 4*370:10*x^2 + 12*x +
5*371:10*x^2 + 11*x + 10*372:3*x^2 + 4*x + 12*373:11*x^2 + 2*374:7*x^2 +
7*375:8*x^2 + 7*x + 11*376:8*x^2 + 11*x + 3*377:10*x^2 + 6*x + 5*378:7*x^2 + 6*x
+ 10*379:11*x^2 + 7*x + 7*380:4*x^2 + 4*x + 9*381:x^2 + 12*x + 12*382:9*x^2 +
10*x + 3*383:6*x^2 + 10*x + 11*384:10*x^2 + 6*x + 4*385:7*x^2 + 12*x + 7*386:x^2
+ 4*x + 11*387:5*x^2 + 5*x*388:11*x^2 + 11*x + 4*389:6*x^2 + 8*x*390:9*x^2 + x +
10*391:8*x^2 + 6*x + 6*392:x^2 + 12*x + 1*393:9*x^2 + 11*x + 9*394:3*x +
3*395:8*x^2 + 4*x + 9*396:x + 10*397:7*x^2 + 8*x + 4*398:12*x^2 + 10*x +
2*399:2*x^2 + 11*x*400:5*x^2 + 8*x + 12*401:6*x^2 + 1*402:5*x^2 + 10*x*403:7*x^2
+ 4*404:8*x^2 + 12*x + 2*405:4*x^2 + 2*x + 2*406:9*x + 4*407:11*x^2 + 3*x +
12*408:2*x^2 + x + 11*409:3*x + 6*410:8*x^2 + 12*x + 5*411:4*x^2 + 10*x +
11*412:4*x^2 + 5*x + 5*413:8*x^2*414:11*x^2 + 4*x + 9*415:9*x^2 + 9*x +
2*416:12*x^2 + 8*417:10*x^2 + 10*x + 5*418:9*x^2 + 5*x + 10*419:10*x^2 + 5*x +
6*420:10*x*421:5*x^2 + 4*x*422:4*x^2 + 8*x + 4*423:3*x^2 + 2*x + 10*424:10*x^2 +
6*x + 9*425:7*x^2 + 8*x + 9*426:12*x^2 + 6*x + 4*427:6*428:3*x + 5*429:8*x^2 +
5*x + 2*430:7*x^2 + 7*x + 2*431:5*x^2 + 6*x + 9*432:5*x^2 + 12*x + 5*433:8*x^2 +
2*x + 6*434:12*x^2 + 1*435:10*x^2 + 10*436:4*x^2 + 10*x + 12*437:4*x^2 + 12*x +
8*438:5*x^2 + 3*x + 9*439:10*x^2 + 3*x + 5*440:12*x^2 + 10*x + 10*441:2*x^2 +
2*x + 11*442:7*x^2 + 6*x + 6*443:11*x^2 + 5*x + 8*444:3*x^2 + 5*x + 12*445:5*x^2
+ 3*x + 2*446:10*x^2 + 6*x + 10*447:7*x^2 + 2*x + 12*448:9*x^2 + 9*x*449:12*x^2
+ 12*x + 2*450:3*x^2 + 4*x*451:11*x^2 + 7*x + 5*452:4*x^2 + 3*x + 3*453:7*x^2 +
6*x + 7*454:11*x^2 + 12*x + 11*455:8*x + 8*456:4*x^2 + 2*x + 11*457:7*x +
5*458:10*x^2 + 4*x + 2*459:6*x^2 + 5*x + 1*460:x^2 + 12*x*461:9*x^2 + 4*x +
6*462:3*x^2 + 7*463:9*x^2 + 5*x*464:10*x^2 + 2*465:4*x^2 + 6*x + 1*466:2*x^2 + x
+ 1*467:11*x + 2*468:12*x^2 + 8*x + 6*469:x^2 + 7*x + 12*470:8*x + 3*471:4*x^2 +
6*x + 9*472:2*x^2 + 5*x + 12*473:2*x^2 + 9*x + 9*474:4*x^2*475:12*x^2 + 2*x +
11*476:11*x^2 + 11*x + 1*477:6*x^2 + 4*478:5*x^2 + 5*x + 9*479:11*x^2 + 9*x +
5*480:5*x^2 + 9*x + 3*481:5*x*482:9*x^2 + 2*x*483:2*x^2 + 4*x + 2*484:8*x^2 + x
+ 5*485:5*x^2 + 3*x + 11*486:10*x^2 + 4*x + 11*487:6*x^2 + 3*x + 2*488:3*489:8*x
+ 9*490:4*x^2 + 9*x + 1*491:10*x^2 + 10*x + 1*492:9*x^2 + 3*x + 11*493:9*x^2 +
6*x + 9*494:4*x^2 + x + 3*495:6*x^2 + 7*496:5*x^2 + 5*497:2*x^2 + 5*x +
6*498:2*x^2 + 6*x + 4*499:9*x^2 + 8*x + 11*500:5*x^2 + 8*x + 9*501:6*x^2 + 5*x +
5*502:x^2 + x + 12*503:10*x^2 + 3*x + 3*504:12*x^2 + 9*x + 4*505:8*x^2 + 9*x +
6*506:9*x^2 + 8*x + 1*507:5*x^2 + 3*x + 5*508:10*x^2 + x + 6*509:11*x^2 +
11*x*510:6*x^2 + 6*x + 1*511:8*x^2 + 2*x*512:12*x^2 + 10*x + 9*513:2*x^2 + 8*x +
8*514:10*x^2 + 3*x + 10*515:12*x^2 + 6*x + 12*516:4*x + 4*517:2*x^2 + x +
12*518:10*x + 9*519:5*x^2 + 2*x + 1*520:3*x^2 + 9*x + 7*521:7*x^2 +
6*x*522:11*x^2 + 2*x + 3*523:8*x^2 + 10*524:11*x^2 + 9*x*525:5*x^2 + 1*526:2*x^2
+ 3*x + 7*527:x^2 + 7*x + 7*528:12*x + 1*529:6*x^2 + 4*x + 3*530:7*x^2 + 10*x +
6*531:4*x + 8*532:2*x^2 + 3*x + 11*533:x^2 + 9*x + 6*534:x^2 + 11*x +
11*535:2*x^2*536:6*x^2 + x + 12*537:12*x^2 + 12*x + 7*538:3*x^2 + 2*539:9*x^2 +
9*x + 11*540:12*x^2 + 11*x + 9*5
** WARNING: Output too long, hence truncated.
'203.217'
************** MAGMA *****************
Host 203.217.8.66 (203.217.8.66)
Time: Thu Sep 23 23:07:53 2004

Input: Z13:=FiniteField(13);
P<x>:=PolynomialRing(Z13);

zlist:=[* *]; nlist:=[* *]; mlist:=[* *];

i:=0; n:=0; m:=0;

xx:=3+7*x; yy:=2+x^2; z:=P!1; q:=0;

for i in [0..(61*12)] do
printf "%o:%[email protected]",i,Modexp(xx, i, x^3-x+1);
end for;

Output: Magma V2.11-6     Thu Sep 23 2004 23:07:53 on modular  [Seed = 2274707807]
-------------------------------------

0:[email protected]:7*x + [email protected]:10