CoCalc Public Fileswww / talks / harvard-talk-2004-12-08 / e2heights / yesOpen with one click!
Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$ [email protected]:~/papers/padic_cyclotomic_height/e2heights$ Magma V2.11-10 Mon Nov 29 2004 13:14:13 on form [Seed = 1820740565]
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Type ? for help. Type <Ctrl>-D to quit.
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Loading startup file "/home/was/magma/local/emacs.m"
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Loading "/home/was/magma/local/init.m"
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> Attach("padic_height.m");
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> E := EC("11A");
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> F := QuadraticTwist(E,-47);
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> Rank(F);
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2
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> time G,f := MordellWeilGroup(F);
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[Interrupted]
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> time G,f := MordellWeilGroup(F);
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Time: 0.450
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> G;
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Abelian Group isomorphic to Z + Z
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Defined on 2 generators (free)
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> regulator(F,3,100);
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>> regulator(F,3);
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^
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Runtime error in 'regulator': Bad argument types
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Argument types given: CrvEll[FldRat], RngIntElt
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> regulator(F,3,100);
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regulator(
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E: E,
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p: 3,
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prec: 100
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)
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ap(
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E: E,
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p: 3
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)
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In file "/home2/was/papers/padic_cyclotomic_height/e2heights/pad\
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ic_height.m", line 811, column 27:
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>> return TraceOfFrobenius(ChangeRing(E,GF(p)));
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^
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Runtime error in 'TraceOfFrobenius': Bad argument types
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Argument types given: Crv[FldFin]
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> TraceOfFrobenius(ChangeRing(E,GF(3)));
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-1
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> TraceOfFrobenius(ChangeRing(E,GF(11)));
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>> TraceOfFrobenius(ChangeRing(E,GF(11)));
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^
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Runtime error in 'TraceOfFrobenius': Bad argument types
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Argument types given: Crv[FldFin]
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> F;
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Elliptic Curve defined by y^2 = x^3 - 29582928*x + 112173691536
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over Rational Field
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> Conductor(F);
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24299
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> TraceOfFrobenius(ChangeRing(F,GF(11)));
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>> TraceOfFrobenius(ChangeRing(F,GF(11)));
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^
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Runtime error in 'TraceOfFrobenius': Bad argument types
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Argument types given: Crv[FldFin]
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> factor(24299);
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[ <11, 1>, <47, 2> ]
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1
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> Discriminant(F);
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-3778901553663057684639744
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> factor($1);
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[ <2, 12>, <3, 12>, <11, 5>, <47, 6> ]
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> regulator(F,3,20);
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regulator(
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E: E,
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p: 3,
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prec: 20
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)
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height_function(
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E: E,
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p: 3,
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prec: 20
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)
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sigma_using_e2(
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E: E,
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p: 3,
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prec: 22
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)
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In file "/home2/was/papers/padic_cyclotomic_height/e2heights/pad\
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ic_height.m", line 556, column 12:
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>> e2 := E2(E,p,e2prec);
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^
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Runtime error in 'E2': Argument 2 must be at least 5.
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> regulator(F,3,20);
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WARNING: p <= 3.
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regulator(
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E: E,
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p: 3,
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prec: 20
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)
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height_function(
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E: E,
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p: 3,
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prec: 20
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)
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sigma_using_e2(
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E: E,
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p: 3,
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prec: 22
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)
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E2(
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E: E,
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p: 3,
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prec: 20
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)
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In file "/home2/was/papers/padic_cyclotomic_height/e2heights/pad\
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ic_height.m", line 475, column 24:
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>> S := quo<P1 | X^3+a4*X+a6 - T^-1>;
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^
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Runtime error in '*': Bad argument types
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Argument types given: FldRatElt,
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RngUPolElt[RngSerLaur[RngPadRes]]
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> regulator(E,7,20);
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regulator(
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E: E,
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p: 7,
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prec: 20
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)
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height_function(
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E: E,
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p: 7,
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prec: 20
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)
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sigma_using_e2(
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E: E,
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p: 7,
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prec: 22
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)
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E2(
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E: E,
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p: 7,
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prec: 20
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)
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In file "/home2/was/papers/padic_cyclotomic_height/e2heights/pad\
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ic_height.m", line 482, column 11:
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>> A,B := myXGCD(precs[1],precs[2]);
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^
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Runtime error: Package "/home2/was/papers/padic_cyclotomic_heigh\
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t/e2heights/kedlaya.m" has not been attached
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> Attach("kedlaya.m");
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> regulator(E,7,20);
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regulator(
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E: E,
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p: 7,
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prec: 20
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)
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In file "/home2/was/papers/padic_cyclotomic_height/e2heights/pad\
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ic_height.m", line 792, column 19:
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>> K := Parent(h(B[1]));
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^
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Runtime error in '[]': Sequence element 1 not defined
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> regulator(E,7,20);
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1
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> regulator(F,7,20);
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9504340477315487 + O(7^20)
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> F := MinimalModel(F);
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> regulator(F,7,20);
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-13275121094488961 + O(7^20)
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> regulator(F,5,20);
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-122626690196634 + O(5^21)
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> regulator(F,17,20);
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-892642658454118243405888 + O(17^20)
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> regulator(F,23,20);
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-1336529660411339595374261*23^-2 + O(23^16)
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> qEigenform(F,24);
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q - 2*q^2 - q^3 + 2*q^4 - q^5 + 2*q^6 - 2*q^7 - 2*q^9 + 2*q^10 -
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q^11 - 2*q^12 - 4*q^13 + 4*q^14 + q^15 - 4*q^16 - 2*q^17 +
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4*q^18 - 2*q^20 + 2*q^21 + 2*q^22 + q^23 + O(q^24)
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> mazur_comp(-47);
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In file "/home2/was/papers/padic_cyclotomic_height/e2heights/pad\
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ic_height.m", line 914, column 10:
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>> E := EC("11A");
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^
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Runtime error: Undefined reference 'EC' in package
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"/home2/was/papers/padic_cyclotomic_height/e2heights/padic_heigh\
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t.m"
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> time mazur_comp(-47);
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Time: 0.000
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[ -47 + O(5^22), 5 + O(5^23), -122626690196634 + O(5^21), O(5^22)
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]
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[ -47 + O(7^22), 7 + O(7^23), -13275121094488961 + O(7^20),
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O(7^22) ]
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[ -47 + O(13^22), 13 + O(13^23), 100303162051520858090087 +
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O(13^21), O(13^22) ]
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[ -47 + O(17^21), 17 + O(17^22), -892642658454118243405888 +
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O(17^20), O(17^21) ]
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[ -47 + O(23^21), 23 + O(23^22), -1336529660411339595374261*23^-2
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+ O(23^16), -2 + O(23^21) ]
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[ -47 + O(31^21), 31 + O(31^22), -330930890508775818003179485695
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+ O(31^20), O(31^21) ]
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[ -47 + O(37^21), 37 + O(37^22), 7572135911444888633588653815879
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+ O(37^20), O(37^21) ]
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[ -47 + O(41^21), 41 + O(41^22),
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-39134738157737309207985312955640 + O(41^20), O(41^21) ]
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[ -47 + O(43^21), 43 + O(43^22),
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-178660769887294476009988570260306 + O(43^20), O(43^21) ]
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mazur_comp(
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d: -47
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)
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In file "/home2/was/papers/padic_cyclotomic_height/e2heights/pad\
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ic_height.m", line 925, column 24:
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>> reg := regulator(F, p, 20);
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^
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Runtime error in 'regulator': Curve must have good ordinary
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reduction at p.
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> time mazur_comp(-47);
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Time: 0.000
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<-47, 5, -122626690196634 + O(5^21), 0>
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<-47, 7, -13275121094488961 + O(7^20), 0>
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<-47, 13, 100303162051520858090087 + O(13^21), 0>
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<-47, 17, -892642658454118243405888 + O(17^20), 0>
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<-47, 23, -1336529660411339595374261*23^-2 + O(23^16), -2>
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<-47, 31, -330930890508775818003179485695 + O(31^20), 0>
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<-47, 37, 7572135911444888633588653815879 + O(37^20), 0>
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<-47, 41, -39134738157737309207985312955640 + O(41^20), 0>
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<-47, 43, -178660769887294476009988570260306 + O(43^20), 0>
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<-47, 53, 8172099236547658056150877348285133 + O(53^20), 0>
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[Interrupted]
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> time mazur_comp(-47);
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Time: 0.000
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<-47, 5, -122626690196634 + O(5^21), 0>
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<-47, 7, -13275121094488961 + O(7^20), 0>
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<-47, 13, 100303162051520858090087 + O(13^21), 0>
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<-47, 17, -892642658454118243405888 + O(17^20), 0>
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<-47, 23, -1336529660411339595374261*23^-2 + O(23^16), -2>
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Time: 3.190
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> time mazur_comp(-103);
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[Interrupt twice in half a second; exiting]
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Total time: 180.240 seconds, Total memory usage: 5.91MB
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$ [email protected]:~/papers/padic_cyclotomic_height/e2heights$ [email protected]:~/papers/padic_cyclotomic_height/e2heights$ me
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$ [email protected]:~/papers/padic_cyclotomic_height/e2heights$ me
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Magma V2.11-10 Mon Nov 29 2004 13:36:20 on form [Seed = 2923725765]
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Type ? for help. Type <Ctrl>-D to quit.
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Loading startup file "/home/was/magma/local/emacs.m"
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Loading "/home/was/magma/local/init.m"
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> Attach("kedlaya.m");
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>> );
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^
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User error: bad syntax
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> Attach("kedlaya.m");Attach("padic_height.m");
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> mazur_comp(232);
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Time: 1.210
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<232, 5, -942716651353 + O(5^18), 0>
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<232, 7, -7873472415490835 + O(7^20), 0>
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<232, 13, -81615990685573318597276 + O(13^21), 0>
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<232, 17, -1216922723508463140745468 + O(17^20), 0>
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<232, 23, -35316800327085548057299999 + O(23^20), 0>
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> mazur_comp(265);
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[Interrupt twice in half a second; exiting]
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Total time: 124.260 seconds, Total memory usage: 4.23MB
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$ me
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$ [email protected]:~/papers/padic_cyclotomic_height/e2heights$
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$ me
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Magma V2.11-10 Mon Nov 29 2004 13:39:15 on form [Seed = 1837580528]
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Type ? for help. Type <Ctrl>-D to quit.
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Loading startup file "/home/was/magma/local/emacs.m"
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Loading "/home/was/magma/local/init.m"
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> Attach("kedlaya.m");Attach("padic_height.m");
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> mazur_comp(273);
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[Interrupt twice in half a second; exiting]
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Total time: 316.089 seconds, Total memory usage: 3.56MB
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[email protected]:~/papers/padic_cyclotomic_height/e2heights$