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(/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 12. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) (height.toc) \tf@toc=\write3 \openout3 = `height.toc'. ! LaTeX Error: There's no line here to end. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.46 \caption{\bf 389A, p=3}\vspace{1ex}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: There's no line here to end. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.72 \caption{\bf 433A, p=3}\vspace{1ex}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: There's no line here to end. See the LaTeX manual or LaTeX Companion for explanation. 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[1 ] [2] Overfull \hbox (61.79471pt too wide) in paragraph at lines 284--284 []\OT1/cmtt/m/n/10 H_2(3^4*P_1)/3^8 := 3^-7 - 3^-6 - 3^-4 - 3^-3 - 3^-2 + 3^-1 - 1 - 3 - 3^3 + 3^4 + O(3^5)[] [] [3] Overfull \hbox (30.29498pt too wide) in paragraph at lines 284--284 []\OT1/cmtt/m/n/10 H_2(3^3*P_1)/3^6 := -3^-5 + 3^-4 + 3^-3 + 3^-2 - 3^-1 - 1 - 3 - 3^2 - 3^4 + O(3^5)[] [] Overfull \hbox (72.29462pt too wide) in paragraph at lines 284--284 []\OT1/cmtt/m/n/10 H_2(3^4*P_2)/3^8 := 3^-6 - 3^-5 + 3^-4 - 3^-3 + 3^-2 - 3^-1 + 1 - 3^2 - 3^3 + 3^4 + O(3^5)[] [] [4] [5] Overfull \hbox (35.54494pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 {True if rank(E) is odd, which for all practical purposes in our cases means 1.}[] [] [6] Overfull \hbox (67.04466pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 if Evaluate(KroneckerCharacter(D),-N) eq 1 then // the re's no chance to have rank 1[] [] Overfull \hbox (98.54439pt too wide) in paragraph at lines 719--719 []\OT1/cmtt/m/n/10 intrinsic FindAcceptableK(E::CrvEll, p::RngIntElt, Dmin::Rng IntElt, Dmax::RngIntElt) -> SeqEnum[] [] Overfull \hbox (98.54439pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 {The fields K whose discriminant lie between Dmin and Dma x and satisfy conditions (a)--(d).}[] [] Overfull \hbox (19.79507pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 require Dmin le Dmax: "Argument 3 must be less than or eq ual to argument 4.";[] [] [7] Overfull \hbox (14.54512pt too wide) in paragraph at lines 719--719 []\OT1/cmtt/m/n/10 intrinsic rhotilde(I::RngOrdIdl , pi::RngLocElt, pibar::RngL ocElt) -> FldLocElt[] [] Overfull \hbox (46.04485pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 vprint ac_height : "Computing embeddings of canonical pow er of generator into Qp";[] [] [8] Overfull \hbox (51.2948pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 {I and J, where I is the numerator ideal of x and J is th e denominator ideal of x.}[] [] Overfull \hbox (19.79507pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 {The function H_2 defined in Mazur's note. This is rhoti lde(J*x(P))/2, where[] [] Overfull \hbox (114.29425pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 "The base field of the parent of argument 1 must be a quadratic imaginary number field.";[] [] Overfull \hbox (51.2948pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 f := PolynomialRing(pAdicRing(p : Precision := 40))!Minim alPolynomial(Basis(O)[2]);[] [] [9] Overfull \hbox (93.29443pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 require #fac eq 2 : "Argument 2 must split in the base fi eld of the parent of argument 1.";[] [] Overfull \hbox (40.79489pt too wide) in paragraph at lines 719--719 []\OT1/cmtt/m/n/10 intrinsic Pairing(P::CrvEllPt, Q::CrvEllPt, p::RngIntElt, n: :RngIntElt) -> FldLocElt[] [] Overfull \hbox (124.79416pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 // require TorsionFreeRank(G) eq 1 : "The twist of argu ment 1 by argument 2 must have rank 1.";[] [] Overfull \hbox (93.29443pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 print "WARNING: rank of E_D computed is < 1. We have E = ", aInvariants(E), " D = ", D;[] [] [10] Overfull \hbox (72.29462pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 require Conductor(E) mod p ne 0 : "Argument 1 must have g ood reduction at argument 2.";[] [] Overfull \hbox (82.79453pt too wide) in paragraph at lines 719--719 []\OT1/cmtt/m/n/10 intrinsic TestNontrivialityConjecture(E::CrvEll, p::RngIntEl t, n::RngIntElt, Dlist::SeqEnum)[] [] Overfull \hbox (56.54475pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 Let P = P1 + P0, where P0 is a point of infinite order in E _D(Q) subset E(Q(sqrt(D))).[] [] Overfull \hbox (51.2948pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 [] [] Overfull \hbox (72.29462pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 require Conductor(E) mod p ne 0 : "Argument 1 must have g ood reduction at argument 2.";[] [] [11] Overfull \hbox (9.29517pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 curves := ["389A","433A","446D", "563A","571B","643A","65 5A","664A","681C",[] [] [12] Overfull \hbox (46.04485pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 "707A","709A","718B","794A","817A","916C","944 E","997B","997C","1001C",[] [] Overfull \hbox (51.2948pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 "1028A","1034A","1058C","1070A","1073A","1077A ","1088J","1094A","1102A",[] [] Overfull \hbox (25.04503pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 require n ge 1 and n le #curves : "Argument 1 must be bet ween 1 and", #curves;[] [] Overfull \hbox (145.79398pt too wide) in paragraph at lines 719--719 []\OT1/cmtt/m/n/10 intrinsic EquidisTest(curve::MonStgElt, p::RngIntElt, n::Rng IntElt, Dstart::RngIntElt, Dstop::RngIntElt)[] [] Overfull \hbox (30.29498pt too wide) in paragraph at lines 719--719 [] \OT1/cmtt/m/n/10 out := Open(Sprintf("equidis_test_%o_p%o_n%o_d%o.m", curv e, p, n, Dstart),"w");[] [] [13] [14] (height.aux) ) Here is how much of TeX's memory you used: 1535 strings out of 20898 14624 string characters out of 196686 71855 words of memory out of 350001 4481 multiletter control sequences out of 10000+15000 12946 words of font info for 50 fonts, out of 400000 for 1000 14 hyphenation exceptions out of 1000 31i,9n,24p,259b,311s stack positions out of 1500i,100n,500p,50000b,4000s Output written on height.dvi (14 pages, 29968 bytes).