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@Original used for 2nd edition as delivered to CUP 20/11/96
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\centerline{\bf CONTENTS}
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\widestnumber\head{2.15}
\widestnumber\subhead{2.15.3}

\title\chapter{1} Introduction \page{1}\endtitle

\title\chapter{2} Modular symbol algorithms  \page{7}\endtitle

\head 2.1 Modular Symbols and Homology \page{7}\endhead
\subhead 2.1.1 The upper half-plane, the modular group and cusp forms 
\page{7}\endsubhead
\subhead 2.1.2 The duality between cusp forms and homology \page{9}\endsubhead
\subhead 2.1.3 Real structure \page{11}\endsubhead
\subhead 2.1.4 Modular symbol formalism \page{12}\endsubhead
\subhead 2.1.5 Rational structure and the Manin-Drinfeld Theorem \page{12}\endsubhead
\subhead 2.1.6 Triangulations and homology \page{13}\endsubhead
\head 2.2 M-symbols and $\Gamma_0(N)$ \page{15}\endhead
\head 2.3 Conversion between modular symbols and M-symbols\page{18}\endhead
\head 2.4 Action of Hecke and other operators\page{18}\endhead
\head 2.5 Working in $H^+(N)$\page{23}\endhead
\head 2.6 Modular forms and modular elliptic curves\page{24}\endhead
\head 2.7 Splitting off one-dimensional eigenspaces\page{25}\endhead
\head 2.8 $L(f,s)$ and the evaluation of $L(f,1)/\RP(f)$\page{29}\endhead
\head 2.9 Computing Fourier coefficients\page{31}\endhead
\head 2.10 Computing periods I\page{33}\endhead
\head 2.11 Computing periods II: Indirect method\page{37}\endhead
\head 2.12 Computing periods III: Evaluation of the sums\page{41}\endhead
\head 2.13 Computing $L^{(r)}(f,1)$ \page{42}\endhead
\head 2.14 Obtaining equations for the curves\page{45}\endhead
\head 2.15  Computing the degree of a modular parametrization\page{46}\endhead
\subhead 2.15.1 Modular Parametrizations \page{47}\endsubhead
\subhead 2.15.2 Coset representatives and Fundamental Domains \page{48}\endsubhead
\subhead 2.15.3 Implementation for  $\G0(N)$ \page{50}\endsubhead

\title Appendix to Chapter II.  Examples  \page{52}\endtitle
\subhead{} Example~1. $N=11$ \page{52}\endsubhead
\subhead{} Example~2. $N=33$ \page{57}\endsubhead
\subhead{} Example~3. $N=37$ \page{58}\endsubhead
\subhead{} Example~4. $N=49$ \page{60}\endsubhead

\title\chapter{3} Elliptic curve algorithms  \page{62}\endtitle

\head 3.1 Terminology and notation \page{62}\endhead
\head 3.2 The Kraus--Laska--Connell algorithm and Tate's algorithm \page{64}\endhead
\head 3.3 The Mordell--Weil group I: finding torsion points\page{68}\endhead
\head 3.4 Heights and the height pairing\page{71}\endhead
\head 3.5 The Mordell--Weil group II: generators \page{75}\endhead
\head 3.6 The Mordell--Weil group III: the rank\page{78}\endhead
\head 3.7 The period lattice\page{97}\endhead
\head 3.8 Finding isogenous curves\page{98}\endhead
\head 3.9 Twists and complex multiplication \page{101}\endhead

\title\chapter{4} The tables  \page{104}\endtitle
\subhead{} Table~1.  Elliptic curves \page{109}\endsubhead
\subhead{} Table~2.  Mordell--Weil generators \page{255}\endsubhead
\subhead{} Table~3.  Hecke eigenvalues \page{264}\endsubhead
\subhead{} Table~4.  Birch--Swinnerton-Dyer data \page{313}\endsubhead
\subhead{} Table~5.  Parametrization degrees \page{362}\endsubhead

\title Bibliography \page{374}\endtitle

\endtoc

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% ALGORITHMS FOR MODULAR ELLIPTIC CURVES       Last change: 19/12/91
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\topmatter

\title Contents \endtitle

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\bigskip
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\widestnumber\head{2.13}
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\title\chapter{2} Modular symbol algorithms  \page{4}\endtitle
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\head 2.1 Description of homology in terms of modular symbols\page{4}\endhead
\head 2.2 M-symbols\page{7}\endhead
\head 2.3 Conversion between modular symbols and M-symbols\page{10}\endhead
\head 2.4 Action of Hecke and other operators\page{11}\endhead
\head 2.5 Working in $H^+(N)$\page{13}\endhead
\head 2.6 Modular forms and modular elliptic curves\page{14}\endhead
\head 2.7 Splitting off one-dimensional eigenspaces\page{16}\endhead
\head 2.8 $L(f,s)$ and the evaluation of $L(f,1)/\RP(f)$\page{19}\endhead
\head 2.9 Computing Fourier coefficients\page{22}\endhead
\head 2.10 Computing periods I\page{24}\endhead
\head 2.11 Computing periods II: Indirect method\page{26}\endhead
\head 2.12 Computing periods III: Evaluation of the sums\page{29}\endhead
\head 2.13 Computing $L^{(r)}(f,1)$ \page{30}\endhead
\head 2.14 Obtaining equations for the curves\page{33}\endhead

\title Appendix to Chapter II.  Examples  \page{36}\endtitle

\title\chapter{3} Elliptic curve algorithms  \page{45}\endtitle

\head 3.1 Terminology and notation \page{45}\endhead
\head 3.2 The Kraus--Laska--Connell algorithm and Tate's algorithm \page{47}\endhead
\head 3.3 The Mordell--Weil group I: torsion\page{52}\endhead
\head 3.4 Heights and the height pairing\page{55}\endhead
\head 3.5 The Mordell--Weil group II: generators \page{58}\endhead
\head 3.6 The Mordell--Weil group III: the rank\page{62}\endhead
\head 3.7 The period lattice\page{76}\endhead
\head 3.8 Finding isogenous curves\page{77}\endhead
\head 3.9 Twists and complex multiplication \page{81}\endhead

\title\chapter{4} The tables  \page{84}\endtitle
\title Table~1.  Elliptic curve data \page{89}\endtitle
\title Table~2.  Mordell--Weil generators \page{234}\endtitle
\title Table~3.  Hecke eigenvalues \page{243}\endtitle
\title Table~4.  Birch--Swinnerton-Dyer data \page{292}\endtitle
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\title Bibliography \page{341}\endtitle
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