Algorithms for Modular Elliptic Curves

For a description of what is new in the Second Edition, see the Introduction to the Second Edition.

Summary of contents:

1. Detailed description of the computation of the modular elliptic curves of conductor N using modular symbols, as implemented by the author;
2. Description of algorithms for studying the arithmetic of elliptic curves defined over Q, including Tate's algorithm for the conductor and minimal model, determining the rank via 2-descent and the the Mordell-Weil group, the canonical height of rational points, and the computation of isogenies;
3. Tables of all modular elliptic curves of conductor less than 1000, containing coefficients, L-series, generators, the quantities appearing in the Birch Swinnerton-Dyer formula for the order of the Tate-Shafarevitch group, and the degree of the modular parametrization.

The First Edition was published by CUP in 1992.

Errata to the first edition
The final text errata list for the first edition is available as a dvi file or as TeX source. Also available are a summary of the omissions in the tables, and a supplement to the tables containing the missing data, either as a plain text file or as a dvi file.

The Second Edition corrects numerous typographical errors, and has substantial revisions of some sections, as well as a new section and table on the degree of modular parametrizations. It was published in May 1997. The following parts of the Second Edition may be viewed:

• Contents page
• Chapter One
  • Introduction to the First Edition
  • Introduction to the Second Edition
  • web and ftp sites
  (with apologies for not being able to display the mathematics properly in HTML).

Errata to the second edition
The errata list for the second edition is available as a dvi file or as a postscript file or as a pdf file. Please send further corrections to me by email.