# Algorithms for Modular Elliptic Curves

## Second Edition

**Now available online**

## J. E. Cremona

**Publisher**: Cambridge University Press (UK, USA)

**Publication date** for Second Edition: 15 May 1997 in the
UK.

**Price** of Second Edition: £45 or $69.95.
*For a description of what is new in the Second Edition, see
the Introduction to the Second
Edition.*

*Summary of contents:*

- Detailed description of the computation of the modular elliptic
curves of conductor N using modular symbols, as implemented by the
author;
- 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;
- 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:

**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.

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