Algorithms for modular elliptic curves

Includes bibliography (p. 374-376) and references.

Ch. I. Introduction
Ch. II. Modular symbol algorithms
Ch. III. Elliptic curve algorithms
Ch. IV. The tables

Elliptic curves are of central and growing importance in computational number theory, with numerous applications in such areas as cryptography, primality testing and factorisation. This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves, with remarks on computer implementation. It is in three parts. First, the author describes in detail the construction of modular elliptic curves, giving an explicit algorithm for their computation using modular symbols. Secondly, a collection of algorithms for the arithmetic of elliptic curves is presented; some of these have not appeared in book form before. They include: finding torsion and non-torsion points, computing heights, finding isogenies and periods, and computing the rank.