LMS Journal of Computation and Mathematics

Research Article

Computing the Rank of Elliptic Curves over Number Fields

Denis Simona1

a1 Université de Caen – France, Campus II – Boulevard Maréchal Juin, BP 5186, 14032 Caen cedex, France, Denis.Simon@math.unicaen.fr

Abstract

This paper describes an algorithm of 2-descent for computing the rank of an elliptic curve without 2-torsion, defined over a general number field. This allows one, in practice, to deal with fields of degree from 1 to 5.

(Received March 29 2000)

(Revised February 27 2002)

(Accepted April 17 2002)