LMS Journal of Computation and Mathematics

Research Article

The Mordell–Weil sieve: proving non-existence of rational points on curves

Nils Bruina1 and Michael Stolla2

a1 Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada (email: nbruin@cecm.sfu.ca)

a2 Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany (email: Michael.Stoll@uni-bayreuth.de)

Abstract

We discuss the Mordell–Weil sieve as a general technique for proving results concerning rational points on a given curve. In the special case of curves of genus 2, we describe quite explicitly how the relevant local information can be obtained if one does not want to restrict to mod p information at primes of good reduction. We describe our implementation of the Mordell–Weil sieve algorithm and discuss its efficiency.

Supplementary materials are available with this article.

(Received June 15 2009)

(Revised November 30 2009)

(Online publication August 2010)

2000 Mathematics Subject Classification

  • 11D41;
  • 11G30;
  • 11Y50 (primary);
  • 14G05;
  • 14G25;
  • 14H25;
  • 14H45;
  • 14Q05 (secondary)

Footnotes

Research by the first author was supported by NSERC.