The Mordell–Weil sieve: proving non-existence of rational points on curves
Nils Bruin, Michael Stoll · LMS Journal of Computation and Mathematics · 2010
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.