Elsevier

Journal of Algebra

Volume 320, Issue 2, 15 July 2008, Pages 853-884
Journal of Algebra

Finding rational points on elliptic curves using 6-descent and 12-descent

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Abstract

We explain how recent work on 3-descent and 4-descent for elliptic curves over Q can be combined to search for generators of the Mordell–Weil group of large height. As an application we show that every elliptic curve of prime conductor in the Stein–Watkins database has rank at least as large as predicted by the conjecture of Birch and Swinnerton-Dyer.

Keywords

Elliptic curves
Computational number theory
Invariant theory

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