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

Tom Fisher

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arXiv · 0711.3774

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

Tom Fisher

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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.

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Tom Fisher. 2007-11-23. Finding rational points on elliptic curves using 6-descent and 12-descent. https://arxiv.org/abs/0711.3774

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