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

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

2007-11-23

arxiv.org/abs/0711.3774v1

Mathematics

Number Theory

33 pages

Scientific paper

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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