Explicit isogeny descent on elliptic curves

Details Explicit isogeny descent on elliptic curves Explicit isogeny descent on elliptic curves

2010-10-16

arxiv.org/abs/1010.3334v2

Mathematics

Number Theory

17 pages, accepted for publication in Mathematics of Computation

Scientific paper

In this note, we consider an l-isogeny descent on a pair of elliptic curves over Q. We assume that l > 3 is a prime. The main result expresses the relevant Selmer groups as kernels of simple explicit maps between finite- dimensional F_l-vector spaces defined in terms of the splitting fields of the kernels of the two isogenies. We give examples of proving the l-part of the Birch and Swinnerton-Dyer conjectural formula for certain curves of small conductor.

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