Explicit isogeny descent on elliptic curves
Number Theory
2011-12-22 v2
Abstract
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.
Cite
@article{arxiv.1010.3334,
title = {Explicit isogeny descent on elliptic curves},
author = {R. L. Miller and M. Stoll},
journal= {arXiv preprint arXiv:1010.3334},
year = {2011}
}
Comments
17 pages, accepted for publication in Mathematics of Computation