On several families of elliptic curves with arbitrary large Selmer groups

Details On several families of elliptic curves with arbitrary large Selmer groups On several families of elliptic curves with arbitrary large Selmer groups

2009-11-02

arxiv.org/abs/0911.0236v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

In this paper, we calculate the $ \phi (\hat{\phi})-$Selmer groups $
S^{(\phi)} (E / \Q) $ and $ S^{(\hat{\varphi})} (E^{\prime} / \Q) $ of elliptic
curves $ y^{2} = x (x + \epsilon p D) (x + \epsilon q D) $ via descent theory
(see [S, Chapter X]), in particular, we obtain that the Selmer groups of
several families of such elliptic curves can be arbitrary large.

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