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

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 Author Li, Fei ♦ Qiu, Derong Source arXiv.org Content type Text File Format PDF Date of Submission 2009-11-02 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Algebraic Geometry ♦ Mathematics - Number Theory ♦ 14H52 ♦ 11G05 ♦ math Abstract 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. Description Reference: Science China, Mathematics, vol. 53, 9 (2010), 2329-2340 Educational Use Research Learning Resource Type Article Page Count 22