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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


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