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arXiv · 0911.0236

On several families of elliptic curves with arbitrary large Selmer groups

Fei Li·Derong Qiu
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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.

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Fei Li, Derong Qiu. 2009-11-02. On several families of elliptic curves with arbitrary large Selmer groups. https://doi.org/10.1007/s11425-010-4035-2

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