On the Selmer groups and Mordell-Weil groups of elliptic curves $ y^{2} = x (x \pm p) (x \pm q) $ over imaginary quadratic number fields of class number one

Xiumei Li

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arXiv · 1207.0287

On the Selmer groups and Mordell-Weil groups of elliptic curves $ y^{2} = x (x \pm p) (x \pm q) $ over imaginary quadratic number fields of class number one

Xiumei Li

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Abstract

Let $ p $ and $ q $ be odd prime numbers with $ q - p = 2, $ the $φ-$Selmer groups, Shafarevich-Tate groups ($ φ- $ and $ 2-$part) and their dual ones as well the Mordell-Weil groups of elliptic curves $ y^{2} = x (x \pm p) (x \pm q) $ over imaginary quadratic number fields of class number one are determined explicitly in many cases.

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Xiumei Li. 2012-07-02. On the Selmer groups and Mordell-Weil groups of elliptic curves $ y^{2} = x (x \pm p) (x \pm q) $ over imaginary quadratic number fields of class number one. https://arxiv.org/abs/1207.0287

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