Non-trivial Shafarevich-Tate Groups of Elliptic Curves

Zhangjie Wang

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arXiv · 1703.05909

Non-trivial Shafarevich-Tate Groups of Elliptic Curves

Zhangjie Wang

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Abstract

We characterize quadratic twists of $y^2=x(x-a^2)(x+b^2)$ with Mordell-Weil groups and $2$-primary part of Shafarevich-Tate groups being isomorphic to $(\mathb Z/2\mathbb Z)^2$ under certain conditions. We also obtain the distribution result of these elliptic curves.

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Zhangjie Wang. 2017-03-17. Non-trivial Shafarevich-Tate Groups of Elliptic Curves. https://arxiv.org/abs/1703.05909

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