Zhang-Xiong Wang

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20172026

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math.NT2023

On the quadratic twist of elliptic curves with full $2$ -torsion

Zhangjie Wang, Shenxing Zhang

Let $E : y^{2} = x (x - a^{2}) (x + b^{2})$ be an elliptic curve with full $2$ -torsion group, where $a$ and $b$ are coprime integers and $2 (a^{2} + b^{2})$ is a square. Assume that the $2$ -Selmer group…

math.NT2017

Non-trivial Shafarevich-Tate Groups of Elliptic Curves

Zhangjie Wang

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 $(\mathb Z/2\mathbb Z)^2$ und…

On the quadratic twist of elliptic curves with full 2-torsion

Non-trivial Shafarevich-Tate Groups of Elliptic Curves

On the quadratic twist of elliptic curves with full $2$ -torsion