Shenxing Zhang

collaborators

2 papers

math.NT2023

On a comparison of Cassels pairings of different elliptic curves

Shenxing Zhang

Let $e_{1}, e_{2}, e_{3}$ be nonzero integers satisfying $e_{1} + e_{2} + e_{3} = 0$ . Let $(a, b, c)$ be a primitive triple of odd integers satisfying $e_{1} a^{2} + e_{2} b^{2} + e_{3} c^{2} = 0$ . Denote by $E: y^2=x(x-e_1…

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…

On a comparison of Cassels pairings of different elliptic curves

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

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