On the algebraic and analytic ranks of the twin-prime elliptic curve $y^2=x(x-2)(x-p)$

Ruihan Chen

Let $p\ge 7$ and suppose that $p$ and $p-2$ are prime. We study $E_p:y^2=x(x-2)(x-p)$ using the classical $2$-Selmer calculation of Qiu-Zhang and the Cassels-Tate pairing. These gi…