The $3$-isogeny Selmer groups of the elliptic curves $y^2=x^3+n^2$

Stephanie Chan

Consider the family of elliptic curves $E_n:y^2=x^3+n^2$, where $n$ varies over positive cubefree integers. There is a rational $3$-isogeny $\varphi$ from $E_n$ to $\hat{E}_n:y^2=x^3-27n…