Experiments on $3$-isogeny Selmer groups of elliptic curves with a $3$-torsion point

Ariel Weiss, Dongchen Zou

Let $E_{A,B}:y^2+Axy+By=x^3$ be an elliptic curve over $\mathbb{Q}$. The $3$-torsion point $(0,0)$ induces a $3$-isogeny $\varphi :E_{A,B}\to E_{A,B}^{\prime }$. Assuming $E_{A,B}…