Dong-Chen Zou

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

Let $E_{A,B}\colon y^2 +Axy + By = x^3$ be an elliptic curve over $\mathbb{Q}$. The $3$-torsion point $(0,0)$ induces a $3$-isogeny $\phi\colon E_{A,B}\to E_{A,B}'$. Assuming $E_{A,B}$ has good reduction at $3$, we construct an explicit $(m+t)\times m$ matrix $M_{A,B}'$ over $\mathbb{F}_3$, whose kernel encodes the dua...