Isogeny relations in products of families of elliptic curves
Isogeny relations in products of families of elliptic curves
Let $E_{\lambda}$ be the Legendre family of elliptic curves with equation $Y^2=X(X-1)(X-\lambda)$. Given a curve $\mathcal{C}$, satisfying a condition on the degrees of some of its coordinates and parametrizing $m$ points $P_1, \ldots, P_m \in E_{\lambda}$ and $n$ points $Q_1, \ldots, Q_n \in E_{\mu}$ and assuming that those points are …