Unlikely intersections in products of families of elliptic curves and the multiplicative group

Fabrizio Barroero, Laura Capuano

Let $E_{\lambda }$ be the Legendre elliptic curve of equation $Y^2=X(X-1)(X-\lambda )$. We recently proved that, given $n$ linearly independent points $P_1(\lambda ),\dots ,P_n(\lambda )$ on $E_{\lambda }$ with coordina…