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

Let Eλ be the Legendre elliptic curve of equation Y XX X 1 2 = ( - )( - ) l . We recently proved that, given n linearly independent points P P 1( )¼ ( ) l l , , n on Eλ with coordinates in ( ) l , there are at most finitely many complex numbers l0 such that the points P P 10 0 ( )¼ ( ) l l , , n satisfy two independent relations on El0. In this article, we continue our investigations on Unlikely Intersections in families of abelian varieties, and consider the case of a curve in a product of two non-isogenous families of elliptic curves and in a family of split semi-abelian varieties