On the $v$-adic values of G-functions II

This is the second paper in a series by the author, centered on the study of values of G-functions associated to a $1$-parameter family of abelian varieties $f:\text{CX}\to S$ and a point $s_0\in S(K)$ over some number field $K$. Here we study the case where $f:\text{CX}\to S$ is a family of elliptic curves. Extending work of André and Beukers, we construct relations among the values of G-functions in this setting at points whose fibers are CM elliptic curves.