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Let $E$ be an elliptic curve over a number field $k$, and for an extension $K/k$ we denote by $E_K$ the base change $E \times_k K$. By fixing an embedding $k \hookrightarrow \mathbb{C}$, the etale ...

Suppose you have a relative elliptic curves $f : E\rightarrow S$ (say $S$ is connected). Then suppose you have two sections $g,g' : S\rightarrow E$, corresponding to two sections $g_*,g'_*$ to the map ...