Definition: A surface is called $S$ bielliptic if $S \cong (E \times F) /G$, where $E,F$ are elliptic curves and $G$ is a finite group of translations of $E$ acting on $F$ such that $F /G \cong \mathbb{P}^1$.

How can $F /G \cong \mathbb{P}^1$? Can you give an example with an geometric intuition?

Thanks

Peter