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Let $C$ be a curve and $K(C)$ be it's its function field of genus 2, where $K$ = $\mathbb{C}$.

The number of essential elliptic subfields of $K(C)$ is 0 or 2 or $\infty$.

Edit: I am looking for a proof. Thanks!

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# NumberofessentialellipticElliptic subfields ofafunctionfield

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