Suppose $C$ is a curve with genus one. What can be said about its automorphism group in relation with its Jacobian $E$? As it is a torsor over its Jacobian, we have an injective morphism from the automorphism group of $E$ to that of $C$. When is this an isomorphism? Does the image of Aut$(E)$ have finite index in general? (Here I consider translations on $E$ as automorphisms.)
2026-04-07 23:02:12.1775602932
Automorphisms of curves of genus one
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