I am looking for the proof of the following statement: Two elliptic curves which are birationally equivalent are isomorphic. Hopefully someone can mention to me some material to prove it. Thanks in advance!
2026-03-26 20:39:40.1774557580
Proof that "Two elliptic curves which are birationally equivalent are isomorphic".
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This is a special case of a more general statement: If $C$ and $C'$ are smooth projective curves and $f : C \to C'$ is a rational map, then $f$ is a morphism.
See here, or see Hartshorne I.6.