An **isomorphism** between two elliptic curves $E$, $E'$ defined over a field $K$ is an isogeny $f:E\to E'$ such that there exist an isogeny $g:E'\to E$ with the compositions $g\circ f$ and $f\circ g$ being the identity maps. Equivalently, an isomorphism $E\to E'$ is an isogeny of degree $1$.

Isomorphism is an equivalence relation, the equivalnce classes being called **isomorphism classes**.

When $E$ and $E'$ are defined by Weierstrass models, such an isomorphism is uniquely represented as a Weierstrass isomorphism between these models.

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- Last edited by John Jones on 2018-06-19 22:24:01

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- 2018-06-19 22:24:01 by John Jones (Reviewed)