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An isomorphism between two elliptic curves EE, EE' defined over a field KK is an isogeny f:EEf:E\to E' such that there exist an isogeny g:EEg:E'\to E with the compositions gfg\circ f and fgf\circ g being the identity maps. Equivalently, an isomorphism EEE\to E' is an isogeny of degree 11.

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

When EE and EE' 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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