New York Journal of Mathematics
Volume 26 (2020), 207-217


John Cullinan

A remark on the group structure of 2-isogenous elliptic curves in towers of finite fields

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Published: February 13, 2020.
Keywords: elliptic curve, finite field, isogeny.
Subject: 11G25, 14G15.

Let A and B be ordinary 2-isogenous elliptic curves defined over a finite field F of odd characteristic. Suppose the groups A(F) and B(F) are isomorphic. We determine necessary and sufficient conditions for the groups A(L) and B(L) to be isomorphic for all finite extensions L/F. This complements recent work in which we considered the similar question for l-isogenous curves, when l is odd.


We thank the anonymous referee for a careful reading of the draft and detailed comments which improved the exposition and content of the paper.

Author information

John Cullinan:
Department of Mathematics
Bard College
Annandale-On-Hudson, NY 12504, USA