 

John Cullinan
A remark on the group structure of 2isogenous elliptic curves in towers of finite fields
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Published: 
February 13, 2020. 
Keywords: 
elliptic curve, finite field, isogeny. 
Subject: 
11G25, 14G15. 


Abstract
Let A and B be ordinary 2isogenous 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 lisogenous curves, when l is odd. 

Acknowledgements
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
AnnandaleOnHudson, NY 12504, USA
cullinan@bard.edu

