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arXiv · 2011.08471

On Isomorphic K-rational Groups of Isogenous Elliptic Curves over Finite Fields

Liljana Babinkostova·Andrew Gao·Ben Kuehnert·Geneva Schlafly·Zecheng Yi
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Abstract

We show that two ordinary isogenous elliptic curves have isomorphic groups of rational points if they have the same $j$-invariant and we extend this result to certain isogenous supersingular elliptic curves, namely those with equal $j$-invariant of either 0 or 1728. Using a result by Heuberger and Mazzoli we establish a general case of this relationship within isogenous elliptic curves not necessarily having equal $j$-invariant.

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Liljana Babinkostova, Andrew Gao, Ben Kuehnert, Geneva Schlafly, Zecheng Yi. 2020-11-17. On Isomorphic K-rational Groups of Isogenous Elliptic Curves over Finite Fields. https://arxiv.org/abs/2011.08471

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