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arXiv · 1605.03474

Elliptic Curves with Isomorphic Groups of Points over Finite Field Extensions

Clemens Heuberger·Michela Mazzoli
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Abstract

Consider a pair of ordinary elliptic curves $E$ and $E'$ defined over the same finite field $\mathbb{F}_q$. Suppose they have the same number of $\mathbb{F}_q$-rational points, i.e. $|E(\mathbb{F}_q)|=|E'(\mathbb{F}_q)|$. In this paper we characterise for which finite field extensions $\mathbb{F}_{q^k}$, $k\geq 1$ (if any) the corresponding groups of $\mathbb{F}_{q^k}$-rational points are isomorphic, i.e. $E(\mathbb{F}_{q^k}) \cong E'(\mathbb{F}_{q^k})$.

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Clemens Heuberger, Michela Mazzoli. 2016-05-11. Elliptic Curves with Isomorphic Groups of Points over Finite Field Extensions. https://doi.org/10.1016/j.jnt.2017.05.028

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