Elliptic curves over Hasse pairs

arXiv:2406.03399v1 Announce Type: cross
Abstract: We call a pair of distinct prime powers $(q_1,q_2) = (p_1^{a_1},p_2^{a_2})$ a Hasse pair if $|\sqrt{q_1}-\sqrt{q_2}| \leq 1$. For such pairs, we study the relation between the set $\mathcal{E}_1$ of isomorphism classes of elliptic curves defined over $\mathbb{F}_{q_1}$ with $q_2$ points, and the set $\mathcal{E}_2$ of isomorphism classes of elliptic curves over $\mathbb{F}_{q_2}$ with $q_1$ points. When both families $\mathcal{E}_i$ contain only ordinary elliptic curves, we prove that their isogeny graphs are isomorphic. When supersingular …

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