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arXiv · 2606.31687

Supersingular elliptic curves and twisting endomorphisms

Sarah Arpin·Josep M. Miret·Jordi Pujolàs·Javier Valera
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Abstract

We generalize the notion of twisting endomorphisms, first defined by Castryck-Panny-Vercauteran, to the setting of $\mathcal{O}$-oriented supersingular elliptic curves. We give an algorithm to find supersingular elliptic curves over $\mathbb{F}_p$ with a twisting endomorphism of prime degree $\ell$, and we use it to compute a basis of their full endomorphism rings.

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Sarah Arpin, Josep M. Miret, Jordi Pujolàs, Javier Valera. 2026-06-30. Supersingular elliptic curves and twisting endomorphisms. https://arxiv.org/abs/2606.31687

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