Supersingular elliptic curves and twisting endomorphisms

Sarah Arpin; Josep M. Miret; Jordi Pujolàs; Javier Valera

Supersingular elliptic curves and twisting endomorphisms

Number Theory 2026-06-30 v1

Authors: Sarah Arpin , Josep M. Miret , Jordi Pujolàs , Javier Valera

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.

Cite

@article{arxiv.2606.31687,
  title  = {Supersingular elliptic curves and twisting endomorphisms},
  author = {Sarah Arpin and Josep M. Miret and Jordi Pujolàs and Javier Valera},
  journal= {arXiv preprint arXiv:2606.31687},
  year   = {2026}
}

Comments

33 pages, comments welcome