Supersingular elliptic curves and twisting endomorphisms

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.

33 pages, comments welcome