On the distribution of orders of Frobenius action on $\ell$-torsion of abelian surfaces

Nikita Kolesnikov, Semyon Novoselov

The computation of the order of Frobenius action on the $\ell$-torsion is a part of Schoof-Elkies-Atkin algorithm for point counting on an elliptic curve $E$ over a finite field $\…