The absolute discriminant of the endomorphism ring of most reductions of a non-CM elliptic curve is close to maximal

Alina Carmen Cojocaru, Matthew Fitzpatrick

Let $E/\mathbb{Q}$ be a non-CM elliptic curve. Assuming GRH, we prove that, for a set of primes $p$ of density $1$, the absolute discriminant of the ${\mathbb{F}}_p$-endomorphism rin…