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arXiv · 2003.01253

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
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Abstract

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 ring of the reduction of $E$ modulo $p$ is close to maximal.

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Alina Carmen Cojocaru, Matthew Fitzpatrick. 2020-03-02. The absolute discriminant of the endomorphism ring of most reductions of a non-CM elliptic curve is close to maximal. https://arxiv.org/abs/2003.01253

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