Big prime factors in orders of elliptic curves over finite fields

Abstract

Let $E$ be an elliptic curve over the finite field ${\mathbb{F}}_q$. We prove that, when $n$ is a sufficiently large positive integer, $\#E({\mathbb{F}}_{q^n})$ has a prime factor exceeding $n\exp (c\log n/\log \log n)$.

14 pages. arXiv admin note: text overlap with arXiv:2108.09857