Big prime factors in orders of elliptic curves over finite fields

Yuri Bilu                <meta name=

2023/102/3-4 (12) — DOI: 10.5486/PMD.2023.9460 — pp. 459-474

Big prime factors in orders of elliptic curves over finite fields

Authors: Yuri Bilu, Haojie Hong and Florian Luca

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 $n\exp(c\log n/\log\log n)$.

Keywords: prime factors, linear recurrent sequences

Mathematics Subject Classification: 11B37, 11G20