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arXiv · 2112.07046

Big prime factors in orders of elliptic curves over finite fields

Yuri Bilu·Haojie Hong·Florian Luca
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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 $n\exp(c\log n/\log\log n)$.

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Yuri Bilu, Haojie Hong, Florian Luca. 2021-12-13. Big prime factors in orders of elliptic curves over finite fields. https://arxiv.org/abs/2112.07046

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