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arXiv · 2111.02562

On the density of a set of primes associated to an Elliptic Curve

Nuno Arala
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Abstract

For a given elliptic curve $E$ defined over the rationals, we study the density of primes $p$ satisfying $\mathrm{gcd}(\#E(\mathbb{F}_p),p-1)=1$ and give a conjectural value for this density with strong heuristic evidence for most elliptic curves, in an appropriate sense.

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Nuno Arala. 2021-11-03. On the density of a set of primes associated to an Elliptic Curve. https://doi.org/10.1016/j.jnt.2022.06.007

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