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arXiv · 2401.06815

Counting elliptic curves with a cyclic $m$-isogeny over $\mathbb{Q}$

Grant Molnar
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Abstract

Using methods from analytic number theory, for $m > 5$ and for $m = 4$, we obtain asymptotics with power-saving error terms for counts of elliptic curves with a cyclic $m$-isogeny up to quadratic twist over the rational numbers. For $m > 5$, we then apply a Tauberian theorem to achieve asymptotics with power saving error for counts of elliptic curves with a cyclic $m$-isogeny up to isomorphism over the rational numbers.

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Grant Molnar. 2024-01-11. Counting elliptic curves with a cyclic $m$-isogeny over $\mathbb{Q}$. https://arxiv.org/abs/2401.06815

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