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

Fuente: arXiv
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Autore principale: Molnar, Grant
Natura: Preprint
Pubblicazione: 2024
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author Molnar, Grant
author_facet Molnar, Grant
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_06815
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Counting elliptic curves with a cyclic $m$-isogeny over $\mathbb{Q}$
Molnar, Grant
Number Theory
Algebraic Geometry
11N45, 11G05, 11Y40
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.
title Counting elliptic curves with a cyclic $m$-isogeny over $\mathbb{Q}$
topic Number Theory
Algebraic Geometry
11N45, 11G05, 11Y40
url https://arxiv.org/abs/2401.06815