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

Grant Molnar

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

Number Theory 2024-01-17 v1 Algebraic Geometry

Authors: Grant Molnar

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.

Keywords

isogeny of elliptic curves elliptic curves asymptotic analysis

Cite

@article{arxiv.2401.06815,
  title  = {Counting elliptic curves with a cyclic $m$-isogeny over $\mathbb{Q}$},
  author = {Grant Molnar},
  journal= {arXiv preprint arXiv:2401.06815},
  year   = {2024}
}

Comments

PhD thesis. The official manuscript for this thesis can be found here: https://digitalcommons.dartmouth.edu/dissertations/214/ 285 pages, 14 graphics

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

Abstract

Keywords

Cite

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