English

Counting elliptic curves with a rational $N$-isogeny for small $N$

Number Theory 2020-09-14 v1 Algebraic Geometry

Abstract

We count the number of rational elliptic curves of bounded naive height that have a rational NN-isogeny, for N{2,3,4,5,6,8,9,12,16,18}N \in \{2,3,4,5,6,8,9,12,16,18\}. For some NN, this is done by generalizing a method of Harron and Snowden. For the remaining cases, we use the framework of Ellenberg, Satriano and Zureick-Brown, in which the naive height of an elliptic curve is the height of the corresponding point on a moduli stack.

Keywords

Cite

@article{arxiv.2009.05223,
  title  = {Counting elliptic curves with a rational $N$-isogeny for small $N$},
  author = {Brandon Boggess and Soumya Sankar},
  journal= {arXiv preprint arXiv:2009.05223},
  year   = {2020}
}