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 -isogeny, for . For some , 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.
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}
}