Modular curves $X_0(N)$ with infinitely many quartic points
Number Theory
2024-10-10 v3
Abstract
We determine all modular curves with infinitely many quartic points. To do this, we define a pairing that induces a quadratic form representing all possible degrees of a rational morphism from to a positive rank elliptic curve.
Cite
@article{arxiv.2308.11694,
title = {Modular curves $X_0(N)$ with infinitely many quartic points},
author = {Maarten Derickx and Petar Orlić},
journal= {arXiv preprint arXiv:2308.11694},
year = {2024}
}