English

Modular curves $X_0(N)$ with infinitely many quartic points

Number Theory 2024-10-10 v3

Abstract

We determine all modular curves X0(N)X_0(N) 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 X0(N)X_0(N) to a positive rank elliptic curve.

Keywords

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}
}
R2 v1 2026-06-28T12:01:51.355Z