Tetragonal modular quotients $X_0^{+d}(N)$

Petar Orlić

Tetragonal modular quotients $X_0^{+d}(N)$

Number Theory 2025-01-29 v2

Authors: Petar Orlić

Abstract

Let $N$ be a positive integer. For every $d | N$ such that $(d, N/d) = 1$ there exists an Atkin-Lehner involution $w_d$ of the modular curve $X_0(N)$ . In this paper we determine all quotient curves $X_0(N)/w_d$ whose $\mathbb{Q}$ -gonality is equal to $4$ and all quotient curves $X_0(N)/w_d$ whose $\mathbb{C}$ -gonality is equal to $4$ .

Keywords

algebraic curves

Cite

@article{arxiv.2404.08014,
  title  = {Tetragonal modular quotients $X_0^{+d}(N)$},
  author = {Petar Orlić},
  journal= {arXiv preprint arXiv:2404.08014},
  year   = {2025}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2311.09955

Related papers

View all related →