Tetragonal modular quotients X₀^*(N)

2025/10/25 by Orlić, Petar
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.22291

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 X₀(N). The curve X₀^*(N) is a quotient curve of X₀(N) by B(N), the group of all involutions w_d. In this paper we determine all quotient curves X₀^*(N) whose \mathbb C-gonality is equal to 4. We also determine all curves X₀^*(N) whose \mathbb Q-gonality is equal to 4 with the exception of level N=378.

Citations

• Tetragonal modular quotients X₀⁺(N)
• Gonality of the modular curve X₀(N)
• Quadratic points on modular curves with infinite Mordell--Weil group
• Galois descent for the gonality of curves
• Explicit Solution By Radicals, Gonal Maps and Plane Models of Algebraic\n Curves of Genus 5 or 6
• A linear lower bound on the gonality of modular curves

Related

• Tetragonal modular quotients X₀^+d(N)
• Tetragonal modular quotients of X₀(N)
• Tetragonal modular quotients X₀⁺(N)
• Tetragonal intermediate modular curves
• The modular automorphisms of quotient modular curves