Tetragonal intermediate modular curves

2024/06/26 by Orlić, Petar
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2407.14512

Abstract

For every group \±1\⊆ Δ⊆ (ℤ/Nℤ)^×, there exists an intermediate modular curve X_Δ(N). In this paper we determine all curves X_Δ(N) whose ℚ-gonality is equal to 4, all curves X_Δ(N) whose ℂ-gonality is equal to 4, and all curves X_Δ(N) whose ℚ-gonality is equal to 5. We also determine the ℚ-gonality of all curves X_Δ(N) for N≤ 40 and \±1\\subsetneq Δ\subsetneq (ℤ/Nℤ)^×.

Related

• Tetragonal modular quotients X₀⁺(N)
• Intermediate modular curves with infinitely many quartic points
• Tetragonal modular quotients X₀^*(N)
• Gonality of the modular curve X₀(N)
• Tetragonal modular quotients X₀^+d(N)