Gonality of the modular curve X₀(N)

2022/07/24 by Filip Najman, Petar Orlić, Najman, Filip +1 · 3 citations
Arts and Humanities · Mathematics · Social Sciences · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #North African History and Literature #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2207.11650

openalex publication_date 2022/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we determine the \mathbb Q-gonalities of the modular curves X₀(N) for all N<145. We determine the \mathbb C-gonality of many of these curves and the \mathbb Q-gonalities and \mathbb C-gonalities for many larger values of N. Using these results and some further work, we determine all the modular curves X₀(N) of gonality 4, 5 and 6 over \mathbb Q. We also find the first known instances of pentagonal curves X₀(N) over \mathbb C.

Cited by

• Tetragonal modular quotients of X₀(N)
• Tetragonal modular quotients X₀^*(N)
• Point counts, automorphisms, and gonalities of Shimura curves

Related

• Tetragonal modular quotients X₀⁺(N)
• A Divisor Formula and a Bound on the ℚ-gonality of the Modular Curve X₁(N)
• Tetragonal intermediate modular curves
• d-gonality of modular curves and bounding torsions
• Modular curves X₀(N) of density degree 5