Modular curves 𝑋₀(𝑁) of density degree 5

2026/07/27 by Maarten Derickx, Wontae Hwang, Daeyeol Jeon +1

paper · doi:10.1090/mcom/4221

Abstract

We determine all modular curves X 0 ( N ) X₀(N) with minimum density degree 5 5 , i.e. all curves X 0 ( N ) X₀(N) with infinitely many points of degree 5 5 and only finitely many points of degree d ≤ 4 d≤ 4 . As a consequence, the problem of determining all curves X 0 ( N ) X₀(N) with infinitely many points of degree 5 5 remains open for only 30 30 levels N N .

Related

• Modular curves X₀(N) of density degree 5
• Modular curves with infinitely many cubic points
• Intermediate modular curves with infinitely many quartic points
• Low Degree Places on the Modular Curve X1(N)
• Intermediate modular curves with infinitely many cubic points over ℚ