Bielliptic and Hyperelliptic modular curves X(N) and the group Aut(X(N))

2012/07/10 by Francesc Bars, Aristides Kontogeorgis, Bars, Francesc +3
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1207.2273

Abstract

We determine all modular curves X(N) (with N≥ 7) which are hyperelliptic or bielliptic. We make available a proof that the automorphism group of X(N) coincides with the normalizer of Γ(N) in PSL₂(ℝ).

Related

• Bielliptic modular curves X₀^*(N) with square-free levels
• Equations of Bielliptic Modular Curves
• Families of hyperelliptic curves
• Hyperelliptic parametrizations of ℚ-curves
• Quadratic points on bielliptic modular curves