Genus formulas for families of modular curves
Abstract
For each open subgroup H ≤ G L 2 ( Z ^ ) H\leq GL_2(\widehat {\mathbb {Z}}) , there is a modular curve X H X_H , defined as a quotient of the full modular curve X ( N ) X(N) , where N N is the level of H H . A formula for the genus of a modular curve is well known for the modular curves X 0 ( N ) X_0(N) , X 1 ( N ) X_1(N) , X ( N ) X(N) , X s p ( N ) X_{\mathrm {sp}}(N) , X s p ∗ ( N ) X_{\mathrm {sp}}^*(N) , X
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Polynomial and algebraic computation
Advanced Numerical Analysis Techniques
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 293–310
- Publication date
- 1 May 2026
- Language
- EN