Maximal curves over finite fields and a modular isogeny
Abstract
We prove the existence of curves of genus $7$ and $12$ over the field with $11^5$ elements, reaching the Hasse-Weil-Serre upper bound. These curves are quotients of modular curves and we give explicit equations. We compute the number of points of many quotient modular curves in the same family without providing equations. For various pairs (genus, finite field) we find new records for the largest known number of points. In other instances we find quotient modular curves that are maximal, matching already known results. To perform these computations, we provide a generalization of Chen's isogeny result.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Cryptography and Residue Arithmetic
Coding theory and cryptography
Publication details
- Journal / source
- Finite Fields and Their Applications
- Volume
- 113
- Pages
- 102831–102831
- Publication date
- 9 April 2026
- Language
- EN