manYPoints – Table of Curves with Many Points
Entry details for q = 22 = 4, g = 39
Table About Recent changes References
Username
Password
Log in Register

Lower bound Nmin = 68

Submitted by Everett Howe
Date 08-12-2025
Reference Valerio Dose, Guido Lido, Pietro Mercuri, and Claudio Stirpe
Maximal curves over finite fields and a modular isogeny
Finite Fields Appl. 113 (2026), article 102831
Comments
Tags Quotients of curves with many points

User comments

Another construction     
Everett Howe
04-14-2026 00:28
This bound is also attained by the quotient of the Shimura curve X_0^65(31) by the Atkin-Lehner involution w_2015. See Pietro Mercuri, Oana Padurariu, Frederick Saia, and Claudio Stirpe: "Point counts, automorphisms, and gonalities of Shimura curves," arXiv:2507.15992 [math.NT].
Upper bound Nmax = 75

Submitted by Everett Howe
Date 04-14-2010
Reference Jean-Pierre Serre
Rational points on curves over finite fields. With contributions by Everett Howe, Joseph Oesterlé and Christophe Ritzenthaler. Edited by Alp Bassa, Elisa Lorenzo García, Christophe Ritzenthaler and René Schoof
Documents Mathématiques 18, Société Mathématique de France, Paris, 2020
Comments
The Oesterlé bound
Tags Oesterlé bound

User comments

No comments have been made.