manYPoints – Table of Curves with Many Points
Entry details for q = 22 = 4, g = 39
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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
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Tags Quotients of curves with many points

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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 Gerrit Oomens
Date 01-01-1900
Reference Gerard van der Geer, Marcel van der Vlugt
Constructing curves over finite fields with many rational points by solving linear equations
In: Applications of Curves over Finite Fields, M. Fried Ed., Contemporary Math. 245, AMS, Providence, 1999, p. 41-47.
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