Entry details for q = 132 = 169, g = 13
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Lower bound Nmin = 456

Submitted by Everett Howe
Date 05-18-2023
Reference Valerio Dose, Guido Lido, Pietro Mercuri, and Claudio Stirpe
Modular curves with many points over finite fields
J. Algebra 635 (2023) 790–821
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Tags Elliptic modular curves

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Another construction     
Everett Howe
04-14-2026 00:30
This bound is also attained by the quotient of the Shimura curve X_0^10(99) by the group generated by the Atkin-Lehner involutions w_10 and w_22. 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 = 508

Submitted by Everett Howe
Date 04-14-2010
Reference Jean-Pierre Serre
Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini
C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397–402. (= Œuvres III, No. 128, 658–663).
Comments
The Hasse-Weil-Serre bound
Tags Hasse-Weil-Serre bound

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