Entry details for q = 55 = 3125, g = 6
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Lower bound Nmin = 3772

Submitted by Everett Howe
Date 08-13-2016
Reference Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = f1*f2, z^2 = f1*f3, where f1 = x^3 + x + 1, f2 = x^3 + r^488*x^2 + r^1816*x + r^2170, f3 = 2*x^3 + r^54*x^2 + r^1183*x + r^127, and where r^5 + 4*r + 3 = 0.
Tags Explicit curves

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Upper bound Nmax = 3792

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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