manYPoints – Table of Curves with Many Points
Entry details for q = 23 = 8, g = 3
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Lower bound Nmin = 24

Submitted by Gerrit Oomens
Date 01-01-1900
Reference Jean-Pierre Serre
Nombre de points des courbes algébriques sur F_q
Sém. de Théorie des Nombres de Bordeaux, 1982/83, exp. no. 22. (= Oeuvres III, No. 129, p. 664-668).
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Tags Explicit curves

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Explicit example     
Everett Howe
05-20-2010 21:54
In his Harvard notes, Serre notes that a model of the Klein curve gives an example of a genus-3 curve with 24 points over F_8:
(x + y + z)^4 + (x*y + x*z + y*z)^2 + x*y*z*(x + y + z)
Upper bound Nmax = 24

Submitted by Everett Howe
Date 06-10-2010
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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