manYPoints – Table of Curves with Many Points
Entry details for q = 231 = 23, g = 4
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Lower bound Nmin = 57

Submitted by Everett Howe
Date 08-30-2011
Reference Everett W. Howe
New bounds on the maximum number of points on genus-4 curves over small finite fields
Arithmetic, Geometry, Cryptography and Coding Theory (Y. Aubry, C. Ritzenthaler, and A. Zykin, eds.), Contemporary Mathematics 574, American Mathematical Society, Providence, RI, 2012, pp. 69–86
Comments
Here is a genus-4 curve with 57 points: y^2 = x^3 - 6*x^2 - 3*x - 7, z^2 = x*y + 2*x^3 - 11*x^2 + 7*x + 1
Tags Explicit curves

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Upper bound Nmax = 60

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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