manYPoints – Table of Curves with Many Points
Entry details for q = 191 = 19, g = 3
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Lower bound Nmin = 44

Submitted by C. Ritzenthaler
Date 04/07/2009
Reference Jean-Pierre Serre
Résumé des cours de 1983-1984
Annuaire du College de France (1984), 79-83. Reprinted in Vol. 3 of Jean-Pierre Serre, OEvres, Collected Papers. Springer- Verlag, New York (1985).
Comments
This number of points is reached by the curve x^4+y^4+z^4+6*(x^2*y^2+x^2*z^2+y^2*z^2)=0 (see J-P. Serre, Rational points on curves over finite fields, Lectures given at
Harvard University, 1985. Notes by F. Q. Gouvêa p.72 -computation of M. Nitzberg-).

Its Weil polynomial is (X^2+8*X+19)^3.

Its automorphism group (over F_19 and geometric) is S_4.
Tags Explicit curves

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Upper bound Nmax = 44

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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