Entry details for q = 51 = 5, g = 3
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Lower bound Nmin = 16

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
an equation of such a curve can be found explicitly in "J.P. Serre, Rational points on curves over finite fields, Lectures given at Harvard University. Notes by F. Q. Gouvea (1985)." One has C : x^4+y^4-2*z^4=0. It is a twist of the Fermat quartic x^4+y^4+z^4=0. Its Weil polynomial is
(X^2+2*X+5)*(X^2+4*X+1)^2
Tags Explicit curves

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Upper bound Nmax = 16

Submitted by Everett Howe
Date 06/10/2010
Reference Yasutaka Ihara
Some remarks on the number of rational points of algebraic curves
J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981) 721–724 (1982)
Comments
Tags Ihara bound

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