Entry details for q = 52 = 25, g = 3
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Lower bound Nmin = 56

Submitted by C. Ritzenthaler
Date 06/29/2009
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
Non explicit example found as a twist of the Klein quartic. An explicit example is given by Top with C: x^4+y^4+z^4-(a+1)(x^2*y^2+x^2*z^2+y^2*z^2)=0 where a is a root of x^2+4x+1=0. For reference, see the other p^2 entries for g=3.
Tags Explicit curves

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Upper bound Nmax = 56

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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