Entry details for q = 195 = 2476099, g = 3
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Lower bound Nmin = 2485541

Submitted by C. Ritzenthaler
Date 11/15/2009
Reference Not available
This number of point is reached by the curve

a0*s1^4+a1*s1^2*s2+a2*s4=0 where

a0:= 16*a^4 + 5*a^3 + 9*a^2 + 13*a + 17;
a1:=15*a^4 + 4*a^3 + 5*a + 9;
a2:=3*a^4 + 4*a^2 + 3*a + 15;

where a is a root of u^5+5*u+17=0 in F_{19^5}.

This curve has been found thanks to Mestre's preprint

"courbes de genre 3 avec S_3 comme groupe d'automorphismes".

Tags Explicit curves

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Upper bound Nmax = 2485541

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).
The Hasse-Weil-Serre bound
Tags Hasse-Weil-Serre bound

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