Entry details for q = 55 = 3125, g = 3
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Lower bound Nmin = 3459

Submitted by C. Ritzenthaler
Date 11/15/2009
Reference Not available
Comments
This number is reached bu the following curve

a1*t1^4+a2*t1^2*t2+2*t1*t3+t2^2=0;

where

t1:=X+Y+Z;t2:=X*Y+X*Z+Y*Z;t3:=X*Y*Z;
a1:=a^1827;a2:=a^2281;

where a is a root of u^5+4*u+3=0 in F_{5^5}.

This curve has been found by J.-F. Mestre using his preprint

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

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Upper bound Nmax = 3459

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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