Entry details for q = 115 = 161051, g = 3
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Lower bound Nmin = 163458

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

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

s1:=X+Y=Z;s2:=X^2+Y^2+Z^2;s4:=X^4+Y^4+Z^4;
a0:=a^154149;a1:=a^80748;a2:=a^135587;

where a is a root of u^5+10*u^2+9=0 in F_{11^5}.

This curve has been found thanks to Mestre's preprint

"courbes de genre 3 avec S_3 comme groupe d'automorphismes".
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Upper bound Nmax = 163458

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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