manYPoints – Table of Curves with Many Points
Entry details for q =
11
5
= 161051
, g =
3
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Lower bound
N
min
= 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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None
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Upper bound
N
max
= 163458
Earlier entry
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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