manYPoints – Table of Curves with Many Points
Entry details for q =
17
3
= 4913
, g =
3
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Lower bound
N
min
= 5334
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:=2;a2:=0;
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
N
max
= 5334
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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