manYPoints – Table of Curves with Many Points
Entry details for q =
5
3
= 125
, g =
3
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Lower bound
N
min
= 192
Submitted by
C. Ritzenthaler
Date
02/05/2009
Reference
Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn
Large torsion subgroups of split Jacobians of curves of genus two or three
Forum Math. 12 (2000), no. 3, 315–364
Comments
It is the curve X^4+Y^4+Z^4=0
It was obtained as a quotient of E^3 with E: y^2=x^3+x by a (2-2-2) torsion subgroup using the explicit computation of the loc. cit. article.
Tags
Explicit curves
User comments
Automorphism group
C. Ritzenthaler
02/20/2009 14:51
This curve is the Fermat curve. It has G=(Z/4Z*Z/4Z) \rtimes S_3 as automorphism group. In particular #G=96.
Upper bound
N
max
= 192
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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