manYPoints – Table of Curves with Many Points
Entry details for q =
5
3
= 125
, g =
3
Table
About
Recent changes
References
Username
Password
Log in
Register
Lower bound
N
min
= 192
Submitted by
C. Ritzenthaler
Date
02-05-2009
Reference
Everett W. Howe, Franck Leprévost, Bjorn Poonen
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
User comments
No comments have been made.