manYPoints – Table of Curves with Many Points
Entry details for q =
11
3
= 1331
, g =
3
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Lower bound
N
min
= 1548
Submitted by
C. Ritzenthaler
Date
02-20-2009
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
Explicit curve C given by
(a^2+8)*(x^4+y^4+z^4)+(2+3*a)*(x^2*y^2+x^2*z^2+y^2*z^2) where a is solution of u^3+2*u+9=0 in GF(11^3). It was found using the explicit computations of loc. cit. with the elliptic curve E : y^2+x*y=x^3+10*x+7.
Hence the Jacobian of C is a quotient of E^3 by a rational (2,2,2)-subgroup.
The geometric group of automorphism of C is S_4.
Tags
Explicit curves
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Upper bound
N
max
= 1548
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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