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
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
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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