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.
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Explicit curves
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Upper bound
N
max
= 1548
Later entry
Submitted by
C. Ritzenthaler
Date
02-20-2009
Reference
Not available
Comments
Tags
None
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