manYPoints – Table of Curves with Many Points
Entry details for q = 53 = 125, g = 3
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Lower bound Nmin = 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 Nmax = 192

Submitted by C. Ritzenthaler
Date 02-05-2009
Reference Not available
Comments
Tags None

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