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

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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 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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