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 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
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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