Entry details for q = 34 = 81, g = 7
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Lower bound Nmin = 196

Submitted by Everett Howe
Date 09/02/2016
Reference Everett W. Howe
Curves of medium genus with many points
arXiv:1609.01838 [math.NT]
Comments
Explicit curve: y^2 = x^6 + r^70*x^2 + r^50, z^2 = x^6 + r^50*x^2 + r^70, where r^4 + 2*r^3 + 2 = 0.
Tags Explicit curves

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Explicit Curve     
S.E.Fischer
03/20/2017 16:20
Another equation is given by
2*y^6 + x^5*y^5 + 2*x^4*y^4 + 2*x^3*y^3 + 2*x^2*y^2 + x*y + x^6 = 0.
Upper bound Nmax = 208

Submitted by Everett Howe
Date 04/14/2010
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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