Entry details for q = 54 = 625, g = 5
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Lower bound Nmin = 868

Submitted by Everett Howe
Date 08/12/2016
Reference Everett W. Howe
Curves of medium genus with many points
arXiv:1609.01838 [math.NT]
Comments
Explicit curve: y^2 = x^6 + r^259*x^4 + r^50*x^2 + r^179, z^2 = x^6 + r^51*x^4 + r^258*x^2 + r^283, where r^4 + 4*r^2 + 4*r + 2 = 0.
Tags Explicit curves

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Upper bound Nmax = 876

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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