Entry details for q = 175 = 1419857, g = 7
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Lower bound Nmin = 1436416

Submitted by Everett Howe
Date 03/30/2017
Reference Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve:

y^2 = 3*x^3 + r^341372*x^2 + r^1082004*x
z^2 = x^3 + r^554990*x^2 + r^1056124*x + r^1195369
w^2 = x^3 + r^686356*x^2 + r^553295*x

where r^5 + r + 14 = 0.
Tags Explicit curves

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Upper bound Nmax = 1436539

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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