Entry details for q = 175 = 1419857, g = 5
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Lower bound Nmin = 1431768

Submitted by Everett Howe
Date 08-12-2016
Reference Everett W. Howe
Curves of medium genus with many points
Finite Fields Appl. 47 (2017) 145–160
Comments
Explicit curve: y^2 = x^5 + r^1125553*x^4 + r^1010313*x^3 + r^429298*x^2 + r^89566*x, z^2 = x^5 + r^585597*x^4 + r^35606*x^3 + r^142308*x^2 + r^917040*x, where r^5 + r + 14 = 0.
Tags Explicit curves

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Upper bound Nmax = 1431773

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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