manYPoints – Table of Curves with Many Points
Entry details for q = 174 = 83521, g = 3
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Lower bound Nmin = 85256

Submitted by Everett Howe
Date 05-21-2010
Reference Not available
Comments
If n is a nonsquare in F_{17^4}, then the hyperelliptic curve n*y^2 = (x + 2)*(x + 10)*(x^2 + 6)*(x^2 + 10)*(x^2 + 6*x + 3) has 85256 points.
Tags Explicit curves

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Upper bound Nmax = 85256

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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