manYPoints – Table of Curves with Many Points
Entry details for q = 55 = 3125, g = 4
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Lower bound Nmin = 3566

Submitted by Everett Howe
Date 02-16-2014
Reference Everett W. Howe
Quickly constructing curves of genus 4 with many points
Frobenius Distributions: Sato–Tate and Lang–Trotter conjectures (D. Kohel and I. Shparlinski, eds.), Contemporary Mathematics 663, American Mathematical Society, Providence, RI, 2016, pp. 149–173
Comments
Explicit curve: y^2 = x^3 + a^1013*x + a^514, z^2 = x^3 + x^2 + a^1419*x + a^2772, where a^5 + 4*a + 3 = 0.
Tags Explicit curves

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Upper bound Nmax = 3570

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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