Entry details for q = 54 = 625, g = 19
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Lower bound Nmin = 1308

Submitted by Everett Howe
Date 10/24/2021
Reference Rohit Gupta, Erik A. R. Mendoza, and Luciane Quoos
Reciprocal polynomials and curves with many points over a finite field
Comments
Explicit curve: y^6 = x^4 * (x^4 + x^2 + u^7) / (u^7*x^4 + x^2 + 1), where u satisfies u^2 + 4*u + 2 = 0.
Tags Explicit curves

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Upper bound Nmax = 1576

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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