Entry details for q = 54 = 625, g = 3
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Lower bound Nmin = 776

Submitted by Everett Howe
Date 05/20/2010
Reference Not available
Comments
If r is an element of F_{5^4} with r^4 - r^2 - r + 2 = 0, then the hyperelliptic curve
y^2 = r*x^8 + r^464*x^6 + r^298*x^2 + r^449
has 776 points.
Tags Explicit curves

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Upper bound Nmax = 776

Submitted by Everett Howe
Date 05/20/2010
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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