Entry details for q = 134 = 28561, g = 3
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Lower bound Nmin = 29576

Submitted by Everett Howe
Date 05/20/2010
Reference Not available
Comments
If n is a nonsquare in F_{13^4}, then the hyperelliptic curve n*y^2 = (x + 1)*(x^2 + 5)*(x^2 + 6)*(x^2 + 7) has 29576 points.
Tags Explicit curves

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Simpler model     
Everett Howe
06/17/2010 16:58
The curve given above is isomorphic to n*y^2 = x^7 + 1.
Upper bound Nmax = 29576

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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