Entry details for q = 132 = 169, g = 3
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Lower bound Nmin = 248

Submitted by C. Ritzenthaler
Date 06-29-2009
Reference Jaap Top
Maximal quartics over F_p^2
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Tags Explicit curves

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Explicit examples     
Everett Howe
06-17-2010 16:51
The cited reference gives both a hyperelliptic example, y^2 = x^7 + 1, and a plane quartic example:
x^4 + y^4 + z^4 + c*(x^2*y^2 + x^2*z^2 + y^2*z^2) = 0
where c satisfies c^2 + 8*c + 8 = 0.
Upper bound Nmax = 248

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).
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The Hasse-Weil-Serre bound
Tags Hasse-Weil-Serre bound

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