manYPoints

Submitted by	C. Ritzenthaler
Date	11/15/2009
Reference	T. Ibukiyama ON RATIONAL POINTS OF CURVES OF GENUS 3 OVER FINITE FIELDS Tόhoku Math. J. 45 (1993), 311-329
Comments	This number is reached by a supersingular hyperelliptic curve of genus 3. This is proved using the class number formula of ternary quaternion Hermitian forms by Hashimoto.
Tags	None

Explicit example	Everett Howe 05/20/2010 23:47
One such hyperelliptic curve is n*y^2 = x^7 - x, where n is any element of F_{7^4} that is not a square.

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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