Entry details for q = 891 = 89, g = 3
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Lower bound Nmin = 144

Submitted by C. Ritzenthaler
Date 06/01/2009
Reference Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Comments
This number of points is reached by the curve C: x^4+y^4+z^4+2*a*(x^2*y^2+y^2*z^2+z^2*x^2)=0 with a=20. This curve was found by M. Nitzberg (see loc. cit. p.72). See also Top : Curves of genus 3 over small finite fields.

Its Jacobian is isogenous to E^3 with trace(E)=-18 and the automorphism group of C is S_4.
Tags Explicit curves

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Upper bound Nmax = 144

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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