manYPoints – Table of Curves with Many Points
Entry details for q =
89
1
= 89
, g =
3
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Lower bound
N
min
= 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
N
max
= 144
Earlier entry
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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