manYPoints – Table of Curves with Many Points
Entry details for q =
79
1
= 79
, g =
3
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Lower bound
N
min
= 131
Submitted by
C. Ritzenthaler
Date
06/01/2009
Reference
Jaap Top
Curves of genus 3 over small finite fields
Indag. Math. (N.S.) 14 (2003), no. 2, 275–283
Comments
This number of point is reached by the curve C: x^3*z+y^3*z+x^2*y^2+a*x*y*z^2+b*z^4=0 with a=11 and b=8.
The Jacobian of C is isogenous to E^3 with trace(E)=-17 and its automorphism group is S_3 (over F_q and geometric).
Tags
Explicit curves
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Upper bound
N
max
= 131
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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