manYPoints – Table of Curves with Many Points
Entry details for q =
47
1
= 47
, g =
3
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Lower bound
N
min
= 87
Submitted by
C. Ritzenthaler
Date
06/25/2009
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 points is reached by the curve C : x^4+(1/9)* y^4+(2/3)*x^2*y^2-190*y^2*z^2-570*x^2*z^2+(152/9)*y^3*z-152* x^2*y*z-1083*z^4=0.
Its Jacobian is isomorphic to E^3 with trace(E)=-13. The automorphism group of C contains S_3.
This curve is actually missing in loc. cit. but can be found at http://arxiv.org/abs/0901.2920.
Tags
Explicit curves
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Upper bound
N
max
= 87
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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