manYPoints – Table of Curves with Many Points
Entry details for q = 21 = 2, g = 13
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Lower bound Nmin = 15

Submitted by Gerrit Oomens
Date 01/01/1900
Reference J-P. Serre
Letter to G. van der Geer
September 1, 1997.
Comments
Tags Methods from general class field theory

User comments

Explicit Curve     
S.E.Fischer
12/19/2014 23:31
We can assume such a curve C as an extension E of degree 2 of a curve F of genus 4 as follows:
F := y^4 + (x+1)*y^2 + (x^3+x)*y +x^7+x^3 ;
E/F := z^2 + z + x*y .
Defining equation     
Isabel Pirsic
06/18/2012 13:02
y^8 +
(x^3 + x^2 + 1)*y^4 +
(x^6 + x^4 + x^3 + x^2)*y^2 +
(x^6 + x^4)*y +
x^11 + x^7
Upper bound Nmax = 15

Submitted by Everett Howe
Date 04/14/2010
Reference Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Comments
The Oesterlé bound. Here is a real Weil polynomial that we don't know how to eliminate: (x + 2) * (x^2 + x - 1) * (x^3 + 4*x^2 + 3*x - 1) * (x^7 + 5*x^6 - 28*x^4 - 20*x^3 + 35*x^2 + 14*x - 13)
Tags Oesterlé bound

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