Entry details for q = 21 = 2, g = 4
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Lower bound Nmin = 8

Submitted by Gerrit Oomens
Date 01/01/1900
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
Tags Explicit curves

User comments

Deg2 Extension     
S.E.Fischer
12/07/2014 03:29
We can assume such a curve C as an extension F/G of degree 2 of a curve G of genus 1 as follows:
G:= (x + y + x*y) * x*y + x + 1 ;
F/G := z^2 * x + z + x^2 * y^2 .

Defining equation     
Isabel Pirsic
06/18/2012 11:19
E.g.,

y4([0],[1,0],[3,1],[7,3]) =

y^4 + (x+1)*y^2 + (x^3+x)*y +x^7+x^3
Upper bound Nmax = 8

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 + 1) * (x + 2) * (x^2 + 2*x - 2)
Tags Oesterlé bound

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