Entry details for q = 21 = 2, g = 15
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Lower bound Nmin = 17

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).
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Tags Methods from general class field theory

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Explicit Curve     
S.E.Fischer
12/20/2014 05:10
We can assume such a curve C as an extension E of degree 2 of a curve F of genus 5 as follows:
F:= y^4 + (x^2 + x + 1)*y^2 + (x^2 + x)*y + x^7 + x^3 ;
E/F := z^2*x^2 + z*(y+1) + x^3 + x^7 .
Defining equation     
Isabel Pirsic
06/18/2012 13:04
x^19*y^8 +
(x^14 + x^13)*y^7 +
(x^13 + x^8)*y^6 +
(x^14 + x^8 + x^7 + x^6)*y^5 +
(x^17 + x^16 + x^15 + x^13 + x^9 + x^8 + x^7 + x^5 + x^3 + x^2)*y^4 +
(x^6 + x^5)*y^3 +
(x^15 + x^9 + x^7 + x^5 + x + 1)*y^2 +
(x^13 + x^8 + x^7 + x^5)*y +
x^18
Upper bound Nmax = 17

Submitted by Gerrit Oomens
Date 01/01/1900
Reference Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
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