Entry details for q = 21 = 2, g = 19
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Lower bound Nmin = 20

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 Methods from general class field theory

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Defining equation     
Isabel Pirsic
06/18/2012 13:08

(x^18 + x^16 + x^14 + x^8 + x^6 + x^4 + 1)*y^8 +
(x^22 + x^19 + x^17 + x^16 + x^15 + x^13 + x^8 + x^7 + x^6 +
x^5 + x^4 + x^2 + 1)*y^4 +
(x^22 + x^21 + x^19 + x^18 + x^17 + x^15 + x^14 + x^9 + x^7 + x^2)*y^2 +
(x^21 + x^13 + x^9 + x^5)*y +
x^30 + x^26 + x^25 + x^18 + x^16 + x^15 + x^9 + x^8 + x^7 + x^6
Upper bound Nmax = 20

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
Tags Oesterlé bound

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