Entry details for q = 31 = 3, g = 4
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Lower bound Nmin = 12

Submitted by Gerrit Oomens
Date 01/01/1900
Reference J-P. Serre
Quel est le nombre maximum de points rationnels que peut avoir une courbe algébrique de genre g sur un corps fini F_q?
Résumé des Cours de 1983-1984 (=Oeuvres III, No. 132, p. 701-705).
Comments
Tags Explicit curves

User comments

An explicit defining equation     
Isabel Pirsic
06/08/2012 15:57
(y^3-y)*(x^2+1)^2-(x^3-x)

Source:
H. Niederreiter, C. P. Xing, Cyclotomic function fields, Hilbert class fields and global function fields with many rational places, Acta Arithm. 79 (1997), p. 59-76.
Upper bound Nmax = 12

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 * (x + 2) * (x + 3)^2
Tags Oesterlé bound

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