manYPoints – Table of Curves with Many Points
Entry details for q =
2
1
= 2
, g =
8
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Lower bound
N
min
= 11
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
User comments
Defining equation
Isabel Pirsic
06/18/2012 11:27
E.g.,
y4([8,4,0],[9,6,5,1,0],[9,8,6,5,4,1],[8,7,4,3])
=
(x^8+x^4+1)*y^4+
(x^9+x^6+x^5+x+1)*y^2+
(x^9+x^8+x^6+x^5+x^4+x)*y+
(x^8+x^7+x^4+x^3)
Upper bound
N
max
= 11
Earlier entry
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)^2 * (x^2 + x - 5) * (x^2 + 3*x + 1)
Tags
Oesterlé bound
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