manYPoints – Table of Curves with Many Points
Entry details for q =
2
1
= 2
, g =
8
Table
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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. With contributions by Everett Howe, Joseph Oesterlé and Christophe Ritzenthaler. Edited by Alp Bassa, Elisa Lorenzo García, Christophe Ritzenthaler and René Schoof
Documents Mathématiques 18, Société Mathématique de France, Paris, 2020
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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