manYPoints – Table of Curves with Many Points
Entry details for q = 31 = 3, g = 8
Table About Recent changes References
Username
Password
Log in Register

Lower bound Nmin = 17

Submitted by Gerrit Oomens
Date 01-01-1900
Reference Ignacio Luengo, Bartolomé López
Algebraic curves over F_3 with many rational points
pp. 619–626 in: Algebra, arithmetic and geometry with applications (West Lafayette, IN, 2000), C. Christensen, G. Sundaram, A. Sathaye, C. Bajaj (eds.)., Springer-Verlag, Berlin 2004
Comments
Tags Explicit curves

User comments

Defining equation     
Isabel Pirsic
06-08-2012 16:15
(2*x^2 + 2*x)*y^5 + (x^3 + 2*x^2 + x + 2)*y^4 + (2*x^2 + 2*x)*y^3 + (x^4 + x^2 + 1)*y^2 + (2*x^5 + 2*x^4 +
2*x^3 + 2*x^2 + 2*x)*y + 2*x^5 + x^3

(Ref. as above)
Upper bound Nmax = 18

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)^2 * (x^2 + 2*x - 2) * (x^2 + 4*x + 2)^2
Tags Oesterlé bound

User comments

No comments have been made.