manYPoints – Table of Curves with Many Points
Entry details for q = 31 = 3, g = 12
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Lower bound Nmin = 22

Submitted by Gerrit Oomens
Date 01-01-1900
Reference 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.
Comments
Tags Methods from general class field theory

User comments

Defining equation     
Isabel Pirsic
06-08-2012 17:10
y^22 + x^2*y^19 + (2*x^4 + 2*x)*y^17 + (x^6 + 2*x + 1)*y^16 + (2*x^5 + 2*x^2 + x)*y^15 + (x^5 + 2*x^3 +
x)*y^14 + (2*x^8 + 2*x^7 + x^6 + 2*x^5 + x^4 + x^3)*y^13 + (2*x^8 + 2*x^7 + x^5 + 2*x^4 + x^3 +
2*x^2)*y^12 + (x^10 + 2*x^9 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^3 + x)*y^11 + (x^12 + 2*x^10 + 2*x^9 + x^8 + x^7
+ 2*x^6 + x^5 + x^4 + x + 1)*y^10 + (x^10 + x^9 + 2*x^8 + x^7 + 2*x^6 + x^5 + x^4 + x^3 + x^2 + 2*x)*y^9 +
(2*x^12 + x^11 + x^10 + 2*x^9 + x^7 + x^5 + 2*x)*y^8 + (x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + x^7 + 2*x^6
+ x^5 + 2*x^2)*y^7 + (x^13 + 2*x^12 + 2*x^11 + x^10 + 2*x^8 + 2*x^5 + 2*x^3 + x^2)*y^6 + (2*x^13 + 2*x^12
+ 2*x^11 + 2*x^7 + x^4)*y^5 + (2*x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^9 + x^7 + 2*x^6 + 2*x^5 + x^4)*y^4
+ (x^14 + 2*x^12 + 2*x^10 + 2*x^9 + x^8 + x^7 + 2*x^6)*y^3 + (2*x^15 + 2*x^14 + x^13 + x^11 + x^10 + 2*x^9
+ x^8 + x^6)*y^2 + (x^14 + x^13 + 2*x^11 + x^10 + x^9 + x^8)*y + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^11 + x^10
+ x^9

(reference as above, calculated with Magma)
Upper bound Nmax = 23

Submitted by Everett Howe
Date 04-14-2010
Reference Angelika Köhnlein
Obere Schranken für die Punktenzahl von Kurven über endlichen Körpern
Diplomarbeit, Technische Universität Darmstadt, 4 December 2003.
Comments
A real Weil polynomial we don't know how to eliminate: (x + 2) * (x^2 + 3*x + 1) * (x^2 + 4*x + 2)^3 * (x^3 + 2*x^2 - 4*x - 4)
Tags None

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