manYPoints – Table of Curves with Many Points
Entry details for q = 31 = 3, g = 8
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Lower bound Nmin = 17

Submitted by Gerrit Oomens
Date 01/01/1900
Reference B. Lopez, I. Luengo
Algebraic curves over F_3 with many rational points
In: Algebra, arithmetic and geometry with applications (West-Lafayette, IN, 2000), C. Christensen, G. Sundaram, A. Sathaye, C. Bajaj Eds., Springer Verlag, Berlin 2004, p. 619-626.
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
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)^2 * (x^2 + 2*x - 2) * (x^2 + 4*x + 2)^2
Tags Oesterlé bound

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