manYPoints

Submitted by	C. Ritzenthaler
Date	04-07-2009
Reference	Jean-Pierre Serre Résumé des cours de 1983-1984 Annuaire du College de France (1984), 79-83. Reprinted in Vol. 3 of Jean-Pierre Serre, OEvres, Collected Papers. Springer- Verlag, New York (1985).
Comments	This number of points is reached by the cubic cover t^3=y-x^2+xy of the elliptic curve y^2-y=x^3-x^2 (see J-P. Serre, Rational points on curves over finite fields, Lectures given at Harvard University, 1985. Notes by F. Q. Gouvêa, p.64-68). Its Weil polynomial is (X^2+2X+7)(X^2+5X+7)^2.
Tags	Explicit curves

Explicit Curve	S.E.Fischer 10-06-2016 11:48
The number of points is reached by the curve x^4+ y^4 +4 + x^2y^2 + 2y^2 + 2*x^2 = 0.

Submitted by	Everett Howe
Date	06-11-2010
Reference	Karl-Otto Stöhr, José Felipe Voloch Weierstrass points and curves over finite fields Proc. London Math. Soc. (3) Vol. 52, No. 1 (1986) 1–19
Comments	This upper bound follows from Prop. 3.1 and Cor. 1.8 of the cited reference.
Tags	None

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