Entry details for q = 71 = 7, g = 3
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Lower bound Nmin = 20

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).
This number of points is reached by the cubic cover t^3=y-x^2+x*y 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+2*X+7)*(X^2+5*X+7)^2.
Tags Explicit curves

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Explicit Curve     
10/06/2016 11:48
The number of points is reached by the curve
x^4+ y^4 +4 + x^2*y^2 + 2*y^2 + 2*x^2 = 0.
Upper bound Nmax = 20

Submitted by Everett Howe
Date 06/11/2010
Reference Karl-Otto Stöhr and José Felipe Voloch
Weierstrass points and curves over finite fields
Proc. London Math. Soc. (3) Vol. 52, No. 1 (1986) 1–19
This upper bound follows from Prop. 3.1 and Cor. 1.8 of the cited reference.
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