Entry details for q = 52 = 25, g = 4
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Lower bound Nmin = 66

Submitted by Carmen Rovi
Date 06/03/2010
Reference Carmen Rovi
Algebraic Curves over Finite Fields
Explicit curve: y^5 + y = x^3

Found by implementing the method given by Arnaldo Garcia in his paper "Curves over Finite Fields Attaining the Hasse-Weil Upper Bound" Progress in Mathematical Physics, Birkhäuser Verlag, Basel, v. 202, p. 199-205, 2001
Tags Explicit curves, Hasse-Weil-Serre bound

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Explicit Curve     
02/24/2017 20:55
Another equation is given by
2*x^3*y^3 + x^2*y^2 + x*y + x^6 = 0.
Upper bound Nmax = 66

Submitted by Everett Howe
Date 04/14/2010
Reference Jean-Pierre Serre
Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini
C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397–402. (= Œuvres III, No. 128, 658–663).
The Hasse-Weil-Serre bound
Tags Hasse-Weil-Serre bound

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