Entry details for q = 55 = 3125, g = 2
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Lower bound Nmin = 3348

Submitted by M. Afzal Soomro
Date 04/10/2010
Reference Not available
Comments
Deuring, Max
Die Typen der Multiplikatorenringe elliptischer Funktionenkörper.
Abh. Math. Sem. Hansischen Univ. 14, (1941). 197--272.

This number of point is reached by the curve

y^2=x^6+x^4+a^(361)*x^2+a^1292, where "a" satisfies Minimal polynomial X^5+4*X+3 in F_5[X].
Tags Formulas for N_q(1) and N_q(2)

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Upper bound Nmax = 3348

Submitted by Everett Howe
Date 05/03/2010
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).
Comments
The Hasse-Weil-Serre bound
Tags Hasse-Weil-Serre bound, Formulas for N_q(1) and N_q(2)

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