manYPoints – Table of Curves with Many Points
Entry details for q =
11
4
= 14641
, g =
2
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Lower bound
N
min
= 15126
Submitted by
M. Afzal Soomro
Date
04-09-2010
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=a*x^6+a, where "a" satisfies Minimal polynomial X^4+8*X^2+10*X+2 in F_11[X].
Tags
Formulas for N_q(1) and N_q(2)
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Upper bound
N
max
= 15126
Earlier entry
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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