Entry details for q = 73 = 343, g = 2
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Lower bound Nmin = 416

Submitted by M. Afzal Soomro
Date 04/10/2010
Reference Not available
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^(115)*x^2+a^192, where "a" satisfies Minimal polynomial X^3+6*X^2+4 in F_7[X].
Tags Formulas for N_q(1) and N_q(2)

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Explicit Curve     
03/20/2017 16:11
Another equation is given by
y^7 + x^4*y^4 + x^2*y^2 + x*y + 6*x^7 + 4 = 0.
Upper bound Nmax = 416

Submitted by Everett Howe
Date 05/03/2010
Reference Jean-Pierre Serre
Rational points on curves over finite fields
Notes by Fernando Q. Gouvêa of lectures at Harvard University, 1985.
Tags Formulas for N_q(1) and N_q(2)

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