manYPoints – Table of Curves with Many Points
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
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^(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)

User comments

Explicit Curve     
S.E.Fischer
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. With contributions by Everett Howe, Joseph Oesterlé and Christophe Ritzenthaler. Edited by Alp Bassa, Elisa Lorenzo García, Christophe Ritzenthaler and René Schoof
Documents Mathématiques 18, Société Mathématique de France, Paris, 2020
Comments
Tags Formulas for N_q(1) and N_q(2)

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