manYPoints – Table of Curves with Many Points
Entry details for q = 75 = 16807, g = 1
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Lower bound Nmin = 17066

Submitted by M. Afzal Soomro
Date 03-11-2010
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^3+x+a^601, where a satisfies Minimal polynomial x^5+X+4 in F_7[X].
Tags Formulas for N_q(1) and N_q(2)

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Upper bound Nmax = 17066

Submitted by Everett Howe
Date 04-27-2010
Reference Max Deuring
Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
Abh. Math. Sem. Hansischen Univ. 14 (1941) 197–272.
Comments
Tags Formulas for N_q(1) and N_q(2)

User comments

Deuring's work     
Everett Howe
04-27-2010 22:27
Waterhouse's thesis contains a nice recap of Deuring's results.
( William C. Waterhouse: Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. (4) 2 (1969) 521–560. http://www.numdam.org/item?id=ASENS_1969_4_2_4_521_0 )