A305494 Let s(D) = Sum_{(a,b,c)} j((-b+sqrt(D))/(2*a)) where (a,b,c) is taken over all the primitive reduced binary quadratic forms a*x^2+b*xy+c*y^2 with b^2-4*ac = D. This sequence is s(D) as D runs through the numbers -3, -4, -7, -8, -11, -12, ... .
0, 1728, -3375, 8000, -32768, 54000, -191025, 287496, -884736, 1264000, -3491750, 4834944, -12288000, 16581375, -39491307, 52250000, -117964800, 153542016, -331531596, 425692800, -884736000, 1122662608, -2257834125, 2835810000, -5541101568, 6896880000, -13136684625
Offset: 1
Keywords
Examples
In the case D = -15,
j((1+sqrt(-15))/2) + j((1+sqrt(-15))/4) = (-191025-85995*sqrt(5))/2 + (-191025+85995*sqrt(5))/2 = -191025.
----+-------------------------------------------+---------
D | Coefficients of Hilbert class polynomial | a(n)
----+-------------------------------------------+---------
-3 | 0, 1; | 0
-4 | -1728, 1; | 1728
-7 | 3375, 1; | -3375
-8 | -8000, 1; | 8000
-11 | 32768, 1; | -32768
-12 | -54000, 1; | 54000
-15 | -121287375, 191025, 1; | -191025
-16 | -287496, 1; | 287496
-19 | 884736, 1; | -884736
-20 | -681472000, -1264000, 1; | 1264000
-23 | 12771880859375, -5151296875, 3491750, 1;| -3491750
-24 | 14670139392, -4834944, 1; | 4834944
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..1000