cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A267195 The j-invariants in A032354 are perfect cubes, except for two terms that have an extra factor of 2 or 3. Ignore these two extra factors and take the cube roots.

Original entry on oeis.org

0, 12, -15, 20, -32, 30, 66, -96, -160, 255, -960, -5280, -640320
Offset: 1

Views

Author

N. J. A. Sloane, Jan 27 2016

Keywords

References

  • H. Cohn, Introduction to the Construction of Class Fields, Cambridge; p. 183.

Crossrefs

Cf. A032354, A133675.

A305474 Coefficients of Hilbert class polynomial H_D(x) as D runs through the numbers -3, -4, -7, -8, -11, -12, ... .

Original entry on oeis.org

0, 1, -1728, 1, 3375, 1, -8000, 1, 32768, 1, -54000, 1, -121287375, 191025, 1, -287496, 1, 884736, 1, -681472000, -1264000, 1, 12771880859375, -5151296875, 3491750, 1, 14670139392, -4834944, 1, 12288000, 1, -16581375, 1, 1566028350940383, -58682638134
Offset: 1

Views

Author

Seiichi Manyama, Jun 02 2018

Keywords

Examples

			D   |                0             1         2  3
----+---------------------------------------------
-3  |                0,            1;
-4  |            -1728,            1;
-7  |             3375,            1;
-8  |            -8000,            1;
-11 |            32768,            1;
-12 |           -54000,            1;
-15 |       -121287375,       191025,        1;
-16 |          -287496,            1;
-19 |           884736,            1;
-20 |       -681472000,     -1264000,        1;
-23 |   12771880859375,  -5151296875,  3491750, 1;
-24 |      14670139392,     -4834944,        1;
-27 |         12288000,            1;
-28 |        -16581375,            1;
-31 | 1566028350940383, -58682638134, 39491307, 1;
-32 |      12167000000,    -52250000,        1;
-35 |    -134217728000,    117964800,        1;
-36 |   -1790957481984,   -153542016,        1;

Links

Crossrefs

Cf. A014600, A014601, A032354, A305475 (constant).

Programs

  • PARI
    d(n) = 2*n+n%2;
T(n, k) = polcoef(polclass(-d(n)), k);
tabf(nn) = for(n=1, nn, for(k=0, poldegree(polclass(-d(n))), print1(T(n, k), ", ")); print)

A305475 Constant of Hilbert class polynomial H_D(x) as D runs through the numbers -3, -4, -7, -8, -11, -12, ... .

Original entry on oeis.org

0, -1728, 3375, -8000, 32768, -54000, -121287375, -287496, 884736, -681472000, 12771880859375, 14670139392, 12288000, -16581375, 1566028350940383, 12167000000, -134217728000, -1790957481984, 20919104368024767633, 9103145472000, 884736000
Offset: 1

Views

Author

Seiichi Manyama, Jun 02 2018

Keywords

Links

Crossrefs

Cf. A014601, A032354, A305474.

Programs

  • PARI
    {a(n) = polcoeff(polclass(-2*n-n%2), 0)}

A305500 a(n) = (-1) * j((1 + sqrt(-A003173(n+2)))/2).

Original entry on oeis.org

0, 3375, 32768, 884736, 884736000, 147197952000, 262537412640768000
Offset: 1

Views

Author

Seiichi Manyama, Jun 03 2018

Keywords

Examples

			j((1+sqrt(  -3))/2) =                   0.
j((1+sqrt(  -7))/2) =               -3375 = (-1) *     15^3.
j((1+sqrt( -11))/2) =              -32768 = (-1) *     32^3.
j((1+sqrt( -19))/2) =             -884736 = (-1) *     96^3.
j((1+sqrt( -43))/2) =          -884736000 = (-1) *    960^3.
j((1+sqrt( -67))/2) =       -147197952000 = (-1) *   5280^3.
j((1+sqrt(-163))/2) = -262537412640768000 = (-1) * 640320^3.

Links

Crossrefs

Cf. A003173, A032354, A199743, A305475.

Formula

a(n) = A199743(n-1)^3 for n > 1.

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, ... .

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Jun 02 2018

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

Crossrefs

Cf. A014601, A032354, A305474.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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