| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 12.0.71229533203125.1 |
$x^{12} - 5 x^{11} + 20 x^{10} - 48 x^{9} + 100 x^{8} - 150 x^{7} + 204 x^{6} - 200 x^{5} + 180 x^{4} - 102 x^{3} + 75 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$3^{4}\cdot 5^{9}\cdot 11^{2}\cdot 61^{2}$ |
$4$ |
$14.268829269$ |
$443.8843268190916$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$10$ |
$5$ |
$448.992833342$ |
| 12.0.125594455078125.1 |
$x^{12} - 7 x^{9} + 19 x^{6} - 23 x^{3} + 11$ |
$12$ |
[0,6] |
$3^{12}\cdot 5^{9}\cdot 11^{2}$ |
$3$ |
$14.9594010522$ |
$84.77753592720103$ |
|
|
✓ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$10$ |
$5$ |
$692.772226297$ |
| 12.0.125594455078125.2 |
$x^{12} - 8 x^{9} + 24 x^{6} - 27 x^{3} + 11$ |
$12$ |
[0,6] |
$3^{12}\cdot 5^{9}\cdot 11^{2}$ |
$3$ |
$14.95940105219326$ |
$84.77753592720103$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$10$ |
$5$ |
$616.9416910157607$ |
| 12.4.350284500000000.1 |
$x^{12} - 3 x^{11} + x^{10} + x^{9} - x^{8} + 8 x^{7} - 11 x^{6} + 14 x^{5} - 9 x^{4} + 5 x^{3} - 10 x^{2} - 5$ |
$12$ |
[4,4] |
$2^{8}\cdot 3^{6}\cdot 5^{9}\cdot 31^{2}$ |
$4$ |
$16.2942763142$ |
$90.7226909805036$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$2$ |
$7$ |
$426.245519832$ |
| 12.4.18260173718028288.1 |
$x^{12} - 8 x^{9} + 20 x^{6} - 16 x^{3} + 2$ |
$12$ |
[4,4] |
$2^{35}\cdot 3^{12}$ |
$2$ |
$22.6529835044$ |
$38.707547039378674$ |
|
|
✓ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$2$ |
$7$ |
$4741.60840804$ |
| 12.4.18260173718028288.23 |
$x^{12} - 8 x^{9} + 12 x^{6} - 4$ |
$12$ |
[4,4] |
$2^{35}\cdot 3^{12}$ |
$2$ |
$22.652983504360645$ |
$38.707547039378674$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$2$ |
$7$ |
$4900.406546260336$ |
| 12.0.446676160500000000.1 |
$x^{12} + 27 x^{10} - 20 x^{9} + 324 x^{8} - 210 x^{7} + 1968 x^{6} - 630 x^{5} + 5661 x^{4} - 520 x^{3} + 7380 x^{2} + 3280$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{12}\cdot 5^{9}\cdot 41^{2}$ |
$4$ |
$29.5687340552$ |
$396.69567102648426$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$10$ |
$5$ |
$27699.7184504$ |
| 12.0.247...000.1 |
$x^{12} - 45 x^{10} - 30 x^{9} + 855 x^{8} + 1050 x^{7} - 6605 x^{6} - 8910 x^{5} + 24885 x^{4} + 34860 x^{3} - 10980 x^{2} - 14640 x + 4880$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{12}\cdot 5^{11}\cdot 61^{2}$ |
$4$ |
$41.3128727171$ |
$676.0566890381432$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$10$ |
$5$ |
$279058.582648$ |
| 12.12.433...000.1 |
$x^{12} - 48 x^{10} - 60 x^{9} + 774 x^{8} + 1830 x^{7} - 3707 x^{6} - 15300 x^{5} - 6999 x^{4} + 22920 x^{3} + 22725 x^{2} - 6060 x - 9595$ |
$12$ |
[12,0] |
$2^{12}\cdot 3^{12}\cdot 5^{9}\cdot 101^{2}$ |
$4$ |
$43.2944588791$ |
$667.0219987733675$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$2$ |
$11$ |
$1110052.15261$ |
| 12.12.720...000.1 |
$x^{12} - 39 x^{10} - 26 x^{9} + 531 x^{8} + 708 x^{7} - 2653 x^{6} - 5778 x^{5} + 1089 x^{4} + 12320 x^{3} + 13176 x^{2} + 5856 x + 976$ |
$12$ |
[12,0] |
$2^{8}\cdot 3^{18}\cdot 5^{9}\cdot 61^{2}$ |
$4$ |
$54.720621536$ |
$865.6110187539238$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$2$ |
$11$ |
$3902244.46053$ |
| 12.0.627...000.1 |
$x^{12} + 135 x^{8} - 180 x^{7} + 75 x^{6} + 3645 x^{4} - 7290 x^{3} + 4455 x^{2} - 810 x + 45$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{22}\cdot 5^{11}$ |
$3$ |
$65.53522577575333$ |
$109.72597855991624$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$[2, 2]$ |
$2$ |
$5$ |
$318978.7584460358$ |
