| 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 |
| 12.4.2282521714753536.1 |
$x^{12} - 8 x^{9} - 18 x^{8} - 24 x^{7} - 28 x^{6} - 24 x^{5} + 30 x^{4} + 32 x^{3} + 48 x^{2} - 32$ |
$12$ |
[4,4] |
$2^{32}\cdot 3^{12}$ |
$2$ |
$19.0488126236$ |
$29.715621574744997$ |
|
|
? |
$\PSU(3,2)$ (as 12T47) |
trivial |
$2$ |
$7$ |
$3228.03810509$ |
| 12.4.378...000.1 |
$x^{12} - x^{11} + 2 x^{10} + 15 x^{9} - 146 x^{8} + 373 x^{7} - 587 x^{6} + 568 x^{5} - 506 x^{4} + 480 x^{3} - 484 x^{2} + 320 x - 80$ |
$12$ |
[4,4] |
$2^{8}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}$ |
$4$ |
$35.3302081805$ |
$65.60273867532537$ |
|
|
|
$\PSU(3,2)$ (as 12T47) |
$[3]$ |
$2$ |
$7$ |
$76110.238508$ |
| 12.12.162...625.1 |
$x^{12} - 45 x^{10} - 6 x^{9} + 702 x^{8} + 174 x^{7} - 4822 x^{6} - 1551 x^{5} + 14679 x^{4} + 5097 x^{3} - 16002 x^{2} - 5667 x - 341$ |
$12$ |
[12,0] |
$3^{12}\cdot 5^{8}\cdot 23^{8}$ |
$3$ |
$70.9446768664$ |
$130.44222925812892$ |
|
|
|
$\PSU(3,2)$ (as 12T47) |
trivial |
$2$ |
$11$ |
$63896444.0604$ |
| 12.12.108...624.1 |
$x^{12} - 4 x^{11} - 46 x^{10} + 276 x^{9} + 124 x^{8} - 3712 x^{7} + 6880 x^{6} + 7856 x^{5} - 41606 x^{4} + 52664 x^{3} - 22620 x^{2} - 3720 x + 3844$ |
$12$ |
[12,0] |
$2^{32}\cdot 7^{6}\cdot 11^{8}$ |
$3$ |
$83.0916657116$ |
$176.82073610398749$ |
|
|
? |
$\PSU(3,2)$ (as 12T47) |
$[3]$ |
$2$ |
$11$ |
$64864555.3865$ |
