| 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 |
| 12.0.44533203125.1 |
$x^{12} - 2 x^{11} + 7 x^{10} - 7 x^{9} + 14 x^{8} - 6 x^{7} + 13 x^{6} - 2 x^{5} + 10 x^{4} - 2 x^{3} + 5 x^{2} - x + 1$ |
$12$ |
[0,6] |
$5^{9}\cdot 151^{2}$ |
$2$ |
$7.71596640012$ |
$94.81538251069664$ |
|
|
✓ |
$C_3\wr C_4$ (as 12T131) |
trivial |
$10$ |
$5$ |
$6.10223070288$ |
| 12.0.213986328125.1 |
$x^{12} - 2 x^{11} - x^{10} + 9 x^{9} - 7 x^{8} - 11 x^{7} + 20 x^{6} + x^{5} - 19 x^{4} + 8 x^{3} + 6 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$5^{9}\cdot 331^{2}$ |
$2$ |
$8.79425056922$ |
$159.99736578325135$ |
|
|
✓ |
$C_3\wr C_4$ (as 12T131) |
trivial |
$10$ |
$5$ |
$16.35909998$ |
| 12.12.13086728000000000.1 |
$x^{12} - 2 x^{11} - 15 x^{10} + 36 x^{9} + 62 x^{8} - 206 x^{7} + 2 x^{6} + 366 x^{5} - 298 x^{4} + 28 x^{3} + 38 x^{2} - 12 x + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{9}\cdot 1279^{2}$ |
$3$ |
$22.0327778864$ |
$787.960647800511$ |
|
|
? |
$C_3\wr C_4$ (as 12T131) |
trivial |
$2$ |
$11$ |
$9881.73314061$ |
| 12.12.31968008000000000.1 |
$x^{12} - 6 x^{11} - 3 x^{10} + 64 x^{9} - 64 x^{8} - 152 x^{7} + 221 x^{6} + 114 x^{5} - 227 x^{4} - 12 x^{3} + 72 x^{2} - 8 x - 4$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{9}\cdot 1999^{2}$ |
$3$ |
$23.7352037729$ |
$1061.2051810975959$ |
|
|
|
$C_3\wr C_4$ (as 12T131) |
trivial |
$2$ |
$11$ |
$28399.3905732$ |
| 12.12.46769161084392848.1 |
$x^{12} - 5 x^{11} - 6 x^{10} + 56 x^{9} - 30 x^{8} - 162 x^{7} + 157 x^{6} + 158 x^{5} - 176 x^{4} - 66 x^{3} + 64 x^{2} + 12 x - 4$ |
$12$ |
[12,0] |
$2^{4}\cdot 17^{9}\cdot 157^{2}$ |
$3$ |
$24.499842830623887$ |
$386.7732737145528$ |
|
|
? |
$C_3\wr C_4$ (as 12T131) |
trivial |
$2$ |
$11$ |
$25842.46166113395$ |
