| 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 |
| 12.4.1785233613312000.1 |
$x^{12} - 10 x^{9} + 3 x^{8} - 18 x^{7} + 18 x^{6} + 18 x^{5} + 30 x^{3} + 18 x^{2} - 3$ |
$12$ |
[4,4] |
$2^{12}\cdot 3^{20}\cdot 5^{3}$ |
$3$ |
$18.6627048578$ |
$38.59499394931745$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
trivial |
$2$ |
$7$ |
$1711.63277559$ |
| 12.6.2611367412498432.1 |
$x^{12} - 2 x^{10} - 12 x^{9} - 7 x^{8} + 16 x^{7} + 50 x^{6} + 24 x^{5} - 46 x^{4} - 40 x^{3} + 8 x^{2} + 8 x - 1$ |
$12$ |
[6,3] |
$-\,2^{24}\cdot 3^{3}\cdot 7^{8}$ |
$3$ |
$19.2636686016$ |
$36.90432160888472$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
trivial |
$2$ |
$8$ |
$1844.85317679$ |
| 12.4.3515376756641792.1 |
$x^{12} - 6 x^{11} + 13 x^{10} - 56 x^{8} + 100 x^{7} - 81 x^{6} + 2 x^{5} + 34 x^{4} + 8 x^{3} - 40 x^{2} + 40 x - 8$ |
$12$ |
[4,4] |
$2^{12}\cdot 7^{8}\cdot 53^{3}$ |
$3$ |
$19.7468422335$ |
$75.34971632639669$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
trivial |
$2$ |
$7$ |
$1579.14582591$ |
| 12.6.5777633090469888.1 |
$x^{12} - 6 x^{10} - 3 x^{8} - 48 x^{7} - 40 x^{6} + 24 x^{5} + 12 x^{4} - 16 x^{3} + 6 x^{2} + 12 x + 1$ |
$12$ |
[6,3] |
$-\,2^{27}\cdot 3^{16}$ |
$2$ |
$20.5816014074$ |
$39.41801805957117$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
trivial |
$2$ |
$8$ |
$3441.4821481$ |
| 12.0.224984112425074688.1 |
$x^{12} - 4 x^{11} + 6 x^{10} + 11 x^{8} - 50 x^{7} + 72 x^{6} - 130 x^{5} - 38 x^{4} + 48 x^{3} + 608 x^{2} - 266 x + 29$ |
$12$ |
[0,6] |
$2^{18}\cdot 7^{8}\cdot 53^{3}$ |
$3$ |
$27.9262521006$ |
$97.71649256380418$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
$[2]$ |
$2$ |
$5$ |
$2358.67063615$ |
| 12.0.224984112425074688.2 |
$x^{12} - 4 x^{11} + 10 x^{10} - 22 x^{9} + 69 x^{8} - 136 x^{7} + 86 x^{6} + 30 x^{5} + 202 x^{4} - 262 x^{3} + 440 x^{2} - 254 x + 43$ |
$12$ |
[0,6] |
$2^{18}\cdot 7^{8}\cdot 53^{3}$ |
$3$ |
$27.9262521006$ |
$97.71649256380418$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
$[2]$ |
$2$ |
$5$ |
$2383.43565731$ |
| 12.12.316...000.1 |
$x^{12} - 6 x^{11} - 36 x^{10} + 138 x^{9} + 675 x^{8} - 432 x^{7} - 4536 x^{6} - 3816 x^{5} + 7551 x^{4} + 16014 x^{3} + 11196 x^{2} + 3294 x + 333$ |
$12$ |
[12,0] |
$2^{12}\cdot 3^{20}\cdot 5^{3}\cdot 11^{6}$ |
$4$ |
$61.8971895866$ |
$128.0051137159229$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
trivial |
$2$ |
$11$ |
$14375090.647$ |
| 12.12.127...000.1 |
$x^{12} - 6 x^{11} - 21 x^{10} + 152 x^{9} + 111 x^{8} - 1194 x^{7} + 131 x^{6} + 2802 x^{5} - 1887 x^{4} - 906 x^{3} + 843 x^{2} + 60 x - 89$ |
$12$ |
[12,0] |
$2^{12}\cdot 3^{16}\cdot 5^{3}\cdot 7^{6}\cdot 17^{3}$ |
$5$ |
$69.5177040109$ |
$298.51430615557365$ |
|
|
? |
$A_4\wr C_2$ (as 12T129) |
trivial |
$2$ |
$11$ |
$26645947.8038$ |
