| 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 |
| 12.4.31336408949981184.1 |
$x^{12} - 6 x^{10} - 4 x^{9} + 21 x^{8} + 16 x^{7} + 36 x^{6} + 16 x^{5} - 97 x^{4} - 38 x^{2} + 20 x - 1$ |
$12$ |
[4,4] |
$2^{26}\cdot 3^{4}\cdot 7^{8}$ |
$3$ |
$23.6957668944$ |
$36.90432160888472$ |
|
|
? |
$A_4\wr C_2$ (as 12T128) |
$[3]$ |
$2$ |
$7$ |
$5807.15141676$ |
| 12.4.35704672266240000.1 |
$x^{12} - 6 x^{11} + 12 x^{10} - 2 x^{9} - 36 x^{8} + 72 x^{7} - 48 x^{6} - 54 x^{5} + 180 x^{4} - 146 x^{3} - 6 x^{2} + 12 x - 2$ |
$12$ |
[4,4] |
$2^{14}\cdot 3^{20}\cdot 5^{4}$ |
$3$ |
$23.9548664651$ |
$38.59499394931745$ |
|
|
? |
$A_4\wr C_2$ (as 12T128) |
trivial |
$2$ |
$7$ |
$20492.2187429$ |
| 12.4.46221064723759104.1 |
$x^{12} - 12 x^{10} - 24 x^{9} + 48 x^{7} + 32 x^{6} - 24 x^{5} - 30 x^{4} - 64 x^{3} - 96 x^{2} - 48 x - 8$ |
$12$ |
[4,4] |
$2^{30}\cdot 3^{16}$ |
$2$ |
$24.4757868319$ |
$39.41801805957117$ |
|
|
? |
$A_4\wr C_2$ (as 12T128) |
$[3]$ |
$2$ |
$7$ |
$9050.78316338$ |
| 12.4.173911685539840000.1 |
$x^{12} - 4 x^{11} - 6 x^{10} + 48 x^{9} - 26 x^{8} - 192 x^{7} + 216 x^{6} + 400 x^{5} - 416 x^{4} - 394 x^{3} + 314 x^{2} + 120 x - 106$ |
$12$ |
[4,4] |
$2^{14}\cdot 5^{4}\cdot 19^{8}$ |
$3$ |
$27.3334256011$ |
$38.97784406822943$ |
|
|
? |
$A_4\wr C_2$ (as 12T128) |
$[3]$ |
$2$ |
$7$ |
$11625.7878283$ |
| 12.0.652...000.1 |
$x^{12} - x^{11} + 2 x^{10} - 2 x^{9} + 36 x^{8} - 10 x^{7} + 60 x^{6} - 40 x^{5} + 165 x^{4} - 185 x^{3} + 310 x^{2} - 146 x + 170$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{4}\cdot 7^{4}\cdot 19^{8}$ |
$4$ |
$36.9724655141$ |
$66.86873178880111$ |
|
|
? |
$A_4\wr C_2$ (as 12T128) |
$[6]$ |
$2$ |
$5$ |
$16601.8228202$ |
| 12.0.119...464.1 |
$x^{12} - 6 x^{11} + 18 x^{10} - 8 x^{9} - 4 x^{8} - 56 x^{7} + 232 x^{6} - 218 x^{5} + 300 x^{4} - 412 x^{3} + 448 x^{2} - 224 x + 63$ |
$12$ |
[0,6] |
$2^{18}\cdot 7^{8}\cdot 53^{4}$ |
$3$ |
$38.877856286$ |
$97.71649256380418$ |
|
|
? |
$A_4\wr C_2$ (as 12T128) |
$[6]$ |
$2$ |
$5$ |
$21754.3687224$ |
| 12.12.632...000.1 |
$x^{12} - 48 x^{10} - 24 x^{9} + 807 x^{8} + 624 x^{7} - 6174 x^{6} - 6234 x^{5} + 21795 x^{4} + 27658 x^{3} - 26418 x^{2} - 45504 x - 11073$ |
$12$ |
[12,0] |
$2^{14}\cdot 3^{20}\cdot 5^{4}\cdot 11^{6}$ |
$4$ |
$79.4493039677$ |
$128.0051137159229$ |
|
|
? |
$A_4\wr C_2$ (as 12T128) |
trivial |
$2$ |
$11$ |
$172103214.07$ |
| 12.12.108...000.1 |
$x^{12} - 6 x^{11} - 27 x^{10} + 169 x^{9} + 225 x^{8} - 1308 x^{7} - 952 x^{6} + 2796 x^{5} + 1572 x^{4} - 1616 x^{3} - 420 x^{2} + 252 x - 12$ |
$12$ |
[12,0] |
$2^{12}\cdot 3^{16}\cdot 5^{4}\cdot 7^{6}\cdot 17^{4}$ |
$5$ |
$100.665424793$ |
$298.51430615557365$ |
|
|
? |
$A_4\wr C_2$ (as 12T128) |
$[3]$ |
$2$ |
$11$ |
$280832809.107$ |
