| 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 |
| 12.4.630...936.1 |
$x^{12} - 12 x^{10} - 8 x^{9} + 21 x^{8} + 36 x^{7} + 192 x^{6} + 240 x^{5} - 84 x^{4} - 68 x^{3} - 72 x^{2} - 48 x + 5$ |
$12$ |
[4,4] |
$2^{24}\cdot 3^{12}\cdot 29^{4}$ |
$3$ |
$36.8678019082$ |
|
|
|
? |
$M_{12}$ (as 12T295) |
trivial |
$2$ |
$7$ |
$119294.333428$ |
| 12.4.630...936.2 |
$x^{12} - 16 x^{10} - 36 x^{9} + 111 x^{8} + 372 x^{7} - 204 x^{6} - 1500 x^{5} - 384 x^{4} + 2200 x^{3} + 1404 x^{2} - 688 x + 21$ |
$12$ |
[4,4] |
$2^{24}\cdot 3^{12}\cdot 29^{4}$ |
$3$ |
$36.8678019082$ |
$159.54585350123654$ |
|
|
|
$M_{12}$ (as 12T295) |
trivial |
$2$ |
$7$ |
$398404.938394$ |
| 12.0.944...296.1 |
$x^{12} - 4 x^{11} + 4 x^{10} + 12 x^{9} - 72 x^{8} + 168 x^{7} - 132 x^{6} - 324 x^{5} + 1197 x^{4} - 1752 x^{3} + 1500 x^{2} - 672 x + 207$ |
$12$ |
[0,6] |
$2^{24}\cdot 3^{14}\cdot 7^{6}$ |
$3$ |
$38.128566284$ |
$122.79038648593725$ |
|
|
? |
$M_{12}$ (as 12T295) |
trivial |
$2$ |
$5$ |
$130780.174411$ |
| 12.0.849...664.1 |
$x^{12} + 18 x^{10} - 12 x^{9} + 189 x^{8} - 288 x^{7} + 1458 x^{6} - 2796 x^{5} + 7092 x^{4} - 11988 x^{3} + 17010 x^{2} - 19404 x + 10185$ |
$12$ |
[0,6] |
$2^{24}\cdot 3^{16}\cdot 7^{6}$ |
$3$ |
$45.7900042983$ |
$122.79038648593725$ |
|
|
? |
$M_{12}$ (as 12T295) |
$[2]$ |
$2$ |
$5$ |
$130869.789094$ |
| 12.12.111...856.1 |
$x^{12} - 968 x^{10} + 346060 x^{8} - 56221440 x^{6} + 4128059232 x^{4} - 247374336 x^{3} - 114286943232 x^{2} + 19295198208 x + 632319724608$ |
$12$ |
[12,0] |
$2^{24}\cdot 3^{8}\cdot 11^{20}\cdot 197^{4}$ |
$4$ |
$2634.00975154$ |
$18500.07845030721$ |
|
|
|
$M_{12}$ (as 12T295) |
trivial |
$2$ |
$11$ |
$328442425589000000$ |
| 12.12.100...704.1 |
$x^{12} - 4 x^{11} - 3036 x^{10} + 16940 x^{9} + 3435883 x^{8} - 21476268 x^{7} - 1841908992 x^{6} + 11122519452 x^{5} + 490521018900 x^{4} - 2361270759804 x^{3} - 62489273434236 x^{2} + 167503033069380 x + 3005497215363897$ |
$12$ |
[12,0] |
$2^{24}\cdot 3^{10}\cdot 11^{20}\cdot 197^{4}$ |
$4$ |
$3163.27965092$ |
$18500.07845030721$ |
|
|
? |
$M_{12}$ (as 12T295) |
trivial |
$2$ |
$11$ |
$377943984207000000$ |
