| 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 |
| 12.4.364...081.1 |
$x^{12} - 3 x^{11} - 5 x^{10} + 11 x^{9} + 40 x^{8} + 139 x^{7} - 1505 x^{6} + 9090 x^{5} - 24504 x^{4} + 5576 x^{3} + 95056 x^{2} - 153440 x + 59712$ |
$12$ |
[4,4] |
$661^{8}$ |
$1$ |
$75.8812202741$ |
$180.36869686739456$ |
|
|
? |
$M_{11}$ (as 12T272) |
trivial |
$2$ |
$7$ |
$31968632.5563$ |
| 12.4.147...000.1 |
$x^{12} - x^{11} - 16 x^{10} + 15 x^{9} + 145 x^{8} - 8 x^{7} - 392 x^{6} + 88 x^{5} + 415 x^{4} - 255 x^{3} - 64 x^{2} + 89 x - 41$ |
$12$ |
[4,4] |
$2^{18}\cdot 3^{10}\cdot 5^{20}$ |
$3$ |
$103.298983119$ |
$270.8346732868732$ |
|
|
? |
$M_{11}$ (as 12T272) |
$[2]$ |
$2$ |
$7$ |
$279154681.275$ |
| 12.12.273...896.1 |
$x^{12} - 5526 x^{10} - 11000 x^{9} + 11072751 x^{8} + 48056976 x^{7} - 9806288196 x^{6} - 66045530544 x^{5} + 3652512071076 x^{4} + 32827558924192 x^{3} - 401077519158720 x^{2} - 3666673786739256 x + 5270752514492878$ |
$12$ |
[12,0] |
$2^{32}\cdot 3^{12}\cdot 337^{4}\cdot 310501^{4}$ |
$4$ |
$8976.33139558$ |
$303970.38325382833$ |
|
|
? |
$M_{11}$ (as 12T272) |
$[2]$ |
$2$ |
$11$ |
$110704913560000000000$ |
| 12.12.392...000.1 |
$x^{12} - x^{11} - 100067 x^{10} + 4532198 x^{9} + 2259444770 x^{8} - 152359965054 x^{7} - 16041513207467 x^{6} + 1461301745883639 x^{5} + 14413851909825665 x^{4} - 3552570264974645508 x^{3} + 69523530327654696348 x^{2} + 31953284631467426916 x - 861259903428927255084$ |
$12$ |
[12,0] |
$2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 11^{12}\cdot 13^{4}\cdot 17^{4}\cdot 347^{10}$ |
$7$ |
$92510.6546111$ |
$936774.2546036756$ |
|
|
|
$M_{11}$ (as 12T272) |
$[2]$ |
$2$ |
$11$ |
$976514024364000000000000000$ |
