| 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 |
| 12.4.3696640000000000.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 6 x^{9} + 15 x^{8} - 44 x^{7} - 12 x^{6} + 28 x^{5} + 51 x^{4} - 10 x^{3} - 10 x^{2} - 10 x + 5$ |
$12$ |
[4,4] |
$2^{20}\cdot 5^{10}\cdot 19^{2}$ |
$3$ |
$19.8297511078$ |
$164.6933803525864$ |
|
|
|
$C_3^4:\OD_{16}$ (as 12T215) |
trivial |
$2$ |
$7$ |
$2437.31996183$ |
| 12.8.4364666806640625.1 |
$x^{12} - 6 x^{11} + 12 x^{10} + 3 x^{9} - 57 x^{8} + 63 x^{7} + 83 x^{6} - 132 x^{5} - 57 x^{4} + 93 x^{3} + 12 x^{2} - 21 x + 1$ |
$12$ |
[8,2] |
$3^{12}\cdot 5^{10}\cdot 29^{2}$ |
$3$ |
$20.1061657286$ |
$151.35163883687963$ |
|
|
? |
$C_3^4:\OD_{16}$ (as 12T215) |
trivial |
$2$ |
$9$ |
$3891.28108102$ |
| 12.4.17213440000000000.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - 8 x^{9} + x^{8} + 10 x^{7} - 10 x^{6} - 40 x^{5} + 5 x^{4} + 90 x^{3} + 50 x^{2} - 20 x - 20$ |
$12$ |
[4,4] |
$2^{20}\cdot 5^{10}\cdot 41^{2}$ |
$3$ |
$22.5418197382$ |
$275.0191786873034$ |
|
|
|
$C_3^4:\OD_{16}$ (as 12T215) |
trivial |
$2$ |
$7$ |
$5099.27398042$ |
| 12.4.17213440000000000.2 |
$x^{12} - 6 x^{11} + 17 x^{10} - 12 x^{9} - 57 x^{8} + 208 x^{7} - 322 x^{6} + 248 x^{5} - 57 x^{4} - 42 x^{3} - 3 x^{2} + 4 x + 1$ |
$12$ |
[4,4] |
$2^{20}\cdot 5^{10}\cdot 41^{2}$ |
$3$ |
$22.54181973818867$ |
$275.0191786873034$ |
|
|
|
$C_3^4:\OD_{16}$ (as 12T215) |
trivial |
$2$ |
$7$ |
$5455.132348192559$ |
| 12.8.34050628916015625.1 |
$x^{12} - 12 x^{10} - 7 x^{9} + 54 x^{8} + 63 x^{7} - 99 x^{6} - 189 x^{5} + 27 x^{4} + 206 x^{3} + 81 x^{2} - 51 x - 29$ |
$12$ |
[8,2] |
$3^{20}\cdot 5^{10}$ |
$2$ |
$23.8603656527$ |
$47.45543930664761$ |
|
|
? |
$C_3^4:\OD_{16}$ (as 12T215) |
trivial |
$2$ |
$9$ |
$11773.9329883$ |
| 12.4.544...000.1 |
$x^{12} + 12 x^{10} - 4 x^{9} + 54 x^{8} - 36 x^{7} + 84 x^{6} - 108 x^{5} - 63 x^{4} - 92 x^{3} - 216 x^{2} + 48 x + 16$ |
$12$ |
[4,4] |
$2^{20}\cdot 3^{12}\cdot 5^{10}$ |
$3$ |
$36.417733860175034$ |
$118.56738433160712$ |
|
|
|
$C_3^4:\OD_{16}$ (as 12T215) |
trivial |
$2$ |
$7$ |
$103754.14079554578$ |
| 12.12.196...000.1 |
$x^{12} - 42 x^{10} - 28 x^{9} + 594 x^{8} + 792 x^{7} - 3084 x^{6} - 6696 x^{5} + 1692 x^{4} + 15424 x^{3} + 16416 x^{2} + 7296 x + 1216$ |
$12$ |
[12,0] |
$2^{20}\cdot 3^{12}\cdot 5^{10}\cdot 19^{2}$ |
$4$ |
$59.4892533233$ |
$757.4335760470384$ |
|
|
|
$C_3^4:\OD_{16}$ (as 12T215) |
trivial |
$2$ |
$11$ |
$10449270.4272$ |
| 12.12.159...000.1 |
$x^{12} - 108 x^{10} - 136 x^{9} + 4284 x^{8} + 10416 x^{7} - 68656 x^{6} - 258912 x^{5} + 231312 x^{4} + 2075392 x^{3} + 2582784 x^{2} - 58368 x - 1147904$ |
$12$ |
[12,0] |
$2^{20}\cdot 3^{16}\cdot 5^{10}\cdot 19^{2}$ |
$4$ |
$85.7983500435$ |
$1442.5732719579428$ |
|
|
|
$C_3^4:\OD_{16}$ (as 12T215) |
trivial |
$2$ |
$11$ |
$103895287.488$ |
