| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
| 12.0.851162814333.1 |
$x^{12} - x^{9} + 2 x^{6} - 2 x^{3} + 1$ |
$12$ |
(0, 6) |
$3^{18}\cdot 13^{3}$ |
$2$ |
$9.86660450396$ |
$29.311381743553262$ |
|
|
✓ |
$S_3^2:C_6$ (as 12T121) |
trivial |
trivial |
$6$ |
$5$ |
$25.3115784159$ |
$0$ |
| 12.0.2180445558813.1 |
$x^{12} + 4 x^{6} - 3 x^{3} + 1$ |
$12$ |
(0, 6) |
$3^{16}\cdot 37^{3}$ |
$2$ |
$10.6711716062$ |
$40.34685519339305$ |
|
|
? |
$S_3^2:C_6$ (as 12T121) |
trivial |
trivial |
$6$ |
$5$ |
$62.2615055244$ |
$0$ |
| 12.6.25345511310483.1 |
$x^{12} - x^{11} - x^{10} + 9 x^{9} - 5 x^{8} - 23 x^{7} + 8 x^{6} + 25 x^{5} - 5 x^{4} - 17 x^{3} + 2 x^{2} + 5 x - 1$ |
$12$ |
(6, 3) |
$-\,3^{7}\cdot 7^{4}\cdot 13^{6}$ |
$3$ |
$13.0915706789$ |
$47.53481777030535$ |
|
|
? |
$S_3^2:C_6$ (as 12T121) |
trivial |
trivial |
$2$ |
$8$ |
$152.437492172$ |
$6$ |
| 12.0.42845606719488.2 |
$x^{12} - 2 x^{9} + 3 x^{6} + 4 x^{3} + 1$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{21}$ |
$2$ |
$13.677042341728665$ |
$30.883428090661386$ |
|
|
✓ |
$S_3^2:C_6$ (as 12T121) |
trivial |
trivial |
$6$ |
$5$ |
$269.9667589353308$ |
$0$ |
| 12.6.85280185546875.1 |
$x^{12} - 4 x^{11} + x^{10} + 20 x^{9} - 40 x^{8} + x^{7} + 86 x^{6} - 99 x^{5} + 90 x^{3} - 54 x^{2} + 36 x - 9$ |
$12$ |
(6, 3) |
$-\,3^{8}\cdot 5^{10}\cdot 11^{3}$ |
$3$ |
$14.4845167854$ |
$54.86975476352006$ |
|
|
? |
$S_3^2:C_6$ (as 12T121) |
trivial |
trivial |
$2$ |
$8$ |
$231.159453249$ |
$6$ |
| 12.0.92407922456769.1 |
$x^{12} - 7 x^{9} + 30 x^{6} + 11 x^{3} + 1$ |
$12$ |
(0, 6) |
$3^{19}\cdot 43^{3}$ |
$2$ |
$14.58173161488322$ |
$43.94008014870428$ |
|
|
|
$S_3^2:C_6$ (as 12T121) |
trivial |
trivial |
$6$ |
$5$ |
$782.815472345082$ |
$0$ |
| 12.0.57027502543638528.1 |
$x^{12} - 12 x^{10} - 12 x^{9} + 54 x^{8} + 108 x^{7} - 51 x^{6} - 324 x^{5} - 261 x^{4} + 204 x^{3} + 513 x^{2} + 360 x + 96$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{21}\cdot 11^{3}$ |
$3$ |
$24.9080863542$ |
$72.42805891690588$ |
|
|
|
$S_3^2:C_6$ (as 12T121) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$11208.8454231$ |
$0$ |
| 12.0.118...512.1 |
$x^{12} + 12 x^{10} - 3 x^{9} + 54 x^{8} - 27 x^{7} + 111 x^{6} - 81 x^{5} + 99 x^{4} - 78 x^{3} + 27 x^{2} + 9 x + 12$ |
$12$ |
(0, 6) |
$2^{6}\cdot 3^{21}\cdot 11^{6}$ |
$3$ |
$32.0755074737$ |
$72.42805891690588$ |
|
|
|
$S_3^2:C_6$ (as 12T121) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$65753.1409043$ |
$0$ |
| 12.0.126...625.1 |
$x^{12} - 4 x^{11} + 14 x^{10} - 68 x^{9} + 190 x^{8} - 415 x^{7} + 880 x^{6} - 1801 x^{5} + 3457 x^{4} - 4594 x^{3} + 4916 x^{2} - 3360 x + 1280$ |
$12$ |
(0, 6) |
$5^{6}\cdot 7^{8}\cdot 241^{3}$ |
$3$ |
$32.23947464235213$ |
$127.02588132614984$ |
|
|
|
$S_3^2:C_6$ (as 12T121) |
$[9]$ |
$[9]$ |
$2$ |
$5$ |
$5763.340675079222$ |
$0$ |
| 12.12.102...125.1 |
$x^{12} - 30 x^{10} - 15 x^{9} + 315 x^{8} + 315 x^{7} - 1310 x^{6} - 2025 x^{5} + 1350 x^{4} + 4050 x^{3} + 2250 x^{2} + 225 x - 25$ |
$12$ |
(12, 0) |
$3^{16}\cdot 5^{10}\cdot 29^{3}$ |
$3$ |
$38.3915968168$ |
$170.83395556024902$ |
|
|
? |
$S_3^2:C_6$ (as 12T121) |
trivial |
trivial |
$2$ |
$11$ |
$360939.969786$ |
$12$ |
| 12.12.200...125.1 |
$x^{12} - 42 x^{10} - 21 x^{9} + 531 x^{8} + 531 x^{7} - 1966 x^{6} - 2835 x^{5} + 1620 x^{4} + 4320 x^{3} + 1800 x^{2} - 225 x - 175$ |
$12$ |
(12, 0) |
$3^{16}\cdot 5^{7}\cdot 29^{6}$ |
$3$ |
$59.578995183$ |
$170.83395556024902$ |
|
|
? |
$S_3^2:C_6$ (as 12T121) |
trivial |
trivial |
$2$ |
$11$ |
$4892429.43918$ |
$12$ |
| 12.12.526...625.1 |
$x^{12} - x^{11} - 64 x^{10} + 97 x^{9} + 1177 x^{8} - 2061 x^{7} - 6528 x^{6} + 9559 x^{5} + 12273 x^{4} - 8954 x^{3} - 9251 x^{2} - 2308 x - 176$ |
$12$ |
(12, 0) |
$5^{6}\cdot 7^{8}\cdot 3881^{3}$ |
$3$ |
$64.58320689204386$ |
$509.7479840194441$ |
|
|
|
$S_3^2:C_6$ (as 12T121) |
$[3]$ |
$[3]$ |
$2$ |
$11$ |
$13467783.832706252$ |
$12$ |
