| 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 |
| 12.0.406239826673664.1 |
$x^{12} - 6 x^{11} + 18 x^{10} - 32 x^{9} + 27 x^{8} - 18 x^{6} + 45 x^{4} - 38 x^{3} + 12 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{18}$ |
$2$ |
$16.496755644$ |
$21.058405636775934$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
trivial |
$2$ |
$5$ |
$727.46492131$ |
| 12.0.489631389843456.1 |
$x^{12} + 4 x^{10} - 6 x^{9} + x^{8} - 16 x^{7} + 22 x^{6} - 12 x^{5} + 27 x^{4} + 12 x^{3} + 14 x^{2} + 2 x + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{4}\cdot 7^{8}$ |
$3$ |
$16.7554374565$ |
$20.122224041627174$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
$[3]$ |
$2$ |
$5$ |
$296.481209498$ |
| 12.0.722204136308736.21 |
$x^{12} - 6 x^{11} + 24 x^{10} - 58 x^{9} + 105 x^{8} - 132 x^{7} + 128 x^{6} - 84 x^{5} + 45 x^{4} - 18 x^{3} + 12 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 3^{16}$ |
$2$ |
$17.3069948436889$ |
$20.58160140743025$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
$[3]$ |
$2$ |
$5$ |
$467.50283453145306$ |
| 12.0.855355656503296.12 |
$x^{12} - 2 x^{11} + 4 x^{10} + 6 x^{9} - 7 x^{8} + 28 x^{7} + 40 x^{6} + 24 x^{5} + 41 x^{4} + 22 x^{3} + 8 x^{2} + 2 x + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 13^{8}$ |
$2$ |
$17.552765910658255$ |
$18.59650768627035$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
$[3]$ |
$2$ |
$5$ |
$499.9213445903575$ |
| 12.4.41753392563387961.1 |
$x^{12} - 4 x^{11} + 6 x^{10} - 11 x^{9} + 5 x^{8} - 19 x^{7} - 4 x^{6} - 27 x^{5} + 90 x^{4} + 92 x^{3} - 129 x^{2} + 101 x - 29$ |
$12$ |
[4,4] |
$19^{6}\cdot 31^{6}$ |
$2$ |
$24.269322199$ |
$39.64452763115264$ |
|
|
|
$S_3\times A_4$ (as 12T43) |
trivial |
$2$ |
$7$ |
$8959.12599169$ |
| 12.4.223580268118933504.1 |
$x^{12} - 4 x^{11} - 2 x^{10} + 40 x^{9} - 118 x^{8} + 222 x^{7} - 322 x^{6} + 456 x^{5} - 620 x^{4} + 436 x^{3} + 299 x^{2} - 738 x + 353$ |
$12$ |
[4,4] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$49.470511984396374$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
trivial |
$2$ |
$7$ |
$13901.8657632$ |
| 12.0.231203843592945664.1 |
$x^{12} + 8 x^{10} - 14 x^{9} + 32 x^{8} - 20 x^{7} + 26 x^{6} + 28 x^{4} + 4 x^{3} + 4 x^{2} - 4 x + 2$ |
$12$ |
[0,6] |
$2^{20}\cdot 7^{6}\cdot 37^{4}$ |
$3$ |
$27.9897866092$ |
$70.66692841330432$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
trivial |
$2$ |
$5$ |
$8946.89441079$ |
| 12.0.349064245382494464.1 |
$x^{12} + 5 x^{10} - 15 x^{9} + 45 x^{8} - 50 x^{7} + 108 x^{6} - 123 x^{5} + 143 x^{4} - 61 x^{3} + 36 x^{2} + 8 x + 10$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{12}\cdot 37^{6}$ |
$3$ |
$28.9673509184$ |
$41.77814941501269$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
$[2]$ |
$2$ |
$5$ |
$6947.12061608$ |
| 12.0.975381823843467264.1 |
$x^{12} - 6 x^{11} + 6 x^{10} + 16 x^{9} - 9 x^{8} - 12 x^{7} - 138 x^{6} + 180 x^{5} + 393 x^{4} - 1234 x^{3} + 1500 x^{2} - 792 x + 233$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{18}\cdot 7^{4}$ |
$3$ |
$31.557158285951928$ |
$55.715304322429894$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
trivial |
$2$ |
$5$ |
$38380.00263844461$ |
| 12.0.228...000.1 |
$x^{12} + 12 x^{10} - 6 x^{9} + 57 x^{8} - 12 x^{7} + 78 x^{6} + 24 x^{5} + 183 x^{4} - 8 x^{3} + 102 x^{2} + 90 x + 129$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{20}\cdot 5^{4}$ |
$3$ |
$33.87729703971703$ |
$50.05151476499125$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
trivial |
$2$ |
$5$ |
$71703.1838332173$ |
| 12.0.119...464.2 |
$x^{12} - 4 x^{11} + 10 x^{10} - 34 x^{9} + 97 x^{8} - 16 x^{7} - 22 x^{6} + 364 x^{5} + 145 x^{4} + 222 x^{3} + 630 x^{2} + 448 x + 302$ |
$12$ |
[0,6] |
$2^{18}\cdot 7^{8}\cdot 53^{4}$ |
$3$ |
$38.877856285959815$ |
$75.34971632639669$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
$[6]$ |
$2$ |
$5$ |
$21260.880248298723$ |
| 12.12.207...161.1 |
$x^{12} - 4 x^{11} - 17 x^{10} + 82 x^{9} + 19 x^{8} - 414 x^{7} + 336 x^{6} + 516 x^{5} - 645 x^{4} - 172 x^{3} + 344 x^{2} - 43$ |
$12$ |
[12,0] |
$11^{6}\cdot 43^{8}$ |
$2$ |
$40.7075826175$ |
$76.19387402923972$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
trivial |
$2$ |
$11$ |
$885013.210389$ |
| 12.12.159...336.1 |
$x^{12} - 2 x^{11} - 43 x^{10} + 41 x^{9} + 601 x^{8} - 128 x^{7} - 3194 x^{6} - 489 x^{5} + 6471 x^{4} + 2179 x^{3} - 3462 x^{2} - 884 x + 278$ |
$12$ |
[12,0] |
$2^{8}\cdot 11^{6}\cdot 37^{8}$ |
$3$ |
$58.4589246685$ |
$106.71310986078944$ |
|
|
? |
$S_3\times A_4$ (as 12T43) |
trivial |
$2$ |
$11$ |
$12025487.1319$ |
