| 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 |
Max $p$ |
| 12.0.177...637.1 |
$x^{12} - 2 x^{11} + 34 x^{10} - 61 x^{9} + 461 x^{8} - 604 x^{7} + 2749 x^{6} - 764 x^{5} + 6328 x^{4} + 3855 x^{3} + 6423 x^{2} - 5004 x + 11799$ |
$12$ |
(0, 6) |
$3^{6}\cdot 17^{9}\cdot 29^{5}$ |
$3$ |
$58.983401955402236$ |
$78.09016084173805$ |
|
|
|
$D_{12}$ (as 12T12) |
$[12]$ |
$[12]$ |
$2$ |
$5$ |
$596231.4261430828$ |
$0$ |
|
| 12.2.171...491.1 |
$x^{12} - x^{11} + 2 x^{10} - 144 x^{9} + 373 x^{8} - 869 x^{7} + 6724 x^{6} - 17033 x^{5} + 20263 x^{4} - 31002 x^{3} + 80030 x^{2} - 39862 x - 86279$ |
$12$ |
(2, 5) |
$-\,3^{5}\cdot 17^{9}\cdot 29^{6}$ |
$3$ |
$71.25842396970613$ |
$78.09016084173805$ |
|
|
|
$D_{12}$ (as 12T12) |
$[12]$ |
$[12]$ |
$2$ |
$6$ |
$2808018.29398218$ |
$2$ |
|
| 12.0.133...125.1 |
$x^{12} - x^{11} + 23 x^{10} + 269 x^{9} + 453 x^{8} + 5718 x^{7} + 35944 x^{6} + 95984 x^{5} + 471366 x^{4} + 1980888 x^{3} + 3844638 x^{2} + 3334107 x + 1200451$ |
$12$ |
(0, 6) |
$5^{9}\cdot 7^{8}\cdot 17^{9}$ |
$3$ |
$102.438423844$ |
$102.4384238436466$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[3, 780]$ |
$[3, 780]$ |
$2$ |
$5$ |
$3699.65687174$ |
$0$ |
|
| 12.12.654...125.1 |
$x^{12} - x^{11} - 202 x^{10} + 181 x^{9} + 13504 x^{8} - 9703 x^{7} - 357433 x^{6} + 244041 x^{5} + 3695580 x^{4} - 2877336 x^{3} - 11215260 x^{2} + 10066518 x - 576639$ |
$12$ |
(12, 0) |
$5^{9}\cdot 7^{10}\cdot 17^{9}$ |
$3$ |
$141.681309097$ |
$141.681309097028$ |
|
✓ |
? |
$C_{12}$ (as 12T1) |
$[4]$ |
$[2, 2, 4]$ |
$2$ |
$11$ |
$172250980.86$ |
$10$ |
|
| 12.0.210...261.2 |
$x^{12} - x^{11} + 76 x^{10} + 316 x^{9} + 2281 x^{8} + 25919 x^{7} + 234665 x^{6} + 258875 x^{5} + 11235736 x^{4} + 4616640 x^{3} + 184105549 x^{2} - 18829889 x + 1204021043$ |
$12$ |
(0, 6) |
$17^{9}\cdot 37^{11}$ |
$2$ |
$229.27406873$ |
$229.2740687298747$ |
✓ |
✓ |
? |
$C_{12}$ (as 12T1) |
$[9, 3492]$ |
$[9, 3492]$ |
$2$ |
$5$ |
$92664.46751452335$ |
$0$ |
|
| 20.0.958...161.2 |
$x^{20} - 3 x^{19} + 12 x^{18} - 35 x^{17} + 92 x^{16} - 209 x^{15} + 432 x^{14} - 807 x^{13} + 1350 x^{12} - 2080 x^{11} + 2889 x^{10} - 3596 x^{9} + 4057 x^{8} - 4070 x^{7} + 3535 x^{6} - 2544 x^{5} + 1493 x^{4} - 546 x^{3} + 125 x^{2} - 16 x + 1$ |
$20$ |
(0, 10) |
$17^{9}\cdot 97^{7}$ |
$2$ |
$17.7448413818$ |
$258.7709330334581$ |
|
|
? |
$C_2^9.S_5$ (as 20T674) |
trivial |
trivial |
$2$ |
$9$ |
$25210.0036513$ |
$0$ |
|
| 24.0.428...625.1 |
$x^{24} - x^{23} - 38 x^{22} - 52 x^{21} + 750 x^{20} + 3831 x^{19} - 8857 x^{18} - 93456 x^{17} + 229549 x^{16} + 677367 x^{15} + 979593 x^{14} - 16336924 x^{13} - 58223938 x^{12} + 253154180 x^{11} + 926966654 x^{10} - 2580181212 x^{9} + 4834961669 x^{8} - 11702176469 x^{7} + 417459147 x^{6} - 138577938 x^{5} + 289713268554 x^{4} - 803612318853 x^{3} + 885798206526 x^{2} - 424214540513 x + 81335485351$ |
$24$ |
(0, 12) |
$5^{18}\cdot 7^{20}\cdot 17^{18}$ |
$3$ |
$141.681309097$ |
$141.681309097028$ |
✓ |
✓ |
? |
$C_2\times C_{12}$ (as 24T2) |
not computed |
not computed |
$2$ |
$11$ |
|
|
|
