| 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 |
| 22.0.137...419.1 |
$x^{22} - x^{11} + 3$ |
$22$ |
[0,11] |
$-\,3^{10}\cdot 11^{33}$ |
$2$ |
$60.1121588454$ |
$108.06982491208107$ |
|
|
✓ |
$C_{11}:F_{11}$ (as 22T11) |
trivial |
$2$ |
$10$ |
$107658885493$ |
| 22.0.220...963.1 |
$x^{22} - 33 x^{20} + 495 x^{18} - 4356 x^{16} + 24552 x^{14} - 91179 x^{12} - 81 x^{11} + 222156 x^{10} + 594 x^{9} - 343035 x^{8} + 3564 x^{7} + 313632 x^{6} - 31185 x^{5} - 147015 x^{4} + 53460 x^{3} + 29403 x^{2} - 18711 x + 3159$ |
$22$ |
[0,11] |
$-\,3^{21}\cdot 11^{32}$ |
$2$ |
$93.3656062498$ |
$130.24977457085998$ |
|
|
? |
$C_{11}:F_{11}$ (as 22T11) |
trivial |
$6$ |
$10$ |
$25313714393700$ |
| 22.0.220...963.2 |
$x^{22} - 33 x^{20} + 495 x^{18} - 4356 x^{16} + 24552 x^{14} - 91179 x^{12} - 51 x^{11} + 222156 x^{10} + 1584 x^{9} - 343035 x^{8} - 12276 x^{7} + 313632 x^{6} + 31185 x^{5} - 147015 x^{4} - 20790 x^{3} + 29403 x^{2} - 891 x + 2169$ |
$22$ |
[0,11] |
$-\,3^{21}\cdot 11^{32}$ |
$2$ |
$93.36560624983609$ |
$130.24977457085998$ |
|
|
? |
$C_{11}:F_{11}$ (as 22T11) |
trivial |
$6$ |
$10$ |
$27838969049290.547$ |
| 22.22.391...633.1 |
$x^{22} - 66 x^{20} + 1881 x^{18} - 30294 x^{16} + 302940 x^{14} - 1945944 x^{12} - 130 x^{11} + 8027019 x^{10} + 4290 x^{9} - 20640906 x^{8} - 51480 x^{7} + 30961359 x^{6} + 270270 x^{5} - 23816430 x^{4} - 579150 x^{3} + 7144929 x^{2} + 347490 x - 561087$ |
$22$ |
[22,0] |
$3^{10}\cdot 11^{32}\cdot 73^{11}$ |
$3$ |
$460.561599$ |
$1058.6467793270256$ |
|
|
? |
$C_{11}:F_{11}$ (as 22T11) |
trivial |
$2$ |
$21$ |
$189982300459000000000000$ |
| 22.22.199...993.1 |
$x^{22} - 330 x^{20} + 42669 x^{18} - 2784870 x^{16} + 100074348 x^{14} - 2070767160 x^{12} - 62767890 x^{11} + 25255546767 x^{10} + 2424565242 x^{9} - 180180897930 x^{8} - 34101623160 x^{7} + 712727063631 x^{6} + 211943243358 x^{5} - 1357714398150 x^{4} - 577327236750 x^{3} + 841782926853 x^{2} + 648146044458 x + 122440026897$ |
$22$ |
[22,0] |
$3^{21}\cdot 11^{33}\cdot 31^{10}$ |
$3$ |
$495.923435263$ |
$2681.5644401925556$ |
|
|
? |
$C_{11}:F_{11}$ (as 22T11) |
trivial |
$2$ |
$21$ |
$307607921484000000000000$ |
