| 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 |
| 22.0.129...000.1 |
$x^{22} - 2 x^{21} + 9 x^{20} + 110 x^{19} - 145 x^{18} + 762 x^{17} + 4906 x^{16} - 4172 x^{15} + 31155 x^{14} + 134890 x^{13} - 45851 x^{12} + 700482 x^{11} + 2422871 x^{10} + 334550 x^{9} + 8937300 x^{8} + 25194460 x^{7} + 8234605 x^{6} + 63496890 x^{5} + 134263875 x^{4} - 29801250 x^{3} + 8853525 x^{2} + 252450 x + 8100$ |
$22$ |
[0,11] |
$-\,2^{36}\cdot 3^{17}\cdot 5^{36}$ |
$3$ |
$101.169182873$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T27) |
trivial |
$6$ |
$10$ |
$174561035136000$ |
| 22.6.538...000.1 |
$x^{22} - 4 x^{21} - 16 x^{20} + 120 x^{19} + 115 x^{18} - 1424 x^{17} - 504 x^{16} + 14264 x^{15} - 26035 x^{14} - 18220 x^{13} + 156506 x^{12} - 302224 x^{11} + 301914 x^{10} - 196640 x^{9} + 146020 x^{8} + 7356 x^{7} - 682924 x^{6} + 1599944 x^{5} - 1573820 x^{4} + 564960 x^{3} + 82836 x^{2} - 91944 x + 21744$ |
$22$ |
[6,8] |
$2^{36}\cdot 3^{16}\cdot 5^{39}$ |
$3$ |
$119.860201654$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T27) |
trivial |
$2$ |
$13$ |
$961054672237000$ |
| 22.0.110...000.1 |
$x^{22} + 14 x^{20} - 35 x^{18} + 680 x^{16} + 4390 x^{14} + 69824 x^{12} - 549974 x^{10} + 4556900 x^{8} - 480575 x^{6} + 148121250 x^{4} + 9839025 x^{2} + 8100$ |
$22$ |
[0,11] |
$-\,2^{44}\cdot 3^{16}\cdot 5^{36}$ |
$3$ |
$123.830140446$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T27) |
trivial |
$4$ |
$10$ |
$4785285337040000$ |
| 22.6.330...000.1 |
$x^{22} - 4 x^{21} - 39 x^{20} + 40 x^{19} + 980 x^{18} + 24 x^{17} - 8096 x^{16} - 2536 x^{15} + 15180 x^{14} - 287440 x^{13} + 74008 x^{12} + 2140848 x^{11} + 850628 x^{10} - 11080640 x^{9} + 58622580 x^{8} - 105917632 x^{7} - 101665472 x^{6} + 458745408 x^{5} - 596640480 x^{4} + 217405440 x^{3} + 370003392 x^{2} - 1271386368 x + 1866411072$ |
$22$ |
[6,8] |
$2^{44}\cdot 3^{17}\cdot 5^{36}$ |
$3$ |
$130.170836363$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T27) |
trivial |
$2$ |
$13$ |
$12955926374500000$ |
| 22.0.380...952.1 |
$x^{22} + 5481 x^{20} + 12830103 x^{18} + 16760085111 x^{16} + 13399040743938 x^{14} + 6763660792069842 x^{12} + 2145714219228954438 x^{10} + 411884307283617185094 x^{8} + 43869578581905971661981 x^{6} + 2110663170149138275578021 x^{4} + 20751898885985795263838019 x^{2} + 9655790329507504656039075$ |
$22$ |
[0,11] |
$-\,2^{48}\cdot 3^{23}\cdot 337^{8}\cdot 310501^{8}$ |
$4$ |
$11799.2191484$ |
|
✓ |
|
|
$C_2\times M_{11}$ (as 22T27) |
not computed |
$6$ |
$10$ |
|
| 22.22.243...928.1 |
$x^{22} - 5481 x^{20} + 12830103 x^{18} - 16760085111 x^{16} + 13399040743938 x^{14} - 6763660792069842 x^{12} + 2145714219228954438 x^{10} - 411884307283617185094 x^{8} + 43869578581905971661981 x^{6} - 2110663170149138275578021 x^{4} + 20751898885985795263838019 x^{2} - 9655790329507504656039075$ |
$22$ |
[22,0] |
$2^{54}\cdot 3^{23}\cdot 337^{8}\cdot 310501^{8}$ |
$4$ |
$14254.5121054$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T27) |
not computed |
$2$ |
$21$ |
|
