| 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 |
| 22.0.615...816.1 |
$x^{22} - 11 x^{20} + 33 x^{18} - 66 x^{17} - 44 x^{16} + 308 x^{15} + 253 x^{14} - 44 x^{13} + 913 x^{12} + 1840 x^{11} + 1309 x^{10} - 814 x^{9} + 2904 x^{8} + 4752 x^{7} + 7117 x^{6} - 4004 x^{5} + 825 x^{4} - 44 x^{3} + 6721 x^{2} - 5434 x + 1644$ |
$22$ |
[0,11] |
$-\,2^{36}\cdot 11^{23}$ |
$2$ |
$38.1349564411$ |
|
|
|
|
$\PGL(2,11)$ (as 22T14) |
trivial |
$2$ |
$10$ |
$984813482.893$ |
| 22.0.366...000.1 |
$x^{22} - 11 x^{21} + 55 x^{20} - 154 x^{19} + 187 x^{18} + 363 x^{17} - 2255 x^{16} + 5016 x^{15} - 5082 x^{14} - 2046 x^{13} + 13442 x^{12} - 15368 x^{11} + 6358 x^{10} - 33242 x^{9} + 159434 x^{8} - 361944 x^{7} + 546073 x^{6} - 684519 x^{5} + 779031 x^{4} - 754798 x^{3} + 577951 x^{2} - 314545 x + 86485$ |
$22$ |
[0,11] |
$-\,2^{20}\cdot 5^{8}\cdot 11^{23}$ |
$3$ |
$41.3583552595$ |
|
|
|
|
$\PGL(2,11)$ (as 22T14) |
trivial |
$2$ |
$10$ |
$3435709897.46$ |
| 22.6.266...312.1 |
$x^{22} - 11 x^{21} + 44 x^{20} - 44 x^{19} - 231 x^{18} + 825 x^{17} - 550 x^{16} - 1540 x^{15} - 968 x^{14} + 23056 x^{13} - 65956 x^{12} + 98910 x^{11} - 90409 x^{10} + 22077 x^{9} + 172414 x^{8} - 515240 x^{7} + 704264 x^{6} - 400400 x^{5} - 37840 x^{4} + 72512 x^{3} + 32560 x^{2} + 3696 x - 9888$ |
$22$ |
[6,8] |
$2^{24}\cdot 3^{11}\cdot 11^{23}$ |
$3$ |
$45.2569938044$ |
|
|
|
|
$\PGL(2,11)$ (as 22T14) |
trivial |
$2$ |
$13$ |
$158674344921$ |
| 22.6.113...125.1 |
$x^{22} - 9 x^{21} + 41 x^{20} - 140 x^{19} + 383 x^{18} - 720 x^{17} + 530 x^{16} + 1506 x^{15} - 7373 x^{14} + 22033 x^{13} - 51771 x^{12} + 76979 x^{11} - 19458 x^{10} - 188822 x^{9} + 431163 x^{8} - 422621 x^{7} + 84439 x^{6} + 244344 x^{5} - 239399 x^{4} + 37800 x^{3} + 53515 x^{2} - 17850 x - 6300$ |
$22$ |
[6,8] |
$5^{8}\cdot 7^{15}\cdot 11^{19}$ |
$3$ |
$53.6733511187$ |
$86.67991835373819$ |
|
|
? |
$\PGL(2,11)$ (as 22T14) |
trivial |
$2$ |
$13$ |
$118924316463$ |
| 22.22.311...032.1 |
$x^{22} - 187 x^{20} - 198 x^{19} + 14278 x^{18} + 29062 x^{17} - 561253 x^{16} - 1673936 x^{15} + 11663817 x^{14} + 47695890 x^{13} - 112009051 x^{12} - 695875072 x^{11} + 142254739 x^{10} + 4865875674 x^{9} + 4465613977 x^{8} - 13937355960 x^{7} - 24242610414 x^{6} + 8705909278 x^{5} + 39169758474 x^{4} + 16385057678 x^{3} - 12622704501 x^{2} - 10348950480 x - 1841628392$ |
$22$ |
[22,0] |
$2^{24}\cdot 3^{11}\cdot 11^{27}\cdot 41^{8}$ |
$4$ |
$270.082648725$ |
|
|
|
|
$\PGL(2,11)$ (as 22T14) |
trivial |
$2$ |
$21$ |
$800234332751000000000$ |
