| 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 |
| 22.0.131...371.1 |
$x^{22} + 44 x^{18} - 22 x^{17} + 55 x^{16} + 121 x^{15} + 187 x^{14} + 11 x^{13} + 594 x^{12} + 328 x^{11} + 836 x^{10} + 770 x^{9} + 814 x^{8} + 528 x^{7} + 374 x^{6} + 143 x^{5} + 11 x^{4} - 33 x^{3} - 11 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,11^{27}$ |
$1$ |
$18.970240678$ |
$20.6986330715433$ |
|
|
? |
$F_{11}$ (as 22T4) |
trivial |
$2$ |
$10$ |
$302171.954912$ |
| 22.0.213...691.1 |
$x^{22} - 4 x^{21} + 7 x^{20} - 12 x^{19} + 24 x^{18} - 33 x^{17} + 48 x^{16} - 51 x^{15} + 12 x^{14} - 2 x^{13} + 44 x^{12} + 193 x^{11} - 198 x^{10} - 426 x^{9} + 168 x^{8} + 372 x^{7} + 15 x^{6} - 99 x^{5} - 36 x^{4} - 36 x^{3} - 9 x^{2} + 18 x + 9$ |
$22$ |
[0,11] |
$-\,3^{20}\cdot 11^{19}$ |
$2$ |
$21.5343212171$ |
$23.496328849167636$ |
|
|
? |
$F_{11}$ (as 22T4) |
trivial |
$2$ |
$10$ |
$1473183.5094$ |
| 22.22.185...008.1 |
$x^{22} - 11 x^{21} + 363 x^{19} - 924 x^{18} - 3795 x^{17} + 18029 x^{16} + 3872 x^{15} - 133661 x^{14} + 177265 x^{13} + 335500 x^{12} - 1066395 x^{11} + 478390 x^{10} + 1617539 x^{9} - 2643443 x^{8} + 1103938 x^{7} + 829103 x^{6} - 1076977 x^{5} + 385000 x^{4} - 737 x^{3} - 27214 x^{2} + 4235 x - 77$ |
$22$ |
[22,0] |
$2^{20}\cdot 7^{11}\cdot 11^{23}$ |
$3$ |
$60.9454613188$ |
$66.49824652345667$ |
|
|
? |
$F_{11}$ (as 22T4) |
trivial |
$2$ |
$21$ |
$8449061390020$ |
| 22.22.268...152.1 |
$x^{22} - 110 x^{20} - 66 x^{19} + 4180 x^{18} + 5016 x^{17} - 70653 x^{16} - 101112 x^{15} + 642477 x^{14} + 940962 x^{13} - 3450678 x^{12} - 4810374 x^{11} + 11274747 x^{10} + 14632332 x^{9} - 22009119 x^{8} - 27704688 x^{7} + 24186393 x^{6} + 32367456 x^{5} - 12274108 x^{4} - 21398190 x^{3} + 85745 x^{2} + 6107310 x + 1650137$ |
$22$ |
[22,0] |
$2^{33}\cdot 3^{20}\cdot 11^{23}$ |
$3$ |
$94.1933634644$ |
$102.77538915918468$ |
|
|
? |
$F_{11}$ (as 22T4) |
trivial |
$2$ |
$21$ |
$3109756315010000$ |
