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 |
22.0.281...983.1 |
$x^{22} - 4 x^{21} + 6 x^{20} - 8 x^{19} + 15 x^{18} - 9 x^{17} - 28 x^{16} + 46 x^{15} - 14 x^{14} + 23 x^{13} + 13 x^{12} - 297 x^{11} + 488 x^{10} - 240 x^{9} + 28 x^{8} - 134 x^{7} + 194 x^{6} - 130 x^{5} + 72 x^{4} - 28 x^{3} + 8 x^{2} - 2 x + 1$ |
$22$ |
[0,11] |
$-\,167^{11}$ |
$1$ |
$12.9228479833$ |
$12.922847983320086$ |
|
✓ |
|
$D_{11}$ (as 22T2) |
trivial |
$2$ |
$10$ |
$1029.39037079$ |
22.0.578...471.1 |
$x^{22} - 11 x^{21} + 67 x^{20} - 285 x^{19} + 929 x^{18} - 2433 x^{17} + 5271 x^{16} - 9630 x^{15} + 15091 x^{14} - 20633 x^{13} + 25057 x^{12} - 27453 x^{11} + 27302 x^{10} - 24426 x^{9} + 19254 x^{8} - 13050 x^{7} + 7570 x^{6} - 3890 x^{5} + 1921 x^{4} - 927 x^{3} + 362 x^{2} - 87 x + 9$ |
$22$ |
[0,11] |
$-\,271^{11}$ |
$1$ |
$16.4620776332$ |
$16.46207763315433$ |
|
✓ |
|
$D_{11}$ (as 22T2) |
trivial |
$2$ |
$10$ |
$33482.7947011$ |
22.0.191...811.1 |
$x^{22} - 11 x^{21} + 66 x^{20} - 275 x^{19} + 847 x^{18} - 1980 x^{17} + 3454 x^{16} - 4070 x^{15} + 1100 x^{14} + 9482 x^{13} - 30690 x^{12} + 60224 x^{11} - 77803 x^{10} + 49665 x^{9} + 48642 x^{8} - 188375 x^{7} + 271315 x^{6} - 233860 x^{5} + 132748 x^{4} - 52624 x^{3} + 14960 x^{2} - 2816 x + 256$ |
$22$ |
[0,11] |
$-\,11^{31}$ |
$1$ |
$29.3370854252$ |
$29.33708542518522$ |
|
✓ |
|
$D_{11}$ (as 22T2) |
trivial |
$2$ |
$10$ |
$167976253.311$ |
22.22.174...553.1 |
$x^{22} - 44 x^{20} + 816 x^{18} - 8336 x^{16} + 51512 x^{14} - 199186 x^{12} + 481348 x^{10} - 702109 x^{8} + 569938 x^{6} - 220847 x^{4} + 35007 x^{2} - 1297$ |
$22$ |
[22,0] |
$1297^{11}$ |
$1$ |
$36.0138862107$ |
$36.013886210738214$ |
|
✓ |
|
$D_{11}$ (as 22T2) |
trivial |
$2$ |
$21$ |
$10757085477.8$ |
22.22.429...609.1 |
$x^{22} - 10 x^{21} - 29 x^{20} + 529 x^{19} - 69 x^{18} - 11577 x^{17} + 11850 x^{16} + 136774 x^{15} - 182767 x^{14} - 954992 x^{13} + 1314121 x^{12} + 4053245 x^{11} - 5095548 x^{10} - 10389210 x^{9} + 10902904 x^{8} + 15714269 x^{7} - 12265214 x^{6} - 13423268 x^{5} + 6295986 x^{4} + 5702075 x^{3} - 940712 x^{2} - 757690 x - 2957$ |
$22$ |
[22,0] |
$19^{11}\cdot 211^{11}$ |
$2$ |
$63.3166644731$ |
$63.31666447310692$ |
|
✓ |
? |
$D_{11}$ (as 22T2) |
trivial |
$2$ |
$21$ |
$8142471608830$ |