| 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 |
| 22.0.298...003.1 |
$x^{22} - x^{21} - 4 x^{20} + 3 x^{19} + 11 x^{18} - 6 x^{17} - 18 x^{16} + 2 x^{15} + 26 x^{14} - 8 x^{13} - 18 x^{12} + 23 x^{11} + 12 x^{10} - 27 x^{9} - 30 x^{8} + 23 x^{7} + 19 x^{6} + 3 x^{5} + 5 x^{4} - 26 x^{3} + 8 x^{2} + 2 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 167^{10}$ |
$2$ |
$17.7372503584$ |
$22.38302928559939$ |
|
|
|
$D_{22}$ (as 22T3) |
trivial |
$6$ |
$10$ |
$138999.076948$ |
| 22.0.707...496.1 |
$x^{22} - 9 x^{20} + 37 x^{18} - 94 x^{16} + 166 x^{14} - 214 x^{12} + 207 x^{10} - 149 x^{8} + 81 x^{6} - 34 x^{4} + 12 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{10}$ |
$2$ |
$20.4812125382$ |
$25.84569596664017$ |
|
|
? |
$D_{22}$ (as 22T3) |
trivial |
$4$ |
$10$ |
$743434.07758$ |
| 22.2.499...501.1 |
$x^{22} - 2 x^{21} + 5 x^{20} - 4 x^{19} + 4 x^{18} - 14 x^{17} + 63 x^{16} - 228 x^{15} + 497 x^{14} - 686 x^{13} + 792 x^{12} - 793 x^{11} + 1821 x^{10} - 3315 x^{9} + 78 x^{8} + 1215 x^{7} + 1528 x^{6} + 168 x^{5} - 351 x^{4} - 826 x^{3} - 4 x^{2} + 39 x - 5$ |
$22$ |
[2,10] |
$3^{11}\cdot 167^{11}$ |
$2$ |
$22.3830292856$ |
$22.38302928559939$ |
|
|
? |
$D_{22}$ (as 22T3) |
trivial |
$2$ |
$11$ |
$1424457.4515$ |
| 22.2.823...125.1 |
$x^{22} - x^{21} + 14 x^{20} - 11 x^{19} + 83 x^{18} - 46 x^{17} + 290 x^{16} - 162 x^{15} + 710 x^{14} - 312 x^{13} + 966 x^{12} - 47 x^{11} + 930 x^{10} + 311 x^{9} + 628 x^{8} + 309 x^{7} + 259 x^{6} + 141 x^{5} + 87 x^{4} + 44 x^{3} + 16 x^{2} + 2 x - 1$ |
$22$ |
[2,10] |
$5^{11}\cdot 167^{10}$ |
$2$ |
$22.8986917485$ |
$28.89636655359978$ |
|
|
? |
$D_{22}$ (as 22T3) |
trivial |
$2$ |
$11$ |
$1079623.65534$ |
| 22.0.238...203.1 |
$x^{22} - 5 x^{21} + 29 x^{20} - 88 x^{19} + 339 x^{18} - 873 x^{17} + 2485 x^{16} - 4849 x^{15} + 10031 x^{14} - 14957 x^{13} + 25292 x^{12} - 30651 x^{11} + 43592 x^{10} - 40589 x^{9} + 48954 x^{8} - 34229 x^{7} + 36905 x^{6} - 15206 x^{5} + 13618 x^{4} - 596 x^{3} + 3281 x^{2} - 280 x + 25$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 1297^{10}$ |
$2$ |
$45.0332555075$ |
$62.37788069500277$ |
✓ |
|
|
$D_{22}$ (as 22T3) |
$[241]$ |
$6$ |
$10$ |
$15484188.8463$ |
| 22.0.203...619.1 |
$x^{22} - 11 x^{21} + 90 x^{20} - 515 x^{19} + 2404 x^{18} - 9153 x^{17} + 29609 x^{16} - 81730 x^{15} + 195276 x^{14} - 404718 x^{13} + 730608 x^{12} - 1147506 x^{11} + 1565057 x^{10} - 1843981 x^{9} + 1862690 x^{8} - 1595475 x^{7} + 1141091 x^{6} - 667142 x^{5} + 309476 x^{4} - 109065 x^{3} + 27307 x^{2} - 4313 x + 323$ |
$22$ |
[0,11] |
$-\,19^{11}\cdot 211^{10}$ |
$2$ |
$49.644235326$ |
$63.31666447310692$ |
✓ |
|
? |
$D_{22}$ (as 22T3) |
$[23]$ |
$2$ |
$10$ |
$294726306.155$ |
| 22.22.657...125.1 |
$x^{22} - x^{21} - 44 x^{20} + 27 x^{19} + 766 x^{18} - 243 x^{17} - 6909 x^{16} + 676 x^{15} + 35042 x^{14} + 1614 x^{13} - 100878 x^{12} - 11106 x^{11} + 158022 x^{10} + 13148 x^{9} - 122742 x^{8} + 4085 x^{7} + 40785 x^{6} - 4986 x^{5} - 4409 x^{4} + 486 x^{3} + 133 x^{2} - 5 x - 1$ |
$22$ |
[22,0] |
$5^{11}\cdot 1297^{10}$ |
$2$ |
$58.1376828687$ |
$80.52949770115296$ |
|
|
? |
$D_{22}$ (as 22T3) |
trivial |
$2$ |
$21$ |
$3460009379450$ |
| 22.22.115...008.1 |
$x^{22} - 10 x^{21} - 5 x^{20} + 348 x^{19} - 782 x^{18} - 3756 x^{17} + 14826 x^{16} + 11078 x^{15} - 105193 x^{14} + 51552 x^{13} + 328609 x^{12} - 383636 x^{11} - 385652 x^{10} + 777826 x^{9} - 51957 x^{8} - 501290 x^{7} + 287700 x^{6} - 24976 x^{5} - 17977 x^{4} + 4628 x^{3} - 302 x^{2} - 8 x + 1$ |
$22$ |
[22,0] |
$2^{33}\cdot 1297^{10}$ |
$2$ |
$73.5389982999$ |
$101.86265262597475$ |
|
|
|
$D_{22}$ (as 22T3) |
trivial |
$2$ |
$21$ |
$40553964823400$ |
