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 |
22.0.497...411.2 |
$x^{22} - 44 x^{19} - 66 x^{18} + 704 x^{17} + 2673 x^{16} + 2706 x^{15} - 15686 x^{14} - 58828 x^{13} - 64306 x^{12} + 193023 x^{11} + 804166 x^{10} + 1061170 x^{9} - 198088 x^{8} - 4704557 x^{7} - 9674137 x^{6} - 8569429 x^{5} + 12214961 x^{4} + 48915955 x^{3} + 96352960 x^{2} + 90503600 x + 76515613$ |
$22$ |
[0,11] |
$-\,11^{41}$ |
$1$ |
$87.252378947$ |
$106.37578746793879$ |
|
|
? |
$C_{11}\times D_{11}$ (as 22T7) |
trivial |
$2$ |
$10$ |
$1536390870260$ |
22.0.497...411.3 |
$x^{22} - 44 x^{19} - 66 x^{18} + 220 x^{17} + 2673 x^{16} - 7216 x^{15} + 18073 x^{14} - 24948 x^{13} - 71324 x^{12} + 287634 x^{11} + 372922 x^{10} - 259182 x^{9} + 1065273 x^{8} + 873180 x^{7} + 548185 x^{6} + 2092728 x^{5} + 2668061 x^{4} + 545116 x^{3} + 4041697 x^{2} + 459635 x + 2001481$ |
$22$ |
[0,11] |
$-\,11^{41}$ |
$1$ |
$87.252378947$ |
$106.37578746793879$ |
|
|
? |
$C_{11}\times D_{11}$ (as 22T7) |
trivial |
$2$ |
$10$ |
$1205305578130$ |
22.0.497...411.4 |
$x^{22} - 44 x^{19} - 66 x^{18} + 462 x^{17} - 957 x^{16} - 2497 x^{15} + 24365 x^{14} - 60159 x^{13} + 116831 x^{12} - 523132 x^{11} + 1674640 x^{10} - 1138973 x^{9} - 284361 x^{8} - 138501 x^{7} + 1786136 x^{6} - 1167254 x^{5} - 1470744 x^{4} + 2051203 x^{3} - 372262 x^{2} - 594880 x + 350843$ |
$22$ |
[0,11] |
$-\,11^{41}$ |
$1$ |
$87.25237894697881$ |
$106.37578746793879$ |
|
|
? |
$C_{11}\times D_{11}$ (as 22T7) |
trivial |
$2$ |
$10$ |
$1499594510743.29$ |