| 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 |
| 22.0.458...875.1 |
$x^{22} - x^{21} + 21 x^{20} - 40 x^{19} + 325 x^{18} - 597 x^{17} + 2667 x^{16} - 4827 x^{15} + 15510 x^{14} - 22580 x^{13} + 42773 x^{12} - 36183 x^{11} + 50648 x^{10} - 29240 x^{9} + 42285 x^{8} - 15537 x^{7} + 18462 x^{6} - 4332 x^{5} + 5605 x^{4} - 760 x^{3} + 441 x^{2} + 44 x + 16$ |
$22$ |
[0,11] |
$-\,3^{21}\cdot 5^{20}\cdot 11^{16}$ |
$3$ |
$70.5078870181$ |
$83.94123407222604$ |
✓ |
|
? |
$C_{11}:C_{10}$ (as 22T5) |
$[93]$ |
$6$ |
$10$ |
$12475736338.1$ |
| 22.22.763...125.1 |
$x^{22} - 9 x^{21} - 16 x^{20} + 315 x^{19} - 170 x^{18} - 4323 x^{17} + 5307 x^{16} + 30348 x^{15} - 44775 x^{14} - 120705 x^{13} + 180264 x^{12} + 285909 x^{11} - 379689 x^{10} - 406980 x^{9} + 414510 x^{8} + 326688 x^{7} - 216132 x^{6} - 122958 x^{5} + 46165 x^{4} + 13185 x^{3} - 3964 x^{2} - 9 x + 19$ |
$22$ |
[22,0] |
$3^{20}\cdot 5^{21}\cdot 11^{16}$ |
$3$ |
$72.1641887887$ |
$85.91309878831125$ |
|
|
? |
$C_{11}:C_{10}$ (as 22T5) |
trivial |
$2$ |
$21$ |
$73548357254400$ |
| 22.22.610...625.1 |
$x^{22} - 6 x^{21} - 78 x^{20} + 510 x^{19} + 2025 x^{18} - 15807 x^{17} - 18933 x^{16} + 225726 x^{15} + 15870 x^{14} - 1647660 x^{13} + 763635 x^{12} + 6354345 x^{11} - 4837830 x^{10} - 12475935 x^{9} + 12236985 x^{8} + 10413186 x^{7} - 13357071 x^{6} - 1127478 x^{5} + 4770660 x^{4} - 952095 x^{3} - 312471 x^{2} + 60561 x + 9498$ |
$22$ |
[22,0] |
$3^{21}\cdot 5^{20}\cdot 11^{19}$ |
$3$ |
$97.7790454788$ |
$106.68776526385035$ |
|
|
? |
$C_{11}:C_{10}$ (as 22T5) |
trivial |
$2$ |
$21$ |
$6302138028050000$ |
