| 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 |
| 20.4.127...976.1 |
$x^{20} - 2 x^{18} + 9 x^{16} + 12 x^{14} - 6 x^{12} + 30 x^{8} - 60 x^{6} + 45 x^{4} - 14 x^{2} + 1$ |
$20$ |
[4,8] |
$2^{36}\cdot 3^{32}$ |
$2$ |
$20.195192618$ |
$31.655357399783927$ |
|
|
? |
$A_6$ (as 20T89) |
trivial |
$2$ |
$11$ |
$616938.09204$ |
| 20.4.241...376.1 |
$x^{20} - 2 x^{18} - 3 x^{16} - 24 x^{15} - 36 x^{14} - 48 x^{13} - 30 x^{12} + 72 x^{11} + 156 x^{10} + 72 x^{9} - 30 x^{8} - 48 x^{7} - 36 x^{6} - 24 x^{5} - 3 x^{4} - 2 x^{2} + 1$ |
$20$ |
[4,8] |
$2^{20}\cdot 3^{24}\cdot 13^{8}$ |
$3$ |
$20.8522461185$ |
$37.22560348698383$ |
|
|
? |
$A_6$ (as 20T89) |
trivial |
$2$ |
$11$ |
$851623.989731$ |
| 20.20.924...456.1 |
$x^{20} - 10 x^{19} - 21 x^{18} + 474 x^{17} - 319 x^{16} - 9484 x^{15} + 15084 x^{14} + 104446 x^{13} - 210818 x^{12} - 689278 x^{11} + 1526976 x^{10} + 2757056 x^{9} - 6237455 x^{8} - 6302156 x^{7} + 14029271 x^{6} + 6647840 x^{5} - 15500919 x^{4} - 535552 x^{3} + 6241202 x^{2} - 1836338 x + 130054$ |
$20$ |
[20,0] |
$2^{20}\cdot 13127^{8}$ |
$2$ |
$88.7761260694$ |
$257.2079596122173$ |
|
|
? |
$A_6$ (as 20T89) |
trivial |
$2$ |
$19$ |
$60561255281100$ |
| 20.20.451...296.1 |
$x^{20} - 70 x^{18} + 1899 x^{16} - 25784 x^{14} + 191379 x^{12} - 811774 x^{10} + 1994469 x^{8} - 2767108 x^{6} + 1987084 x^{4} - 583424 x^{2} + 15376$ |
$20$ |
[20,0] |
$2^{24}\cdot 7^{12}\cdot 13^{8}\cdot 47^{8}$ |
$4$ |
$96.0973259391$ |
$255.83755265742374$ |
|
|
|
$A_6$ (as 20T89) |
trivial |
$2$ |
$19$ |
$291227711962000$ |
