| 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 |
| 20.2.117...000.1 |
$x^{20} - 6 x^{19} + 8 x^{18} + 40 x^{17} - 121 x^{16} - 62 x^{15} + 378 x^{14} + 6 x^{13} - 17 x^{12} - 92 x^{11} - 1660 x^{10} - 888 x^{9} + 2431 x^{8} + 2410 x^{7} - 914 x^{6} + 714 x^{5} + 2194 x^{4} - 348 x^{3} - 1052 x^{2} - 208 x - 169$ |
$20$ |
[2,9] |
$-\,2^{30}\cdot 5^{10}\cdot 47^{9}$ |
$3$ |
$35.7663013785$ |
$56.69880756905025$ |
|
|
? |
$C_5:S_4$ (as 20T33) |
trivial |
$2$ |
$10$ |
$42178724.6457$ |
| 20.0.509...689.1 |
$x^{20} - x^{19} + 5 x^{18} - 60 x^{17} + 124 x^{16} - 29 x^{15} + 306 x^{14} - 1060 x^{13} - 1828 x^{12} + 5534 x^{11} + 4106 x^{10} - 11239 x^{9} - 7296 x^{8} + 11779 x^{7} + 53197 x^{6} - 108261 x^{5} + 84143 x^{4} - 20458 x^{3} + 1348 x^{2} - 321 x + 87$ |
$20$ |
[0,10] |
$3^{19}\cdot 547^{9}$ |
$2$ |
$48.4573308936$ |
$84.26265266785381$ |
|
|
|
$C_5:S_4$ (as 20T33) |
trivial |
$2$ |
$9$ |
$3446960700.47$ |
| 20.0.534...864.1 |
$x^{20} - 4 x^{19} - 19 x^{18} + 26 x^{17} + 479 x^{16} - 772 x^{15} - 2520 x^{14} - 116 x^{13} + 40588 x^{12} - 58040 x^{11} - 19094 x^{10} - 171860 x^{9} + 886820 x^{8} - 2650572 x^{7} + 1511325 x^{6} + 8671992 x^{5} + 14258529 x^{4} + 2519982 x^{3} + 11292687 x^{2} + 5302152 x + 10205433$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{19}\cdot 547^{9}$ |
$3$ |
$96.9146617872$ |
$168.52530533570763$ |
|
|
|
$C_5:S_4$ (as 20T33) |
$[2]$ |
$2$ |
$9$ |
$2335295541180$ |
