| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 20.0.596...344.3 |
$x^{20} - 8 x^{19} + 22 x^{18} + 6 x^{17} - 147 x^{16} + 198 x^{15} + 322 x^{14} - 948 x^{13} + 44 x^{12} + 1888 x^{11} - 1288 x^{10} - 1752 x^{9} + 2255 x^{8} + 522 x^{7} - 1580 x^{6} + 286 x^{5} + 591 x^{4} - 438 x^{3} + 132 x^{2} - 18 x + 1$ |
$20$ |
[0,10] |
$2^{30}\cdot 11^{18}$ |
$2$ |
$24.4792670483$ |
$33.15118318510912$ |
|
|
? |
$C_2^5:C_{10}$ (as 20T74) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$159636.716542$ |
| 20.0.129...472.1 |
$x^{20} + 58 x^{18} + 1361 x^{16} + 16518 x^{14} + 109704 x^{12} + 387784 x^{10} + 671055 x^{8} + 581130 x^{6} + 245619 x^{4} + 44550 x^{2} + 2673$ |
$20$ |
[0,10] |
$2^{30}\cdot 3^{5}\cdot 11^{17}\cdot 9901^{2}$ |
$4$ |
$71.7095497417$ |
|
✓ |
|
? |
$C_2^{10}.C_{10}$ (as 20T427) |
$[2, 690]$ |
$[2, 690]$ |
$2$ |
$9$ |
$8557350.88327$ |
| 20.12.410...576.1 |
$x^{20} - 264 x^{18} - 976 x^{17} + 26874 x^{16} + 202704 x^{15} - 909396 x^{14} - 15075000 x^{13} - 30990747 x^{12} + 380528352 x^{11} + 2672674146 x^{10} + 3920991528 x^{9} - 30769064512 x^{8} - 203355815760 x^{7} - 607022085426 x^{6} - 1074952849288 x^{5} - 1143465755040 x^{4} - 636507402480 x^{3} - 64156438152 x^{2} + 99783624600 x + 31046369877$ |
$20$ |
[12,4] |
$2^{30}\cdot 3^{20}\cdot 13^{4}\cdot 347^{4}\cdot 5145233^{2}$ |
$5$ |
$214.122013327$ |
|
|
|
? |
$C_2^{10}.C_3^4:S_5$ (as 20T1035) |
$[2]$ |
$[2, 2]$ |
$2$ |
$15$ |
$8321502208490000$ |
