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 |
20.0.428...000.1 |
$x^{20} - 3 x^{19} + 2 x^{18} + 6 x^{17} - 14 x^{16} + 7 x^{15} + 10 x^{14} - 12 x^{13} - 11 x^{12} + 14 x^{11} + 30 x^{10} - 56 x^{9} + 16 x^{8} + 38 x^{7} + 8 x^{6} - 106 x^{5} + 111 x^{4} - 25 x^{3} - 40 x^{2} + 25$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{15}\cdot 11^{8}$ |
$3$ |
$15.1917768977$ |
$39.642921082121845$ |
|
|
? |
$C_5:F_5$ (as 20T27) |
trivial |
$10$ |
$9$ |
$33038.0055622$ |
20.0.255...125.1 |
$x^{20} - 5 x^{19} + 15 x^{18} - 45 x^{17} + 120 x^{16} - 275 x^{15} + 595 x^{14} - 1160 x^{13} + 2010 x^{12} - 3225 x^{11} + 4830 x^{10} - 6490 x^{9} + 7495 x^{8} - 7250 x^{7} + 5800 x^{6} - 3800 x^{5} + 2005 x^{4} - 825 x^{3} + 250 x^{2} - 50 x + 5$ |
$20$ |
[0,10] |
$5^{23}\cdot 11^{8}$ |
$2$ |
$16.6101126958$ |
$43.34406641151844$ |
|
|
|
$C_5:F_5$ (as 20T27) |
trivial |
$10$ |
$9$ |
$56436.2432248$ |
20.20.466...125.1 |
$x^{20} - 5 x^{19} - 75 x^{18} + 515 x^{17} + 1095 x^{16} - 15246 x^{15} + 20785 x^{14} + 128000 x^{13} - 442755 x^{12} + 134935 x^{11} + 1404121 x^{10} - 2101065 x^{9} - 301350 x^{8} + 2772445 x^{7} - 1487715 x^{6} - 957916 x^{5} + 1069270 x^{4} - 110925 x^{3} - 172410 x^{2} + 65070 x - 6759$ |
$20$ |
[20,0] |
$3^{10}\cdot 5^{31}\cdot 19^{8}$ |
$3$ |
$68.1499551662$ |
$251.70081117843628$ |
|
|
|
$C_5:F_5$ (as 20T27) |
trivial |
$2$ |
$19$ |
$1820507440260$ |
20.20.185...125.1 |
$x^{20} - 6 x^{19} - 83 x^{18} + 486 x^{17} + 2769 x^{16} - 15396 x^{15} - 49362 x^{14} + 247119 x^{13} + 530238 x^{12} - 2205189 x^{11} - 3537582 x^{10} + 11214798 x^{9} + 14146635 x^{8} - 31935498 x^{7} - 31272909 x^{6} + 47209428 x^{5} + 32146026 x^{4} - 30429375 x^{3} - 8641610 x^{2} + 6935985 x - 727355$ |
$20$ |
[20,0] |
$3^{16}\cdot 5^{15}\cdot 7^{10}\cdot 29^{8}$ |
$4$ |
$81.9280703769$ |
$315.05902548913$ |
|
|
|
$C_5:F_5$ (as 20T27) |
trivial |
$2$ |
$19$ |
$22123034286000$ |