| 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 |
| 20.4.255...064.1 |
$x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} - 11 x^{16} + 24 x^{15} - 42 x^{14} + 130 x^{13} - 131 x^{12} - 38 x^{11} + 36 x^{10} + 68 x^{9} + 23 x^{8} - 88 x^{7} + 32 x^{6} + 8 x^{5} - 10 x^{4} - 6 x^{3} + 4 x^{2} + 2 x - 1$ |
$20$ |
[4,8] |
$2^{30}\cdot 47^{8}$ |
$2$ |
$13.1942326218$ |
$25.146651949529847$ |
|
|
? |
$C_2^4:D_5$ (as 20T39) |
trivial |
trivial |
$2$ |
$11$ |
$1250.97415971$ |
| 20.4.162...264.1 |
$x^{20} - 4 x^{19} + 2 x^{18} + 8 x^{17} - 20 x^{16} + 34 x^{15} - 56 x^{14} + 98 x^{13} + 3 x^{12} - 330 x^{11} + 548 x^{10} - 616 x^{9} + 521 x^{8} - 136 x^{7} - 48 x^{6} + 24 x^{5} - 105 x^{4} + 70 x^{3} + 12 x^{2} - 8 x + 1$ |
$20$ |
[4,8] |
$2^{30}\cdot 79^{8}$ |
$2$ |
$16.2403666561$ |
$32.60204086987033$ |
|
|
? |
$C_2^4:D_5$ (as 20T39) |
trivial |
trivial |
$2$ |
$11$ |
$13779.1820468$ |
| 20.4.438...761.1 |
$x^{20} - 3 x^{19} + 11 x^{18} - 15 x^{17} + 32 x^{16} - 28 x^{15} + 61 x^{14} - 54 x^{13} + 88 x^{12} - 104 x^{11} + 77 x^{10} - 71 x^{9} + 75 x^{8} - 5 x^{7} - 92 x^{6} + 108 x^{5} - 77 x^{4} + 38 x^{3} - 15 x^{2} + 6 x - 1$ |
$20$ |
[4,8] |
$3^{8}\cdot 401^{8}$ |
$2$ |
$17.0649983623$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T39) |
trivial |
trivial |
$2$ |
$11$ |
$24127.4422646$ |
| 20.4.775...625.1 |
$x^{20} - 10 x^{19} + 49 x^{18} - 156 x^{17} + 349 x^{16} - 548 x^{15} + 531 x^{14} - 43 x^{13} - 1118 x^{12} + 3107 x^{11} - 6043 x^{10} + 9584 x^{9} - 11806 x^{8} + 10409 x^{7} - 5662 x^{6} + 778 x^{5} + 1194 x^{4} - 763 x^{3} + 257 x^{2} - 110 x + 43$ |
$20$ |
[4,8] |
$5^{8}\cdot 19^{8}\cdot 43^{8}$ |
$3$ |
$27.8276687056$ |
$63.914004725099176$ |
|
|
? |
$C_2^4:D_5$ (as 20T39) |
trivial |
trivial |
$2$ |
$11$ |
$4728089.36014$ |
| 20.20.291...376.1 |
$x^{20} - 39 x^{18} + 595 x^{16} - 4586 x^{14} + 19091 x^{12} - 42615 x^{10} + 48673 x^{8} - 26008 x^{6} + 5760 x^{4} - 520 x^{2} + 16$ |
$20$ |
[20,0] |
$2^{24}\cdot 1429^{8}$ |
$2$ |
$41.9999609216$ |
$106.92053123698928$ |
|
|
|
$C_2^4:D_5$ (as 20T39) |
trivial |
trivial |
$2$ |
$19$ |
$9627752284.8$ |
| 20.20.471...064.1 |
$x^{20} - 48 x^{18} + 904 x^{16} - 8514 x^{14} + 42524 x^{12} - 111066 x^{10} + 143033 x^{8} - 78876 x^{6} + 12226 x^{4} - 564 x^{2} + 1$ |
$20$ |
[20,0] |
$2^{30}\cdot 3^{8}\cdot 401^{8}$ |
$3$ |
$48.2671042517$ |
$127.22253810077638$ |
|
|
? |
$C_2^4:D_5$ (as 20T39) |
trivial |
$[2, 2, 2]$ |
$2$ |
$19$ |
$29983684192.7$ |
