| 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 |
| 16.4.419...000.1 |
$x^{16} - 4 x^{15} + 20 x^{13} - 20 x^{12} - 20 x^{11} + 100 x^{9} + 10 x^{8} - 300 x^{7} + 352 x^{6} - 68 x^{5} - 140 x^{4} + 100 x^{3} - 20 x + 5$ |
$16$ |
[4,6] |
$2^{40}\cdot 5^{18}$ |
$2$ |
$34.5872668041$ |
|
|
|
? |
$A_{16}$ (as 16T1953) |
trivial |
$2$ |
$9$ |
$2532102.39235$ |
| 16.4.419...000.2 |
$x^{16} - 4 x^{15} + 20 x^{13} - 40 x^{12} + 44 x^{11} - 16 x^{10} - 60 x^{9} + 290 x^{8} - 460 x^{7} + 336 x^{6} - 4 x^{5} - 160 x^{4} + 100 x^{3} - 20 x + 5$ |
$16$ |
[4,6] |
$2^{40}\cdot 5^{18}$ |
$2$ |
$34.5872668041$ |
|
|
|
? |
$A_{16}$ (as 16T1953) |
trivial |
$2$ |
$9$ |
$2751187.82391$ |
| 16.0.640...000.1 |
$x^{16} - 6 x^{15} + 30 x^{14} - 140 x^{13} + 530 x^{12} - 1522 x^{11} + 3262 x^{10} - 5080 x^{9} + 2940 x^{8} + 7670 x^{7} - 1494 x^{6} - 95116 x^{5} + 366350 x^{4} - 700350 x^{3} + 822650 x^{2} - 563280 x + 169955$ |
$16$ |
[0,8] |
$2^{34}\cdot 5^{28}$ |
$2$ |
$72.9266473722$ |
|
|
|
? |
$A_{16}$ (as 16T1953) |
trivial |
$2$ |
$7$ |
$2085624086.88$ |
| 16.0.180...000.1 |
$x^{16} - 32768 x + 61440$ |
$16$ |
[0,8] |
$2^{38}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$77.8103732791$ |
|
|
|
|
$A_{16}$ (as 16T1953) |
trivial |
$2$ |
$7$ |
$6244054534.66$ |
| 16.8.764...000.1 |
$x^{16} - 648 x^{14} + 21168 x^{12} + 39488904 x^{10} - 1225230300 x^{8} - 857661210000 x^{6} - 170131978800 x^{4} - 66238050412800 x^{3} + 41342070848400 x^{2} + 837176934680100$ |
$16$ |
[8,4] |
$2^{54}\cdot 3^{20}\cdot 5^{16}\cdot 7^{20}$ |
$4$ |
$2331.95603407$ |
|
|
|
|
$A_{16}$ (as 16T1953) |
trivial |
$2$ |
$11$ |
$35342415376800000000000$ |
| 16.12.769...000.1 |
$x^{16} + 40 x^{14} + 1820 x^{12} - 72436 x^{11} - 40040 x^{10} + 569140 x^{9} + 150150 x^{8} - 1138280 x^{7} - 168168 x^{6} + 724360 x^{5} + 60060 x^{4} - 139300 x^{3} - 5720 x^{2} + 5572 x + 65$ |
$16$ |
[12,2] |
$2^{26}\cdot 5^{16}\cdot 7^{12}\cdot 13^{24}$ |
$4$ |
$3110.87317312$ |
|
|
|
|
$A_{16}$ (as 16T1953) |
trivial |
$2$ |
$13$ |
$1784634715930000000000000$ |
