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 |
16.0.149...296.1 |
$x^{16} - 12 x^{14} + 72 x^{12} - 288 x^{10} + 927 x^{8} - 2592 x^{6} + 5832 x^{4} - 8748 x^{2} + 6561$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}$ |
$2$ |
$18.2360564556$ |
$18.23605645563822$ |
✓ |
✓ |
? |
$Q_8\times C_2$ (as 16T7) |
trivial |
$24$ |
$7$ |
$22843.7922823$ |
16.0.179...625.1 |
$x^{16} - 2 x^{15} - 2 x^{14} + 7 x^{13} + 78 x^{12} + 58 x^{11} + 1189 x^{10} + 5376 x^{9} + 12238 x^{8} + 47763 x^{7} + 203726 x^{6} + 650220 x^{5} + 1486133 x^{4} + 2191586 x^{3} + 1857092 x^{2} + 783912 x + 126736$ |
$16$ |
[0,8] |
$3^{12}\cdot 5^{12}\cdot 7^{12}$ |
$3$ |
$32.8013693377$ |
$32.801369337662685$ |
✓ |
✓ |
|
$Q_8\times C_2$ (as 16T7) |
$[2, 2, 2]$ |
$6$ |
$7$ |
$103783.231276$ |
16.0.584...000.1 |
$x^{16} + 28 x^{14} - 24 x^{13} + 298 x^{12} - 312 x^{11} + 1600 x^{10} - 2040 x^{9} + 4399 x^{8} - 4800 x^{7} + 4912 x^{6} - 4584 x^{5} - 5714 x^{4} + 19320 x^{3} - 8468 x^{2} - 8424 x + 6814$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$40.7770618763$ |
$40.77706187633094$ |
✓ |
✓ |
? |
$Q_8\times C_2$ (as 16T7) |
$[2, 8]$ |
$2$ |
$7$ |
$313644.780941$ |
16.16.584...000.1 |
$x^{16} - 8 x^{15} - 4 x^{14} + 168 x^{13} - 250 x^{12} - 1048 x^{11} + 2476 x^{10} + 2184 x^{9} - 8435 x^{8} + 528 x^{7} + 11344 x^{6} - 6152 x^{5} - 4252 x^{4} + 4680 x^{3} - 1336 x^{2} + 104 x + 1$ |
$16$ |
[16,0] |
$2^{48}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$40.7770618763$ |
$40.77706187633094$ |
|
✓ |
? |
$Q_8\times C_2$ (as 16T7) |
trivial |
$2$ |
$15$ |
$58665083.8134$ |
16.0.584...000.2 |
$x^{16} + 36 x^{14} + 396 x^{12} + 1944 x^{10} + 4743 x^{8} + 5832 x^{6} + 3564 x^{4} + 972 x^{2} + 81$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$40.7770618763$ |
$40.77706187633094$ |
✓ |
✓ |
? |
$Q_8\times C_2$ (as 16T7) |
$[2, 6, 6]$ |
$2$ |
$7$ |
$15197.4244561$ |
16.0.584...000.3 |
$x^{16} - 20 x^{14} - 24 x^{13} + 178 x^{12} + 408 x^{11} - 200 x^{10} - 1320 x^{9} - 113 x^{8} + 3840 x^{7} + 11128 x^{6} + 20184 x^{5} + 32086 x^{4} + 39336 x^{3} + 53260 x^{2} + 32616 x + 27646$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$40.7770618763$ |
$40.77706187633094$ |
✓ |
✓ |
? |
$Q_8\times C_2$ (as 16T7) |
$[6, 24]$ |
$2$ |
$7$ |
$45687.5845647$ |
16.0.584...000.4 |
$x^{16} - 60 x^{14} + 1800 x^{12} - 36000 x^{10} + 579375 x^{8} - 8100000 x^{6} + 91125000 x^{4} - 683437500 x^{2} + 2562890625$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$40.7770618763$ |
$40.77706187633094$ |
✓ |
✓ |
? |
$Q_8\times C_2$ (as 16T7) |
$[2, 6, 6]$ |
$24$ |
$7$ |
$313644.780941$ |
16.0.862...096.1 |
$x^{16} + 4 x^{14} - 24 x^{13} + 70 x^{12} - 168 x^{11} + 340 x^{10} + 624 x^{9} + 973 x^{8} - 9984 x^{7} + 12208 x^{6} - 22224 x^{5} + 60292 x^{4} - 12288 x^{3} + 76792 x^{2} + 44064 x + 51937$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}\cdot 7^{8}$ |
$3$ |
$48.2480702762$ |
$48.24807027615272$ |
✓ |
✓ |
? |
$Q_8\times C_2$ (as 16T7) |
$[2, 10, 10]$ |
$2$ |
$7$ |
$32719.5368105$ |
16.16.862...096.1 |
$x^{16} - 44 x^{14} - 24 x^{13} + 670 x^{12} + 552 x^{11} - 4484 x^{10} - 4272 x^{9} + 13957 x^{8} + 14208 x^{7} - 19736 x^{6} - 20784 x^{5} + 11692 x^{4} + 13344 x^{3} - 1664 x^{2} - 3024 x - 383$ |
$16$ |
[16,0] |
$2^{48}\cdot 3^{12}\cdot 7^{8}$ |
$3$ |
$48.2480702762$ |
$48.24807027615272$ |
|
✓ |
? |
$Q_8\times C_2$ (as 16T7) |
trivial |
$2$ |
$15$ |
$155691205.876$ |