| 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 |
Unit signature rank |
Max $p$ |
| 16.4.239...736.3 |
$x^{16} - 60 x^{12} - 288 x^{10} - 666 x^{8} - 864 x^{6} - 540 x^{4} + 81$ |
$16$ |
(4, 6) |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_4^2:C_2$ (as 16T27) |
trivial |
$[2]$ |
$2$ |
$9$ |
$39650.6287333$ |
$3$ |
|
| 16.4.957...944.1 |
$x^{16} - 8 x^{15} + 16 x^{14} + 24 x^{13} - 156 x^{12} + 352 x^{11} - 216 x^{10} - 1008 x^{9} + 2740 x^{8} - 3296 x^{7} + 2032 x^{6} - 256 x^{5} - 624 x^{4} + 576 x^{3} - 256 x^{2} + 64 x - 8$ |
$16$ |
(4, 6) |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.6492393325$ |
$23.64923933252054$ |
|
|
? |
$C_4^2:C_2$ (as 16T27) |
trivial |
$[2]$ |
$2$ |
$9$ |
$84674.9713264$ |
$3$ |
|
| 16.0.228...000.1 |
$x^{16} + 40 x^{14} + 518 x^{12} + 3160 x^{10} + 10099 x^{8} + 17000 x^{6} + 14042 x^{4} + 4520 x^{2} + 121$ |
$16$ |
(0, 8) |
$2^{44}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$51.2744407675$ |
$60.97592977855377$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T27) |
$[2, 2, 2, 10]$ |
$[2, 2, 2, 10]$ |
$2$ |
$7$ |
$152810.396964$ |
$0$ |
|
| 16.16.228...000.1 |
$x^{16} - 40 x^{14} + 518 x^{12} - 3160 x^{10} + 10099 x^{8} - 17000 x^{6} + 14042 x^{4} - 4520 x^{2} + 121$ |
$16$ |
(16, 0) |
$2^{44}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$51.2744407675$ |
$60.97592977855377$ |
|
|
? |
$C_4^2:C_2$ (as 16T27) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$15$ |
$233498579.037$ |
$13$ |
|
| 16.0.228...000.2 |
$x^{16} - 20 x^{14} + 278 x^{12} - 1820 x^{10} + 6859 x^{8} - 17020 x^{6} + 33182 x^{4} - 50680 x^{2} + 52441$ |
$16$ |
(0, 8) |
$2^{44}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$51.2744407675$ |
$60.97592977855377$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T27) |
$[2, 4, 4]$ |
$[2, 4, 4]$ |
$2$ |
$7$ |
$325480.409342$ |
$0$ |
|
| 16.16.354...304.1 |
$x^{16} - 8 x^{15} - 64 x^{14} + 528 x^{13} + 1532 x^{12} - 12448 x^{11} - 20876 x^{10} + 135984 x^{9} + 193408 x^{8} - 696072 x^{7} - 1122272 x^{6} + 1276792 x^{5} + 2949200 x^{4} + 634320 x^{3} - 1252012 x^{2} - 621736 x - 31079$ |
$16$ |
(16, 0) |
$2^{52}\cdot 3^{12}\cdot 23^{6}$ |
$3$ |
$70.2807464461$ |
$104.00455136257506$ |
|
|
? |
$C_4^2:C_2$ (as 16T27) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$15$ |
$5742846751.42$ |
$12$ |
|
