| 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 |
| 16.0.239...736.3 |
$x^{16} + 8 x^{14} + 20 x^{12} + 56 x^{10} + 160 x^{8} - 32 x^{6} - 40 x^{4} + 16 x^{2} + 4$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_4^2:C_2$ (as 16T17) |
$[2]$ |
$2$ |
$7$ |
$9019.16741111$ |
| 16.8.239...736.3 |
$x^{16} - 8 x^{14} + 20 x^{12} - 56 x^{10} + 160 x^{8} + 32 x^{6} - 40 x^{4} - 16 x^{2} + 4$ |
$16$ |
[8,4] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_4^2:C_2$ (as 16T17) |
trivial |
$2$ |
$11$ |
$79205.5923155$ |
| 16.0.429...000.3 |
$x^{16} - 8 x^{14} + 56 x^{12} - 184 x^{10} + 344 x^{8} - 352 x^{6} + 264 x^{4} - 96 x^{2} + 16$ |
$16$ |
[0,8] |
$2^{44}\cdot 5^{12}$ |
$2$ |
$22.4936530076$ |
$26.74961219905688$ |
|
|
? |
$C_4^2:C_2$ (as 16T17) |
trivial |
$10$ |
$7$ |
$73929.9567996$ |
| 16.8.687...000.1 |
$x^{16} - 8 x^{14} - 4 x^{12} + 96 x^{10} + 19 x^{8} - 312 x^{6} - 216 x^{4} - 16 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{48}\cdot 5^{12}$ |
$2$ |
$26.7496121991$ |
$26.74961219905688$ |
|
|
? |
$C_4^2:C_2$ (as 16T17) |
trivial |
$2$ |
$11$ |
$332978.186129$ |
| 16.16.557...000.1 |
$x^{16} - 30 x^{14} + 273 x^{12} - 1170 x^{10} + 2709 x^{8} - 3510 x^{6} + 2457 x^{4} - 810 x^{2} + 81$ |
$16$ |
[16,0] |
$2^{32}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$30.4879648893$ |
$43.116493435570106$ |
|
|
? |
$C_4^2:C_2$ (as 16T17) |
trivial |
$2$ |
$15$ |
$3716406.87604$ |
| 16.0.557...000.3 |
$x^{16} + 6 x^{14} + 39 x^{12} + 252 x^{10} + 1134 x^{8} + 2214 x^{6} + 1836 x^{4} - 162 x^{2} + 81$ |
$16$ |
[0,8] |
$2^{32}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$30.4879648893$ |
$43.116493435570106$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T17) |
$[4, 4]$ |
$10$ |
$7$ |
$55877.3346526$ |
| 16.0.557...000.4 |
$x^{16} + 30 x^{14} + 273 x^{12} + 1170 x^{10} + 2709 x^{8} + 3510 x^{6} + 2457 x^{4} + 810 x^{2} + 81$ |
$16$ |
[0,8] |
$2^{32}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$30.4879648893$ |
$43.116493435570106$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T17) |
$[4, 8]$ |
$2$ |
$7$ |
$3121.7160225$ |
| 16.16.232...000.1 |
$x^{16} - 8 x^{15} - 10 x^{14} + 210 x^{13} - 282 x^{12} - 1402 x^{11} + 3039 x^{10} + 3615 x^{9} - 10981 x^{8} - 3484 x^{7} + 18083 x^{6} - 621 x^{5} - 13448 x^{4} + 3454 x^{3} + 3503 x^{2} - 1669 x + 191$ |
$16$ |
[16,0] |
$2^{12}\cdot 5^{12}\cdot 13^{12}$ |
$3$ |
$38.4997149682$ |
$64.74854461001611$ |
|
|
|
$C_4^2:C_2$ (as 16T17) |
trivial |
$2$ |
$15$ |
$43291466.6921$ |
| 16.0.890...000.1 |
$x^{16} + 24 x^{14} - 8 x^{13} + 154 x^{12} + 56 x^{11} + 592 x^{10} + 168 x^{9} + 1257 x^{8} + 1424 x^{7} + 616 x^{6} + 2544 x^{5} + 4738 x^{4} + 800 x^{3} + 128 x^{2} - 1984 x + 961$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{4}\cdot 5^{12}$ |
$3$ |
$41.8654055757$ |
$60.08476486899934$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T17) |
$[2, 10]$ |
$2$ |
$7$ |
$113788.60182$ |
| 16.0.890...000.2 |
$x^{16} - 16 x^{14} - 8 x^{13} + 174 x^{12} - 24 x^{11} - 848 x^{10} - 352 x^{9} + 3177 x^{8} + 2384 x^{7} - 1704 x^{6} - 9336 x^{5} + 358 x^{4} + 12000 x^{3} + 20608 x^{2} + 11976 x + 4241$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{4}\cdot 5^{12}$ |
$3$ |
$41.8654055757$ |
$60.08476486899934$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T17) |
$[2, 10]$ |
$2$ |
$7$ |
$85299.4255313$ |
