| 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 |
| 16.0.934...456.3 |
$x^{16} + 22 x^{12} - 60 x^{10} + 243 x^{8} - 204 x^{6} + 70 x^{4} - 12 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{12}$ |
$2$ |
$15.3346345019$ |
$18.23605645563822$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
trivial |
$12$ |
$7$ |
$5432.88069635$ |
| 16.0.136...000.1 |
$x^{16} - 2 x^{15} - 8 x^{14} + 10 x^{13} + 63 x^{12} - 98 x^{11} - 86 x^{10} + 48 x^{9} + 757 x^{8} - 1896 x^{7} + 2378 x^{6} - 1668 x^{5} + 404 x^{4} + 296 x^{3} - 184 x^{2} + 16$ |
$16$ |
[0,8] |
$2^{20}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$18.1282523841$ |
$21.558246717785053$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
$[2]$ |
$6$ |
$7$ |
$5165.64894396$ |
| 16.4.149...296.3 |
$x^{16} - 32 x^{12} - 120 x^{10} - 222 x^{8} - 192 x^{6} - 80 x^{4} - 24 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{48}\cdot 3^{12}$ |
$2$ |
$18.2360564556$ |
$18.23605645563822$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
trivial |
$2$ |
$9$ |
$10977.0741836$ |
| 16.4.217...000.2 |
$x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 19 x^{12} - 18 x^{11} + 140 x^{10} - 132 x^{9} + 142 x^{8} - 336 x^{7} + 310 x^{6} - 56 x^{5} - 84 x^{4} + 70 x^{3} - 14 x^{2} - 2 x + 1$ |
$16$ |
[4,6] |
$2^{24}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$21.5582467178$ |
$21.558246717785053$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
$[2]$ |
$2$ |
$9$ |
$14037.4430501$ |
| 16.0.239...736.1 |
$x^{16} + 4 x^{12} - 96 x^{10} + 150 x^{8} + 96 x^{6} + 4 x^{4} + 1$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
$[2]$ |
$4$ |
$7$ |
$46193.7886141$ |
| 16.4.239...736.1 |
$x^{16} - 20 x^{12} - 48 x^{10} - 138 x^{8} + 384 x^{6} + 172 x^{4} + 48 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
trivial |
$2$ |
$9$ |
$53618.6042833$ |
| 16.0.239...736.51 |
$x^{16} - 4 x^{14} - 8 x^{13} + 32 x^{12} - 24 x^{11} + 20 x^{10} - 48 x^{9} - 56 x^{8} + 336 x^{7} - 356 x^{6} - 136 x^{5} + 588 x^{4} - 472 x^{3} + 148 x^{2} - 64 x + 79$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.686448086636275$ |
$23.64923933252054$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
trivial |
$6$ |
$7$ |
$69240.5471694659$ |
| 16.4.957...944.16 |
$x^{16} - 20 x^{12} - 120 x^{10} - 192 x^{8} - 48 x^{6} - 104 x^{4} + 240 x^{2} + 4$ |
$16$ |
[4,6] |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.64923933252054$ |
$23.64923933252054$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
trivial |
$2$ |
$9$ |
$104519.85194942706$ |
| 16.16.228...000.2 |
$x^{16} - 4 x^{15} - 36 x^{14} + 184 x^{13} + 276 x^{12} - 2532 x^{11} + 1576 x^{10} + 10204 x^{9} - 12939 x^{8} - 15196 x^{7} + 25960 x^{6} + 6876 x^{5} - 16638 x^{4} + 32 x^{3} + 1620 x^{2} + 196 x + 1$ |
$16$ |
[16,0] |
$2^{44}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$51.2744407675$ |
$60.97592977855377$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
$[2]$ |
$2$ |
$15$ |
$279059448.286$ |
| 16.0.228...000.3 |
$x^{16} - 4 x^{15} + 4 x^{14} - 16 x^{13} + 156 x^{12} - 652 x^{11} + 1516 x^{10} - 2436 x^{9} + 7441 x^{8} - 30156 x^{7} + 82820 x^{6} - 142404 x^{5} + 136322 x^{4} - 54488 x^{3} + 75320 x^{2} - 199044 x + 167101$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$51.2744407675$ |
$60.97592977855377$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T30) |
$[2, 2, 80]$ |
$2$ |
$7$ |
$55877.3346526$ |
| 16.16.221...144.1 |
$x^{16} - 8 x^{15} - 32 x^{14} + 352 x^{13} + 184 x^{12} - 5432 x^{11} + 2236 x^{10} + 38968 x^{9} - 32168 x^{8} - 135384 x^{7} + 149568 x^{6} + 195744 x^{5} - 285732 x^{4} - 31752 x^{3} + 158652 x^{2} - 67104 x + 8433$ |
$16$ |
[16,0] |
$2^{48}\cdot 3^{12}\cdot 23^{6}$ |
$3$ |
$59.0988277479$ |
$87.45705441086021$ |
|
|
? |
$C_4^2:C_2$ (as 16T30) |
trivial |
$2$ |
$15$ |
$1875974037.6$ |
| 16.0.221...144.1 |
$x^{16} + 24 x^{14} - 24 x^{13} + 388 x^{12} - 552 x^{11} + 4236 x^{10} - 7104 x^{9} + 32370 x^{8} - 73872 x^{7} + 166488 x^{6} - 409752 x^{5} + 576784 x^{4} - 963552 x^{3} + 989808 x^{2} + 1020648 x + 855742$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}\cdot 23^{6}$ |
$3$ |
$59.0988277479$ |
$87.45705441086021$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T30) |
$[2, 4, 4, 8]$ |
$2$ |
$7$ |
$204141.742403$ |
| 16.0.221...144.2 |
$x^{16} - 32 x^{14} - 24 x^{13} + 528 x^{12} + 696 x^{11} - 4340 x^{10} - 8976 x^{9} + 20776 x^{8} + 65760 x^{7} - 11160 x^{6} - 191712 x^{5} + 39996 x^{4} + 850104 x^{3} + 1807452 x^{2} + 1890576 x + 1377009$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}\cdot 23^{6}$ |
$3$ |
$59.0988277479$ |
$87.45705441086021$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T30) |
$[2, 2, 4, 8]$ |
$2$ |
$7$ |
$475824.014517$ |
| 16.0.354...304.1 |
$x^{16} - 8 x^{15} + 48 x^{14} - 88 x^{13} + 240 x^{12} + 1968 x^{11} - 5588 x^{10} + 16184 x^{9} + 11832 x^{8} - 83624 x^{7} + 415672 x^{6} - 951840 x^{5} + 2031636 x^{4} - 2871392 x^{3} + 3696324 x^{2} - 3324304 x + 1977337$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}\cdot 23^{6}$ |
$3$ |
$70.2807464461$ |
$104.00455136257506$ |
✓ |
|
? |
$C_4^2:C_2$ (as 16T30) |
$[2, 4, 4, 16]$ |
$2$ |
$7$ |
$431260.406848$ |
