| 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 |
| 16.0.166...936.1 |
$x^{16} + 8 x^{14} - 8 x^{13} + 29 x^{12} - 48 x^{11} + 86 x^{10} - 126 x^{9} + 180 x^{8} - 216 x^{7} + 228 x^{6} - 216 x^{5} + 171 x^{4} - 104 x^{3} + 38 x^{2} - 6 x + 3$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{4}\cdot 11^{12}$ |
$3$ |
$15.8984513852$ |
$23.485878123082728$ |
|
|
|
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
trivial |
trivial |
$2$ |
$7$ |
$2426.51298845$ |
| 16.0.186...136.1 |
$x^{16} - 8 x^{15} + 32 x^{14} - 80 x^{13} + 139 x^{12} - 178 x^{11} + 182 x^{10} - 160 x^{9} + 119 x^{8} - 52 x^{7} - 16 x^{6} + 40 x^{5} - 17 x^{4} - 6 x^{3} + 6 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{4}\cdot 37^{8}$ |
$3$ |
$16.0107313862$ |
$23.651742983410834$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
trivial |
trivial |
$2$ |
$7$ |
$2483.57263363$ |
| 16.0.526...736.1 |
$x^{16} - 4 x^{14} - 10 x^{13} + 8 x^{12} + 8 x^{11} + 22 x^{10} + 10 x^{9} + 27 x^{8} + 16 x^{7} + 26 x^{6} + 18 x^{5} + 18 x^{4} + 12 x^{3} + 24 x^{2} - 4 x + 9$ |
$16$ |
[0,8] |
$2^{24}\cdot 11^{12}$ |
$2$ |
$17.0839978211$ |
$20.9117280667238$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
trivial |
trivial |
$2$ |
$7$ |
$3875.12414602$ |
| 16.0.589...936.2 |
$x^{16} + 14 x^{12} - 48 x^{10} + 55 x^{8} - 40 x^{6} + 26 x^{4} + 4 x^{2} + 9$ |
$16$ |
[0,8] |
$2^{24}\cdot 37^{8}$ |
$2$ |
$17.2046505341$ |
$21.059413447565383$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
trivial |
trivial |
$2$ |
$7$ |
$5088.52344445$ |
| 16.0.472...625.1 |
$x^{16} - 2 x^{15} + 11 x^{14} - 16 x^{13} + 50 x^{12} - 92 x^{11} + 149 x^{10} - 308 x^{9} + 283 x^{8} - 318 x^{7} + 453 x^{6} - 368 x^{5} + 204 x^{4} + 28 x^{3} + 137 x^{2} - 164 x + 51$ |
$16$ |
[0,8] |
$5^{4}\cdot 229^{8}$ |
$2$ |
$22.6287332135$ |
$33.83784863137726$ |
|
|
|
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$[3]$ |
$[3]$ |
$2$ |
$7$ |
$17934.8862387$ |
| 16.0.477...816.1 |
$x^{16} - 4 x^{15} + 12 x^{14} - 28 x^{13} + 56 x^{12} - 82 x^{11} + 144 x^{10} - 170 x^{9} + 217 x^{8} - 218 x^{7} + 236 x^{6} - 130 x^{5} + 236 x^{4} + 86 x^{3} + 118 x^{2} + 26 x + 11$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{4}\cdot 37^{8}$ |
$3$ |
$22.6425934698$ |
$36.4759740687825$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$21064.1804548$ |
| 16.0.477...816.2 |
$x^{16} - 4 x^{15} + 20 x^{13} - 16 x^{12} - 50 x^{11} + 106 x^{10} - 82 x^{9} - 41 x^{8} + 270 x^{7} - 282 x^{6} - 86 x^{5} + 322 x^{4} - 202 x^{3} + 12 x^{2} + 26 x + 9$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{4}\cdot 37^{8}$ |
$3$ |
$22.6425934698$ |
$36.4759740687825$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$29383.8998438$ |
| 16.0.141...336.1 |
$x^{16} + 6 x^{14} - 10 x^{13} + 20 x^{12} - 48 x^{11} + 96 x^{10} - 188 x^{9} + 251 x^{8} + 140 x^{7} + 2132 x^{6} + 2368 x^{5} + 4286 x^{4} + 1780 x^{3} + 1120 x^{2} - 990 x + 243$ |
$16$ |
[0,8] |
$2^{24}\cdot 7^{4}\cdot 37^{8}$ |
$3$ |
$27.9846813109$ |
$55.71797073914738$ |
|
|
|
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$[8]$ |
$[8]$ |
$2$ |
$7$ |
$80443.548319$ |
| 16.8.546...536.1 |
$x^{16} - 4 x^{15} - 4 x^{14} + 56 x^{13} - 288 x^{12} + 548 x^{11} - 524 x^{10} + 256 x^{9} + 494 x^{8} - 1244 x^{7} + 1732 x^{6} - 2024 x^{5} + 1344 x^{4} - 484 x^{3} + 108 x^{2} - 16 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 3^{4}\cdot 7^{8}\cdot 17^{8}$ |
$4$ |
$40.6068020017$ |
$85.69469191799408$ |
|
|
|
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$22469913.2028$ |
| 16.8.546...536.2 |
$x^{16} - 2 x^{15} - 14 x^{14} + 48 x^{13} - 47 x^{12} - 138 x^{11} + 726 x^{10} - 1564 x^{9} + 2815 x^{8} - 582 x^{7} - 10332 x^{6} + 26564 x^{5} - 44358 x^{4} + 36568 x^{3} - 9352 x^{2} - 7056 x - 588$ |
$16$ |
[8,4] |
$2^{24}\cdot 3^{4}\cdot 7^{8}\cdot 17^{8}$ |
$4$ |
$40.6068020017$ |
$85.69469191799408$ |
|
|
|
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$43586613.7889$ |
| 16.16.102...056.1 |
$x^{16} - 48 x^{14} - 8 x^{13} + 783 x^{12} + 174 x^{11} - 5614 x^{10} - 1696 x^{9} + 17908 x^{8} + 8398 x^{7} - 22354 x^{6} - 14072 x^{5} + 6358 x^{4} + 4634 x^{3} - 182 x^{2} - 414 x - 51$ |
$16$ |
[16,0] |
$2^{24}\cdot 3^{4}\cdot 229^{8}$ |
$3$ |
$56.3304276521$ |
$74.13501197140255$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$[3]$ |
$[2, 6]$ |
$2$ |
$15$ |
$548711917.38$ |
| 16.0.114...184.1 |
$x^{16} - 8 x^{15} + 12 x^{14} + 32 x^{13} - 22 x^{12} - 456 x^{11} + 2284 x^{10} - 7040 x^{9} + 17271 x^{8} - 37448 x^{7} + 68860 x^{6} - 104280 x^{5} + 130226 x^{4} - 114520 x^{3} + 65712 x^{2} - 24824 x + 8395$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{26}$ |
$2$ |
$56.7112898201$ |
$85.20373642867735$ |
✓ |
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$[2, 36]$ |
$[2, 36]$ |
$2$ |
$7$ |
$1249717.03243$ |
| 16.16.114...184.1 |
$x^{16} - 8 x^{15} - 12 x^{14} + 200 x^{13} - 46 x^{12} - 1920 x^{11} + 1228 x^{10} + 8920 x^{9} - 6669 x^{8} - 20816 x^{7} + 15796 x^{6} + 22992 x^{5} - 16594 x^{4} - 10288 x^{3} + 6288 x^{2} + 904 x + 19$ |
$16$ |
[16,0] |
$2^{52}\cdot 3^{26}$ |
$2$ |
$56.7112898201$ |
$85.20373642867735$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$2550688765.33$ |
| 16.0.409...856.1 |
$x^{16} + 36 x^{14} + 438 x^{12} + 2488 x^{10} + 7059 x^{8} + 9288 x^{6} + 4174 x^{4} + 372 x^{2} + 9$ |
$16$ |
[0,8] |
$2^{36}\cdot 3^{16}\cdot 7^{12}$ |
$3$ |
$61.4132774396$ |
$82.78547596251443$ |
✓ |
|
|
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$[2, 2, 28]$ |
$[2, 2, 28]$ |
$2$ |
$7$ |
$3200862.04762$ |
