| 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 |
| 16.8.597...173.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 22 x^{13} - 74 x^{12} - 57 x^{11} + 443 x^{10} - 503 x^{9} - 1832 x^{8} + 7235 x^{7} - 475 x^{6} - 15351 x^{5} + 41216 x^{4} - 5291 x^{3} - 65354 x^{2} + 45062 x - 7957$ |
$16$ |
[8,4] |
$3^{16}\cdot 173^{9}$ |
$2$ |
$54.4530471723$ |
$206.3936114320237$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$125447647.046$ |
| 16.8.597...173.2 |
$x^{16} - 8 x^{15} + 7 x^{14} + 91 x^{13} - 503 x^{12} + 1471 x^{11} - 1697 x^{10} - 1877 x^{9} + 11071 x^{8} - 22275 x^{7} + 26778 x^{6} - 20712 x^{5} + 9031 x^{4} - 578 x^{3} - 1712 x^{2} + 912 x - 144$ |
$16$ |
[8,4] |
$3^{16}\cdot 173^{9}$ |
$2$ |
$54.4530471723$ |
$206.3936114320237$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$126606829.59$ |
| 16.4.213...584.1 |
$x^{16} - 4 x^{15} + 4 x^{14} - 10 x^{13} - 132 x^{12} - 362 x^{11} - 562 x^{10} - 1354 x^{9} - 7271 x^{8} - 27546 x^{7} - 59328 x^{6} - 122492 x^{5} - 275440 x^{4} - 431872 x^{3} - 359660 x^{2} - 135934 x - 18031$ |
$16$ |
[4,6] |
$2^{20}\cdot 389^{9}$ |
$2$ |
$68.0979667911$ |
$238.96183736852862$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$485218868.094$ |
| 16.4.213...584.2 |
$x^{16} - 8 x^{15} + 62 x^{14} - 294 x^{13} + 1002 x^{12} - 2310 x^{11} + 2768 x^{10} + 3364 x^{9} - 18881 x^{8} + 20156 x^{7} + 9274 x^{6} - 22040 x^{5} + 17116 x^{4} - 6518 x^{3} + 734 x^{2} + 128 x - 19$ |
$16$ |
[4,6] |
$2^{20}\cdot 389^{9}$ |
$2$ |
$68.0979667911$ |
$238.96183736852862$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$636345371.649$ |
| 16.8.160...000.1 |
$x^{16} - 24 x^{12} + 2 x^{10} + 149 x^{8} - 14 x^{6} - 254 x^{4} + 40 x^{2} + 5$ |
$16$ |
[8,4] |
$2^{32}\cdot 5^{9}\cdot 61^{8}$ |
$3$ |
$77.2494749469$ |
$373.3097286246537$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$3399198672.89$ |
| 16.8.160...000.2 |
$x^{16} - 24 x^{12} - 2 x^{10} + 149 x^{8} + 14 x^{6} - 254 x^{4} - 40 x^{2} + 5$ |
$16$ |
[8,4] |
$2^{32}\cdot 5^{9}\cdot 61^{8}$ |
$3$ |
$77.2494749469$ |
$373.3097286246537$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$3047402042.2$ |
| 16.12.342...344.1 |
$x^{16} - 38 x^{14} - 20 x^{13} + 150 x^{12} + 200 x^{11} + 4110 x^{10} - 3208 x^{9} - 29880 x^{8} + 16176 x^{7} + 36562 x^{6} + 27276 x^{5} - 638 x^{4} - 48408 x^{3} - 28418 x^{2} + 696 x + 1915$ |
$16$ |
[12,2] |
$2^{24}\cdot 389^{9}$ |
$2$ |
$80.9825866252$ |
$284.17511721277737$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$8425876392.77$ |
| 16.12.342...344.2 |
$x^{16} - 4 x^{15} - 16 x^{14} - 52 x^{13} + 72 x^{12} + 3112 x^{11} + 1992 x^{10} - 29904 x^{9} - 39376 x^{8} + 86752 x^{7} + 199648 x^{6} + 27424 x^{5} - 215328 x^{4} - 177984 x^{3} - 31616 x^{2} + 8448 x + 2240$ |
$16$ |
[12,2] |
$2^{24}\cdot 389^{9}$ |
$2$ |
$80.9825866252$ |
$284.17511721277737$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$21644994461.8$ |
| 16.0.553...000.1 |
$x^{16} + 50 x^{14} + 1004 x^{12} + 10436 x^{10} + 60240 x^{8} + 192312 x^{6} + 317840 x^{4} + 229808 x^{2} + 41552$ |
$16$ |
[0,8] |
$2^{32}\cdot 5^{8}\cdot 53^{9}$ |
$3$ |
$83.4545789105$ |
$413.8174686976992$ |
✓ |
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$[2, 576]$ |
$[2, 576]$ |
$2$ |
$7$ |
$458893.187666$ |
| 16.16.553...000.1 |
$x^{16} - 44 x^{14} + 766 x^{12} - 6722 x^{10} + 31489 x^{8} - 77702 x^{6} + 96496 x^{4} - 51728 x^{2} + 6413$ |
$16$ |
[16,0] |
$2^{32}\cdot 5^{8}\cdot 53^{9}$ |
$3$ |
$83.4545789105$ |
$413.8174686976992$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$21854082582.3$ |
| 16.0.553...000.2 |
$x^{16} + 44 x^{14} + 766 x^{12} + 6722 x^{10} + 31489 x^{8} + 77702 x^{6} + 96496 x^{4} + 51728 x^{2} + 6413$ |
$16$ |
[0,8] |
$2^{32}\cdot 5^{8}\cdot 53^{9}$ |
$3$ |
$83.4545789105$ |
$413.8174686976992$ |
✓ |
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$[6, 384]$ |
$[6, 384]$ |
$2$ |
$7$ |
$458893.187666$ |
| 16.16.553...000.2 |
$x^{16} - 50 x^{14} + 1004 x^{12} - 10436 x^{10} + 60240 x^{8} - 192312 x^{6} + 317840 x^{4} - 229808 x^{2} + 41552$ |
$16$ |
[16,0] |
$2^{32}\cdot 5^{8}\cdot 53^{9}$ |
$3$ |
$83.4545789105$ |
$413.8174686976992$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$34114865421.4$ |
| 16.8.553...000.5 |
$x^{16} - 22 x^{14} - 68 x^{12} + 1468 x^{10} + 1540 x^{8} - 5304 x^{6} - 3408 x^{4} + 2544 x^{2} + 848$ |
$16$ |
[8,4] |
$2^{32}\cdot 5^{8}\cdot 53^{9}$ |
$3$ |
$83.4545789105$ |
$413.8174686976992$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$5383740082.4$ |
| 16.8.553...000.6 |
$x^{16} - 10 x^{14} - 60 x^{12} + 296 x^{10} + 1113 x^{8} - 692 x^{6} - 570 x^{4} + 212 x^{2} + 53$ |
$16$ |
[8,4] |
$2^{32}\cdot 5^{8}\cdot 53^{9}$ |
$3$ |
$83.4545789105$ |
$413.8174686976992$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$7879554244.54$ |
| 16.8.553...000.7 |
$x^{16} + 22 x^{14} - 68 x^{12} - 1468 x^{10} + 1540 x^{8} + 5304 x^{6} - 3408 x^{4} - 2544 x^{2} + 848$ |
$16$ |
[8,4] |
$2^{32}\cdot 5^{8}\cdot 53^{9}$ |
$3$ |
$83.4545789105$ |
$413.8174686976992$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$3116105447.93$ |
| 16.8.553...000.8 |
$x^{16} + 4 x^{14} - 270 x^{12} - 1564 x^{10} + 1526 x^{8} + 16868 x^{6} + 2074 x^{4} - 39432 x^{2} + 2597$ |
$16$ |
[8,4] |
$2^{32}\cdot 5^{8}\cdot 53^{9}$ |
$3$ |
$83.4545789105$ |
$413.8174686976992$ |
|
|
? |
$C_2^4.\GL(2,3)$ (as 16T1069) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$6351829451.53$ |
