| 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 |
| 16.0.398...544.1 |
$x^{16} + 56 x^{14} + 1232 x^{12} + 13720 x^{10} + 81830 x^{8} + 249704 x^{6} + 323792 x^{4} + 96040 x^{2} + 2401$ |
$16$ |
[0,8] |
$2^{58}\cdot 7^{12}$ |
$2$ |
$53.0954449096$ |
$53.0954449095836$ |
✓ |
✓ |
? |
$Q_{16}$ (as 16T14) |
$[2, 14, 14]$ |
$[2, 14, 14]$ |
$2$ |
$7$ |
$44651.6325002$ |
| 16.16.398...544.1 |
$x^{16} - 56 x^{14} + 1232 x^{12} - 13720 x^{10} + 81830 x^{8} - 249704 x^{6} + 323792 x^{4} - 96040 x^{2} + 2401$ |
$16$ |
[16,0] |
$2^{58}\cdot 7^{12}$ |
$2$ |
$53.0954449096$ |
$53.0954449095836$ |
|
✓ |
? |
$Q_{16}$ (as 16T14) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$454146043.187$ |
| 16.0.531...816.1 |
$x^{16} - 4 x^{15} + 74 x^{14} - 352 x^{13} + 2602 x^{12} - 9704 x^{11} + 42818 x^{10} - 121952 x^{9} + 390370 x^{8} - 940332 x^{7} + 2450022 x^{6} - 5077560 x^{5} + 9984474 x^{4} - 14175360 x^{3} + 16341750 x^{2} - 8146152 x + 1385757$ |
$16$ |
[0,8] |
$2^{32}\cdot 3^{12}\cdot 13^{12}$ |
$3$ |
$62.42498499$ |
$62.42498498999099$ |
✓ |
✓ |
? |
$Q_{16}$ (as 16T14) |
$[2, 2, 4, 4, 4, 8]$ |
$[2, 2, 4, 4, 4, 8]$ |
$2$ |
$7$ |
$29886.0391883$ |
| 16.16.531...816.1 |
$x^{16} - 4 x^{15} - 82 x^{14} + 428 x^{13} + 1666 x^{12} - 11264 x^{11} - 11158 x^{10} + 122968 x^{9} + 6103 x^{8} - 634260 x^{7} + 185526 x^{6} + 1445736 x^{5} - 609876 x^{4} - 880416 x^{3} + 770220 x^{2} - 217296 x + 21069$ |
$16$ |
[16,0] |
$2^{32}\cdot 3^{12}\cdot 13^{12}$ |
$3$ |
$62.42498499$ |
$62.42498498999099$ |
|
✓ |
? |
$Q_{16}$ (as 16T14) |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 4]$ |
$2$ |
$15$ |
$835254398.611$ |
| 16.0.275...625.39 |
$x^{16} - x^{15} + 98 x^{14} - 90 x^{13} + 4761 x^{12} - 4435 x^{11} + 130737 x^{10} - 30422 x^{9} + 2024471 x^{8} + 1410010 x^{7} + 20731015 x^{6} + 33449130 x^{5} + 101899505 x^{4} + 367664500 x^{3} + 495143825 x^{2} + 212747625 x + 730770125$ |
$16$ |
[0,8] |
$5^{12}\cdot 101^{12}$ |
$2$ |
$106.529167613$ |
$106.52916761335055$ |
✓ |
✓ |
? |
$Q_{16}$ (as 16T14) |
$[2, 2, 2, 6, 6, 12, 12]$ |
$[2, 2, 2, 6, 6, 12, 12]$ |
$2$ |
$7$ |
$103071.243274$ |
| 16.0.114...321.55 |
$x^{16} - x^{15} + 133 x^{14} - 103 x^{13} + 6081 x^{12} - 5825 x^{11} + 129015 x^{10} - 395763 x^{9} + 2239826 x^{8} - 15443166 x^{7} + 42987317 x^{6} - 243806269 x^{5} + 1187076972 x^{4} - 3260668645 x^{3} + 8997200644 x^{2} - 18857570867 x + 15497228633$ |
$16$ |
[0,8] |
$13^{12}\cdot 53^{12}$ |
$2$ |
$134.482079636$ |
$134.48207963630105$ |
✓ |
✓ |
? |
$Q_{16}$ (as 16T14) |
$[2, 2, 2, 4, 4, 28, 28]$ |
$[2, 2, 2, 4, 4, 28, 28]$ |
$2$ |
$7$ |
$165651.191156$ |
| 16.0.618...401.45 |
$x^{16} - 3 x^{15} + 168 x^{14} - 118 x^{13} + 8143 x^{12} + 19673 x^{11} + 268861 x^{10} + 996458 x^{9} + 6562747 x^{8} + 28125680 x^{7} + 116312303 x^{6} + 424196239 x^{5} + 1236318043 x^{4} + 3216880296 x^{3} + 7235716110 x^{2} + 10185930767 x + 17602483739$ |
$16$ |
[0,8] |
$13^{12}\cdot 61^{12}$ |
$2$ |
$149.435881751$ |
$149.4358817512091$ |
✓ |
✓ |
? |
$Q_{16}$ (as 16T14) |
$[2, 2, 2, 2, 2, 68, 68]$ |
$[2, 2, 2, 2, 2, 68, 68]$ |
$2$ |
$7$ |
$233495.847112$ |
| 16.0.477...625.18 |
$x^{16} - 3 x^{15} + 64 x^{14} - 267 x^{13} - 254 x^{12} - 4890 x^{11} - 7005 x^{10} + 138170 x^{9} + 706440 x^{8} + 2483375 x^{7} + 6028400 x^{6} + 11861450 x^{5} + 42649275 x^{4} + 4094000 x^{3} + 371963750 x^{2} - 453825000 x + 1051559375$ |
$16$ |
[0,8] |
$5^{12}\cdot 89^{14}$ |
$2$ |
$169.802374494$ |
$169.8023744936812$ |
✓ |
✓ |
|
$Q_{16}$ (as 16T14) |
$[4, 8, 8, 8, 8]$ |
$[4, 8, 8, 8, 8]$ |
$2$ |
$7$ |
$14693160.0683$ |
| 16.16.827...489.2 |
$x^{16} - 3 x^{15} - 288 x^{14} + 351 x^{13} + 32164 x^{12} + 6818 x^{11} - 1712220 x^{10} - 2050498 x^{9} + 43855038 x^{8} + 73975139 x^{7} - 504661128 x^{6} - 805577043 x^{5} + 2530948457 x^{4} + 2475352300 x^{3} - 4676812808 x^{2} - 174707192 x + 1104680656$ |
$16$ |
[16,0] |
$17^{14}\cdot 53^{12}$ |
$2$ |
$234.341771376$ |
$234.3417713764912$ |
|
✓ |
|
$Q_{16}$ (as 16T14) |
$[4]$ |
$[2, 2, 2, 2, 8]$ |
$2$ |
$15$ |
$11079174313200$ |
| 16.16.100...681.2 |
$x^{16} - 5 x^{15} - 787 x^{14} + 5051 x^{13} + 224913 x^{12} - 1883696 x^{11} - 26837605 x^{10} + 308362799 x^{9} + 840421984 x^{8} - 20027658582 x^{7} + 49055322017 x^{6} + 242254120296 x^{5} - 1022348955259 x^{4} - 574159811286 x^{3} + 5148673520590 x^{2} - 479019525519 x - 6904626882871$ |
$16$ |
[16,0] |
$41^{14}\cdot 61^{12}$ |
$2$ |
$562.578655609$ |
$562.5786556087241$ |
|
✓ |
|
$Q_{16}$ (as 16T14) |
$[4]$ |
$[2, 2, 2, 2, 8]$ |
$2$ |
$15$ |
$18082637024000000$ |
| 16.16.788...481.1 |
$x^{16} - 5 x^{15} - 1567 x^{14} + 5036 x^{13} + 913132 x^{12} - 2632325 x^{11} - 251203331 x^{10} + 944435243 x^{9} + 33537176305 x^{8} - 194082565895 x^{7} - 1854337101495 x^{6} + 17178191896767 x^{5} + 713563290839 x^{4} - 408109365395354 x^{3} + 1450005309994863 x^{2} - 1532647000809550 x - 134701390338101$ |
$16$ |
[16,0] |
$37^{12}\cdot 149^{12}$ |
$2$ |
$639.795224824$ |
$639.7952248237154$ |
|
✓ |
? |
$Q_{16}$ (as 16T14) |
$[4]$ |
$[2, 2, 2, 2, 2, 2, 2, 2, 8]$ |
$2$ |
$15$ |
$51119672626600000$ |
| 16.0.147...881.43 |
$x^{16} - 3 x^{15} + 1245 x^{14} - 929 x^{13} + 344716 x^{12} + 477002 x^{11} + 9678642 x^{10} + 527271324 x^{9} + 2476254439 x^{8} - 16644451521 x^{7} + 234290252130 x^{6} + 2895427880223 x^{5} + 1622671062847 x^{4} + 13345645225409 x^{3} + 709619381151297 x^{2} + 3629213187441572 x + 5423234506172099$ |
$16$ |
[0,8] |
$37^{12}\cdot 157^{12}$ |
$2$ |
$665.389636416$ |
$665.3896364158364$ |
✓ |
✓ |
? |
$Q_{16}$ (as 16T14) |
$[2, 2, 2, 2, 2, 3196, 3196]$ |
$[2, 2, 2, 2, 2, 3196, 3196]$ |
$2$ |
$7$ |
$11997899.8215$ |
