| 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 |
| 16.6.288...312.1 |
$x^{16} - 2 x^{15} - 26 x^{14} - 12 x^{13} + 52 x^{12} + 46 x^{11} - 24 x^{10} - 30 x^{9} - 3 x^{8} - 30 x^{7} - 24 x^{6} + 46 x^{5} + 52 x^{4} - 12 x^{3} - 26 x^{2} - 2 x + 1$ |
$16$ |
[6,5] |
$-\,2^{24}\cdot 7\cdot 199^{8}$ |
$3$ |
$45.0598933212$ |
|
|
|
? |
$C_2^7.F_8:C_6$ (as 16T1841) |
trivial |
$[2]$ |
$2$ |
$10$ |
$20672668.1747$ |
| 16.12.371...544.1 |
$x^{16} - 2 x^{15} - 28 x^{14} + 2 x^{13} + 244 x^{12} + 152 x^{11} - 862 x^{10} - 314 x^{9} + 2403 x^{8} - 240 x^{7} - 6194 x^{6} - 1726 x^{5} + 5894 x^{4} + 2718 x^{3} - 1890 x^{2} - 920 x + 103$ |
$16$ |
[12,2] |
$2^{24}\cdot 3^{2}\cdot 199^{8}$ |
$3$ |
$45.7732435886$ |
|
|
|
? |
$C_2^7:F_8:C_3$ (as 16T1800) |
trivial |
$[2]$ |
$2$ |
$13$ |
$97496804.5048$ |
| 16.16.202...184.1 |
$x^{16} - 6 x^{15} - 22 x^{14} + 116 x^{13} + 240 x^{12} - 674 x^{11} - 1326 x^{10} + 896 x^{9} + 2305 x^{8} - 158 x^{7} - 1638 x^{6} - 308 x^{5} + 486 x^{4} + 160 x^{3} - 44 x^{2} - 20 x - 1$ |
$16$ |
[16,0] |
$2^{24}\cdot 7^{2}\cdot 199^{8}$ |
$3$ |
$50.8872271422$ |
|
|
|
? |
$C_2^7:F_8:C_3$ (as 16T1800) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$612600928.379$ |
| 16.8.202...184.1 |
$x^{16} - 12 x^{14} - 128 x^{12} + 228 x^{10} + 2764 x^{8} + 2768 x^{6} - 3424 x^{4} + 224 x^{2} + 196$ |
$16$ |
[8,4] |
$2^{24}\cdot 7^{2}\cdot 199^{8}$ |
$3$ |
$50.8872271422$ |
|
|
|
? |
$C_2^7:F_8:C_3$ (as 16T1800) |
$[2]$ |
$[2, 4]$ |
$2$ |
$11$ |
$70342914.5451$ |
| 16.2.259...808.1 |
$x^{16} - 2 x^{15} + 4 x^{14} - 6 x^{13} + 48 x^{12} - 252 x^{11} + 380 x^{10} - 444 x^{9} + 2183 x^{8} - 5788 x^{7} + 14248 x^{6} - 23808 x^{5} + 25968 x^{4} - 23794 x^{3} + 10816 x^{2} - 1530 x - 149$ |
$16$ |
[2,7] |
$-\,2^{24}\cdot 3^{2}\cdot 7\cdot 199^{8}$ |
$4$ |
$51.692830849$ |
|
|
|
? |
$C_2^7.F_8:C_6$ (as 16T1841) |
$[2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$21733759.3915$ |
| 16.12.268...040.1 |
$x^{16} - 34 x^{14} - 10 x^{13} + 342 x^{12} + 134 x^{11} - 1096 x^{10} - 518 x^{9} + 737 x^{8} - 518 x^{7} - 1096 x^{6} + 134 x^{5} + 342 x^{4} - 10 x^{3} - 34 x^{2} + 1$ |
$16$ |
[12,2] |
$2^{24}\cdot 5\cdot 13\cdot 199^{8}$ |
$4$ |
$51.7939003034$ |
|
|
|
? |
$C_2^7.F_8:C_6$ (as 16T1841) |
trivial |
$[2]$ |
$2$ |
$13$ |
$330486924.647$ |
| 16.8.268...040.2 |
$x^{16} - 8 x^{15} + 38 x^{14} - 126 x^{13} + 194 x^{12} + 110 x^{11} - 1928 x^{10} + 6582 x^{9} - 10673 x^{8} + 7842 x^{7} + 23992 x^{6} - 76574 x^{5} + 118206 x^{4} - 110390 x^{3} + 6506 x^{2} + 36228 x - 2493$ |
$16$ |
[8,4] |
$2^{24}\cdot 5\cdot 13\cdot 199^{8}$ |
$4$ |
$51.7939003034$ |
|
|
|
? |
$C_2^7.F_8:C_6$ (as 16T1841) |
trivial |
$[2]$ |
$2$ |
$11$ |
$170592407.997$ |
| 16.8.367...824.1 |
$x^{16} - 2 x^{15} - 14 x^{14} + 46 x^{13} - 38 x^{12} - 140 x^{11} + 216 x^{10} - 696 x^{9} + 5477 x^{8} - 5196 x^{7} - 16792 x^{6} + 64256 x^{5} - 16814 x^{4} - 138382 x^{3} + 65930 x^{2} + 37710 x - 9091$ |
$16$ |
[8,4] |
$2^{24}\cdot 89\cdot 199^{8}$ |
$3$ |
$52.8212174855$ |
|
|
|
? |
$C_2^7.F_8:C_6$ (as 16T1841) |
trivial |
$[2]$ |
$2$ |
$11$ |
$158812121.916$ |
| 16.10.424...448.1 |
$x^{16} - 8 x^{15} + 140 x^{13} - 366 x^{12} + 12 x^{11} + 1640 x^{10} - 4020 x^{9} + 5215 x^{8} - 4044 x^{7} + 1632 x^{6} + 68 x^{5} - 458 x^{4} + 236 x^{3} - 48 x^{2} + 1$ |
$16$ |
[10,3] |
$-\,2^{24}\cdot 103\cdot 199^{8}$ |
$3$ |
$53.3057254627$ |
|
|
|
? |
$C_2^7.F_8:C_6$ (as 16T1841) |
trivial |
$[2]$ |
$2$ |
$12$ |
$306811417.515$ |
| 16.0.179...096.1 |
$x^{16} - 2 x^{15} + 2 x^{14} - 12 x^{13} + 316 x^{12} - 230 x^{11} + 1892 x^{10} - 178 x^{9} + 21037 x^{8} + 150 x^{7} + 169788 x^{6} + 170562 x^{5} - 240804 x^{4} + 2459872 x^{3} + 4057302 x^{2} - 3915814 x + 1426145$ |
$16$ |
[0,8] |
$2^{24}\cdot 199^{8}\cdot 659^{2}$ |
$3$ |
$89.8115534868$ |
|
✓ |
|
? |
$C_2^7:F_8:C_3$ (as 16T1800) |
$[1296]$ |
$[1296]$ |
$2$ |
$7$ |
$1959771.40861$ |
| 18.0.503...328.1 |
$x^{18} - x^{17} - 17325 x^{16} + 586916 x^{15} + 100969422 x^{14} - 6840514058 x^{13} - 107756688858 x^{12} + 23103966036952 x^{11} - 648244174108933 x^{10} - 12963159627315611 x^{9} + 1261163277968542693 x^{8} - 33412433558073113128 x^{7} + 364510918973877952850 x^{6} + 769685556332978149550 x^{5} - 58532398101377222239918 x^{4} + 378837171096696810470652 x^{3} + 2901719520110695942411565 x^{2} - 46560563708186952403102089 x + 167129576003281098226717543$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 7^{12}\cdot 43^{9}\cdot 97^{8}\cdot 6959^{8}$ |
$5$ |
$23567.5535392$ |
|
✓ |
|
|
$\SL(2,8):C_6$ (as 18T427) |
not computed |
not computed |
$2$ |
$8$ |
|
| 18.18.350...552.1 |
$x^{18} - 2624 x^{16} + 2318632 x^{14} - 801660724 x^{12} + 89408416916 x^{10} - 3832834487616 x^{8} + 71863748845664 x^{6} - 569164856577712 x^{4} + 1426110041382340 x^{2} - 9078271257168$ |
$18$ |
[18,0] |
$2^{24}\cdot 7^{12}\cdot 43^{9}\cdot 97^{8}\cdot 6959^{9}$ |
$5$ |
$38529.1409999$ |
|
|
|
|
$\SL(2,8):C_6$ (as 18T427) |
not computed |
not computed |
$2$ |
$17$ |
|
