| 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 |
| 16.0.180...000.1 |
$x^{16} - 12 x^{12} + 114 x^{8} + 300 x^{4} + 625$ |
$16$ |
[0,8] |
$2^{58}\cdot 5^{4}$ |
$2$ |
$18.4491446253$ |
$27.587905929985723$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
trivial |
$8$ |
$7$ |
$11125.0816339$ |
| 16.0.149...896.43 |
$x^{16} + 28 x^{8} + 324$ |
$16$ |
[0,8] |
$2^{64}\cdot 3^{4}$ |
$2$ |
$21.057184207239878$ |
$27.712812921102035$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
trivial |
$8$ |
$7$ |
$39128.59405383013$ |
| 16.0.212...000.1 |
$x^{16} - 30 x^{12} + 415 x^{8} - 1350 x^{4} + 2025$ |
$16$ |
[0,8] |
$2^{32}\cdot 3^{4}\cdot 5^{14}$ |
$3$ |
$21.5247967265$ |
$28.328225605775355$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[4]$ |
$4$ |
$7$ |
$8061.86963365$ |
| 16.0.153...104.128 |
$x^{16} + 36 x^{12} + 288 x^{8} + 1944 x^{4} + 324$ |
$16$ |
[0,8] |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$28.12384367863563$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[2]$ |
$2$ |
$7$ |
$129540.96708111902$ |
| 16.0.153...104.170 |
$x^{16} - 12 x^{12} + 450 x^{8} + 972 x^{4} + 6561$ |
$16$ |
[0,8] |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$28.12384367863563$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[2]$ |
$8$ |
$7$ |
$290180.7746031396$ |
| 16.8.983...864.1 |
$x^{16} - 4 x^{15} - 4 x^{14} + 48 x^{13} - 145 x^{12} + 280 x^{11} - 41 x^{10} - 1014 x^{9} + 844 x^{8} + 2946 x^{7} - 6833 x^{6} + 5144 x^{5} + 3215 x^{4} - 9798 x^{3} + 4391 x^{2} + 3322 x - 2351$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{14}\cdot 11^{12}$ |
$3$ |
$31.5904350898$ |
$31.590435089833612$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
trivial |
$2$ |
$11$ |
$751195.186818$ |
| 16.8.137...936.3 |
$x^{16} - 36 x^{12} + 336 x^{8} - 504 x^{4} + 36$ |
$16$ |
[8,4] |
$2^{58}\cdot 3^{14}$ |
$2$ |
$32.2637491336$ |
$32.263749133641326$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
trivial |
$2$ |
$11$ |
$1533253.77477$ |
| 16.8.137...936.18 |
$x^{16} - 84 x^{12} + 1770 x^{8} - 1404 x^{4} + 9$ |
$16$ |
[8,4] |
$2^{58}\cdot 3^{14}$ |
$2$ |
$32.263749133641326$ |
$32.263749133641326$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
trivial |
$2$ |
$11$ |
$2101527.9701332995$ |
| 16.0.245...664.150 |
$x^{16} - 24 x^{14} + 252 x^{12} - 1440 x^{10} + 4770 x^{8} - 8640 x^{6} + 5832 x^{4} + 2592 x^{2} + 324$ |
$16$ |
[0,8] |
$2^{62}\cdot 3^{12}$ |
$2$ |
$33.44507500385779$ |
$36.47211291127644$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
trivial |
$6$ |
$7$ |
$1275611.8110994499$ |
| 16.0.980...656.279 |
$x^{16} + 252 x^{8} + 26244$ |
$16$ |
[0,8] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$36.47211291127644$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[2]$ |
$8$ |
$7$ |
$3603057.554814803$ |
| 16.0.134...464.1 |
$x^{16} + 40 x^{14} + 608 x^{12} + 4520 x^{10} + 17782 x^{8} + 36792 x^{6} + 36288 x^{4} + 12312 x^{2} + 81$ |
$16$ |
[0,8] |
$2^{58}\cdot 3^{4}\cdot 7^{8}$ |
$3$ |
$42.9598808302$ |
$56.53838276009771$ |
✓ |
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[2, 6, 6]$ |
$2$ |
$7$ |
$44651.6325002$ |
| 16.16.134...464.1 |
$x^{16} - 40 x^{14} + 608 x^{12} - 4520 x^{10} + 17782 x^{8} - 36792 x^{6} + 36288 x^{4} - 12312 x^{2} + 81$ |
$16$ |
[16,0] |
$2^{58}\cdot 3^{4}\cdot 7^{8}$ |
$3$ |
$42.9598808302$ |
$56.53838276009771$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
trivial |
$2$ |
$15$ |
$129617382.619$ |
| 16.16.575...000.1 |
$x^{16} - 50 x^{14} + 920 x^{12} - 8300 x^{10} + 39975 x^{8} - 103500 x^{6} + 137000 x^{4} - 81250 x^{2} + 15625$ |
$16$ |
[16,0] |
$2^{40}\cdot 5^{12}\cdot 11^{8}$ |
$3$ |
$62.7334013138$ |
$81.35515622154537$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[2]$ |
$2$ |
$15$ |
$1655807077.81$ |
| 16.0.575...000.1 |
$x^{16} + 50 x^{14} + 920 x^{12} + 8300 x^{10} + 39975 x^{8} + 103500 x^{6} + 137000 x^{4} + 81250 x^{2} + 15625$ |
$16$ |
[0,8] |
$2^{40}\cdot 5^{12}\cdot 11^{8}$ |
$3$ |
$62.7334013138$ |
$81.35515622154537$ |
✓ |
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[2, 2, 10, 20]$ |
$2$ |
$7$ |
$89318.5652847$ |
