| 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 |
| 16.0.110...624.1 |
$x^{16} - 10 x^{14} - 32 x^{13} + 32 x^{12} + 420 x^{11} + 1436 x^{10} + 2964 x^{9} + 4402 x^{8} + 4824 x^{7} + 4072 x^{6} + 2312 x^{5} + 816 x^{4} + 104 x^{3} + 832 x^{2} + 1352 x + 676$ |
$16$ |
[0,8] |
$2^{32}\cdot 3^{12}\cdot 13^{6}$ |
$3$ |
$23.8577613212$ |
$32.875518306529855$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
$[2]$ |
$12$ |
$7$ |
$142361.959547$ |
| 16.4.281...000.1 |
$x^{16} - 6 x^{12} - 3 x^{8} + 6 x^{4} + 1$ |
$16$ |
[4,6] |
$2^{56}\cdot 5^{8}$ |
$2$ |
$25.2982212813$ |
$27.587905929985723$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$9$ |
$60389.7547999$ |
| 16.0.614...304.1 |
$x^{16} - 5 x^{15} + x^{14} + 67 x^{13} - 239 x^{12} + 250 x^{11} + 697 x^{10} - 3239 x^{9} + 6556 x^{8} - 8508 x^{7} + 7935 x^{6} - 5790 x^{5} + 3645 x^{4} - 1992 x^{3} + 876 x^{2} - 255 x + 93$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{14}\cdot 11^{12}$ |
$3$ |
$26.5642836233$ |
$31.590435089833612$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
$[2]$ |
$6$ |
$7$ |
$135461.540139$ |
| 16.4.687...000.3 |
$x^{16} - 100 x^{12} - 700 x^{10} - 2225 x^{8} - 3500 x^{6} - 1250 x^{4} + 2500 x^{2} + 625$ |
$16$ |
[4,6] |
$2^{48}\cdot 5^{12}$ |
$2$ |
$26.7496121991$ |
$29.170658948868436$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$9$ |
$100677.268017$ |
| 16.4.121...576.64 |
$x^{16} - 28 x^{8} + 4$ |
$16$ |
[4,6] |
$2^{64}\cdot 3^{8}$ |
$2$ |
$27.712812921102035$ |
$27.712812921102035$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$9$ |
$203526.5980818538$ |
| 16.4.153...104.89 |
$x^{16} - 36 x^{12} + 18 x^{8} + 324 x^{4} + 81$ |
$16$ |
[4,6] |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$28.12384367863563$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$9$ |
$384974.68852479925$ |
| 16.4.153...104.91 |
$x^{16} - 24 x^{14} + 216 x^{12} - 936 x^{10} + 1926 x^{8} - 1512 x^{6} - 216 x^{4} + 648 x^{2} + 81$ |
$16$ |
[4,6] |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$28.12384367863563$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$9$ |
$229772.31607001027$ |
| 16.4.171...000.5 |
$x^{16} + 60 x^{12} - 370 x^{8} + 300 x^{4} + 25$ |
$16$ |
[4,6] |
$2^{32}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$28.328225605775355$ |
$28.328225605775355$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
$[2]$ |
$2$ |
$9$ |
$141594.96124053487$ |
| 16.0.344...984.54 |
$x^{16} - 6 x^{12} + 21 x^{8} - 54 x^{4} + 81$ |
$16$ |
[0,8] |
$2^{56}\cdot 3^{14}$ |
$2$ |
$29.5859884044903$ |
$32.263749133641326$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$6$ |
$7$ |
$941640.6449205403$ |
| 16.0.137...936.72 |
$x^{16} + 36 x^{12} + 336 x^{8} + 504 x^{4} + 36$ |
$16$ |
[0,8] |
$2^{58}\cdot 3^{14}$ |
$2$ |
$32.263749133641326$ |
$32.263749133641326$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
$[2]$ |
$2$ |
$7$ |
$394674.9433965808$ |
| 16.4.980...656.208 |
$x^{16} - 36 x^{8} + 81$ |
$16$ |
[4,6] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$36.47211291127644$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$9$ |
$2396964.5115392674$ |
| 16.4.980...656.271 |
$x^{16} - 252 x^{8} + 324$ |
$16$ |
[4,6] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$36.47211291127644$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$9$ |
$3156827.5236954773$ |
| 16.0.222...216.1 |
$x^{16} + 24 x^{14} + 216 x^{12} + 936 x^{10} + 2150 x^{8} + 2664 x^{6} + 1704 x^{4} + 504 x^{2} + 49$ |
$16$ |
[0,8] |
$2^{58}\cdot 3^{8}\cdot 7^{6}$ |
$3$ |
$44.3308569516$ |
$56.53838276009771$ |
✓ |
|
? |
$Q_{16}:C_2$ (as 16T32) |
$[2, 6, 6]$ |
$2$ |
$7$ |
$55074.4803232$ |
| 16.16.222...216.1 |
$x^{16} - 24 x^{14} + 216 x^{12} - 936 x^{10} + 2150 x^{8} - 2664 x^{6} + 1704 x^{4} - 504 x^{2} + 49$ |
$16$ |
[16,0] |
$2^{58}\cdot 3^{8}\cdot 7^{6}$ |
$3$ |
$44.3308569516$ |
$56.53838276009771$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$15$ |
$159873437.742$ |
| 16.16.760...000.1 |
$x^{16} - 4 x^{15} - 56 x^{14} + 296 x^{13} + 564 x^{12} - 5196 x^{11} + 2648 x^{10} + 31228 x^{9} - 51539 x^{8} - 39900 x^{7} + 149508 x^{6} - 94692 x^{5} - 15156 x^{4} + 24840 x^{3} - 2440 x^{2} - 612 x + 71$ |
$16$ |
[16,0] |
$2^{44}\cdot 5^{12}\cdot 11^{6}$ |
$3$ |
$55.2818092724$ |
$81.35515622154537$ |
|
|
? |
$Q_{16}:C_2$ (as 16T32) |
trivial |
$2$ |
$15$ |
$643917823.697$ |
| 16.0.760...000.1 |
$x^{16} - 4 x^{15} + 44 x^{14} - 224 x^{13} + 1224 x^{12} - 4236 x^{11} + 16008 x^{10} - 42732 x^{9} + 116061 x^{8} - 243740 x^{7} + 504548 x^{6} - 792892 x^{5} + 1171864 x^{4} - 1295280 x^{3} + 1278140 x^{2} - 673492 x + 153991$ |
$16$ |
[0,8] |
$2^{44}\cdot 5^{12}\cdot 11^{6}$ |
$3$ |
$55.2818092724$ |
$81.35515622154537$ |
✓ |
|
? |
$Q_{16}:C_2$ (as 16T32) |
$[2, 20, 20]$ |
$2$ |
$7$ |
$17367.3059334$ |
