| 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 |
Unit signature rank |
Max $p$ |
| 16.4.153...104.2 |
$x^{16} - 8 x^{14} - 8 x^{13} + 16 x^{12} + 24 x^{11} - 80 x^{10} - 336 x^{9} - 314 x^{8} + 944 x^{7} + 3520 x^{6} + 5776 x^{5} + 6164 x^{4} + 4864 x^{3} + 2728 x^{2} + 1264 x + 478$ |
$16$ |
(4, 6) |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.1238436786$ |
$33.44507500385779$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2]$ |
$2$ |
$9$ |
$283940.790469$ |
$3$ |
$3$ |
| 16.16.810...016.2 |
$x^{16} - 32 x^{14} - 16 x^{13} + 340 x^{12} + 264 x^{11} - 1448 x^{10} - 1200 x^{9} + 2746 x^{8} + 1936 x^{7} - 2456 x^{6} - 1072 x^{5} + 956 x^{4} + 80 x^{3} - 152 x^{2} + 32 x - 2$ |
$16$ |
(16, 0) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$97751967.49566491$ |
$14$ |
$23$ |
| 16.8.810...016.3 |
$x^{16} - 8 x^{14} - 8 x^{13} + 40 x^{12} - 24 x^{11} - 56 x^{10} + 96 x^{9} + 982 x^{8} - 4624 x^{7} + 7024 x^{6} + 544 x^{5} - 10756 x^{4} + 8128 x^{3} - 152 x^{2} - 1568 x + 382$ |
$16$ |
(8, 4) |
$2^{58}\cdot 3^{12}\cdot 23^{2}$ |
$3$ |
$41.61890549398486$ |
$160.39694500305947$ |
|
|
? |
$C_2^4:Q_8$ (as 16T333) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$6500801.080357627$ |
$7$ |
$23$ |
| 16.0.150...856.1 |
$x^{16} - 288 x^{13} + 1492 x^{12} - 4512 x^{11} + 31344 x^{10} - 146976 x^{9} + 883002 x^{8} - 2430912 x^{7} + 4234848 x^{6} - 20351904 x^{5} + 40473724 x^{4} - 50965728 x^{3} - 11526000 x^{2} + 290739552 x + 281522905$ |
$16$ |
(0, 8) |
$2^{58}\cdot 3^{10}\cdot 11^{10}\cdot 43^{4}$ |
$4$ |
$280.977834199$ |
$1324.6798063293725$ |
✓ |
|
? |
$C_2^6.(C_2\times D_4)$ (as 16T1143) |
$[2, 2, 2, 2, 30516]$ |
$[2, 2, 2, 2, 30516]$ |
$2$ |
$7$ |
$64598388.8936$ |
$0$ |
$43$ |
| 20.4.480...768.1 |
$x^{20} + 6 x^{18} + 20 x^{16} + 40 x^{14} + 6 x^{12} - 236 x^{10} - 524 x^{8} + 72 x^{6} + 737 x^{4} - 298 x^{2} + 32$ |
$20$ |
(4, 8) |
$2^{61}\cdot 113^{6}$ |
$2$ |
$34.2030645343$ |
|
|
|
|
$C_2^9.S_6:C_2$ (as 20T951) |
trivial |
$[2]$ |
$2$ |
$11$ |
$572116182.073$ |
$3$ |
$113$ |
| 20.4.480...768.2 |
$x^{20} - 7 x^{18} + 10 x^{16} - 120 x^{14} + 210 x^{12} - 270 x^{10} + 1100 x^{8} - 728 x^{6} + 193 x^{4} - 23 x^{2} + 2$ |
$20$ |
(4, 8) |
$2^{61}\cdot 113^{6}$ |
$2$ |
$34.2030645343$ |
|
|
|
? |
$C_2^9.S_6:C_2$ (as 20T951) |
trivial |
$[2]$ |
$2$ |
$11$ |
$122691592.972$ |
$3$ |
$113$ |
