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 |
16.0.277...776.1 |
$x^{16} - 4 x^{14} - 22 x^{12} - 4 x^{10} + 667 x^{8} - 1484 x^{6} + 3038 x^{4} - 2744 x^{2} + 2401$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{8}\cdot 7^{4}$ |
$3$ |
$18.9525488822$ |
$30.827771796137323$ |
|
|
? |
$(C_2 \times Q_8):C_2$ (as 16T20) |
trivial |
$24$ |
$7$ |
$28493.4786755$ |
16.0.115...000.1 |
$x^{16} - 16 x^{14} + 80 x^{12} - 8 x^{10} - 929 x^{8} - 120 x^{6} + 18000 x^{4} - 54000 x^{2} + 50625$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{8}\cdot 5^{4}$ |
$3$ |
$20.7201605129$ |
$30.983866769659336$ |
|
|
? |
$(C_2 \times Q_8):C_2$ (as 16T20) |
$[2]$ |
$24$ |
$7$ |
$31143.1180046$ |
16.8.665...176.1 |
$x^{16} - 4 x^{14} - 94 x^{12} + 164 x^{10} + 451 x^{8} - 452 x^{6} - 346 x^{4} - 32 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{44}\cdot 3^{8}\cdot 7^{8}$ |
$3$ |
$30.8277717961$ |
$30.827771796137323$ |
|
|
? |
$(C_2 \times Q_8):C_2$ (as 16T20) |
trivial |
$2$ |
$11$ |
$684312.287607$ |
16.8.721...000.1 |
$x^{16} - 16 x^{14} + 8 x^{12} + 824 x^{10} - 2897 x^{8} - 824 x^{6} + 8 x^{4} + 16 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{48}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$30.9838667697$ |
$30.983866769659336$ |
|
|
? |
$(C_2 \times Q_8):C_2$ (as 16T20) |
trivial |
$2$ |
$11$ |
$694806.379749$ |
16.0.407...000.1 |
$x^{16} - 8 x^{15} + 168 x^{14} - 856 x^{13} + 9606 x^{12} - 34032 x^{11} + 243628 x^{10} - 535048 x^{9} + 2701602 x^{8} - 1786640 x^{7} + 9946672 x^{6} + 21942216 x^{5} + 5432442 x^{4} + 95409688 x^{3} + 73950516 x^{2} + 33597560 x + 246399481$ |
$16$ |
[0,8] |
$2^{40}\cdot 3^{12}\cdot 5^{12}\cdot 13^{4}$ |
$4$ |
$81.8708447557$ |
$155.4587279001545$ |
✓ |
|
? |
$(C_2 \times Q_8):C_2$ (as 16T20) |
$[2, 2, 2, 2, 2, 30, 30]$ |
$2$ |
$7$ |
$15197.4244561$ |
16.16.505...000.1 |
$x^{16} - 4 x^{15} - 92 x^{14} + 224 x^{13} + 3304 x^{12} - 3220 x^{11} - 56336 x^{10} - 9328 x^{9} + 446455 x^{8} + 453156 x^{7} - 1289736 x^{6} - 2383248 x^{5} - 380520 x^{4} + 1605240 x^{3} + 1229976 x^{2} + 305568 x + 16857$ |
$16$ |
[16,0] |
$2^{40}\cdot 3^{12}\cdot 5^{4}\cdot 7^{12}$ |
$4$ |
$82.9816299835$ |
$124.08647925963417$ |
|
|
? |
$(C_2 \times Q_8):C_2$ (as 16T20) |
$[2]$ |
$2$ |
$15$ |
$8268264991.76$ |
16.0.505...000.1 |
$x^{16} - 4 x^{15} + 76 x^{14} - 112 x^{13} + 1624 x^{12} - 364 x^{11} + 19600 x^{10} + 920 x^{9} + 136663 x^{8} + 183684 x^{7} + 338520 x^{6} + 1297464 x^{5} + 2514456 x^{4} + 868392 x^{3} + 12532680 x^{2} - 3082824 x + 13379913$ |
$16$ |
[0,8] |
$2^{40}\cdot 3^{12}\cdot 5^{4}\cdot 7^{12}$ |
$4$ |
$82.9816299835$ |
$124.08647925963417$ |
✓ |
|
? |
$(C_2 \times Q_8):C_2$ (as 16T20) |
$[2, 2, 2, 2, 22, 44]$ |
$2$ |
$7$ |
$32719.5368105$ |
16.16.123...000.1 |
$x^{16} - 84 x^{14} + 2583 x^{12} - 37044 x^{10} + 268128 x^{8} - 981666 x^{6} + 1694763 x^{4} - 1166886 x^{2} + 194481$ |
$16$ |
[16,0] |
$2^{32}\cdot 3^{12}\cdot 5^{8}\cdot 7^{12}$ |
$4$ |
$87.7423909381$ |
$124.08647925963417$ |
|
|
|
$(C_2 \times Q_8):C_2$ (as 16T20) |
$[2]$ |
$2$ |
$15$ |
$16027729714.4$ |