| 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 |
| 16.8.598...184.2 |
$x^{16} - 16 x^{14} + 56 x^{12} - 112 x^{10} + 172 x^{8} - 176 x^{6} + 104 x^{4} - 32 x^{2} + 4$ |
$16$ |
[8,4] |
$2^{50}\cdot 3^{12}$ |
$2$ |
$19.8865605782$ |
$19.88656057819367$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
trivial |
$2$ |
$11$ |
$44199.7606366$ |
| 16.0.598...184.5 |
$x^{16} + 16 x^{14} + 56 x^{12} + 112 x^{10} + 172 x^{8} + 176 x^{6} + 104 x^{4} + 32 x^{2} + 4$ |
$16$ |
[0,8] |
$2^{50}\cdot 3^{12}$ |
$2$ |
$19.8865605782$ |
$19.88656057819367$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2]$ |
$2$ |
$7$ |
$2636.02787055$ |
| 16.8.239...736.1 |
$x^{16} - 8 x^{15} + 28 x^{14} - 40 x^{13} - 64 x^{12} + 424 x^{11} - 820 x^{10} + 368 x^{9} + 1378 x^{8} - 2680 x^{7} + 1328 x^{6} + 1240 x^{5} - 1744 x^{4} + 512 x^{3} + 160 x^{2} - 80 x - 2$ |
$16$ |
[8,4] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
trivial |
$2$ |
$11$ |
$90901.8794542$ |
| 16.8.239...736.2 |
$x^{16} - 8 x^{15} + 20 x^{14} - 16 x^{13} - 4 x^{12} + 32 x^{11} - 96 x^{10} + 168 x^{9} - 128 x^{8} - 144 x^{7} + 300 x^{6} - 112 x^{5} - 88 x^{4} + 56 x^{3} + 8 x^{2} - 8 x + 1$ |
$16$ |
[8,4] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
trivial |
$2$ |
$11$ |
$107901.929008$ |
| 16.0.239...736.4 |
$x^{16} - 8 x^{15} + 20 x^{14} - 8 x^{13} - 20 x^{12} - 16 x^{11} + 80 x^{10} - 64 x^{9} + 64 x^{8} - 144 x^{7} + 156 x^{6} - 120 x^{5} + 144 x^{4} - 72 x^{3} + 72 x^{2} + 9$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2]$ |
$2$ |
$7$ |
$6435.15910617$ |
| 16.0.239...736.6 |
$x^{16} - 8 x^{15} + 28 x^{14} - 48 x^{13} + 24 x^{12} + 64 x^{11} - 144 x^{10} + 192 x^{9} - 320 x^{8} + 544 x^{7} - 308 x^{6} - 880 x^{5} + 2748 x^{4} - 3864 x^{3} + 3416 x^{2} - 1760 x + 409$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2]$ |
$2$ |
$7$ |
$5421.293787$ |
| 16.8.957...944.4 |
$x^{16} - 8 x^{15} + 12 x^{14} + 32 x^{13} - 96 x^{12} + 72 x^{11} - 20 x^{10} - 136 x^{9} + 540 x^{8} - 272 x^{7} - 788 x^{6} + 648 x^{5} + 576 x^{4} - 560 x^{3} - 636 x^{2} - 208 x - 23$ |
$16$ |
[8,4] |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.64923933252054$ |
$23.64923933252054$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
trivial |
$2$ |
$11$ |
$221407.4337253862$ |
| 16.8.957...944.5 |
$x^{16} - 8 x^{14} - 32 x^{13} - 44 x^{12} + 144 x^{11} + 472 x^{10} + 576 x^{9} - 470 x^{8} - 2080 x^{7} - 2120 x^{6} + 160 x^{5} + 2492 x^{4} + 2032 x^{3} + 376 x^{2} - 128 x - 23$ |
$16$ |
[8,4] |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.64923933252054$ |
$23.64923933252054$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
trivial |
$2$ |
$11$ |
$184122.8873085744$ |
| 16.8.957...944.14 |
$x^{16} - 8 x^{15} + 32 x^{14} - 72 x^{13} + 44 x^{12} + 200 x^{11} - 800 x^{10} + 2040 x^{9} - 3110 x^{8} + 1272 x^{7} + 2848 x^{6} - 4712 x^{5} + 5156 x^{4} - 6552 x^{3} + 5600 x^{2} - 2248 x + 313$ |
$16$ |
[8,4] |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.64923933252054$ |
$23.64923933252054$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
trivial |
$2$ |
$11$ |
$223352.96650055132$ |
| 16.0.957...944.53 |
$x^{16} - 8 x^{15} + 16 x^{14} + 16 x^{13} - 32 x^{12} - 224 x^{11} + 592 x^{10} - 320 x^{9} - 548 x^{8} + 336 x^{7} + 864 x^{6} + 288 x^{5} + 864 x^{4} + 288 x^{2} + 36$ |
$16$ |
[0,8] |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.64923933252054$ |
$23.64923933252054$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2]$ |
$2$ |
$7$ |
$13320.53921073396$ |
| 16.0.957...944.65 |
$x^{16} - 8 x^{14} - 16 x^{13} + 28 x^{12} + 48 x^{11} - 8 x^{10} + 336 x^{9} + 250 x^{8} - 1568 x^{7} - 296 x^{6} + 2288 x^{5} - 268 x^{4} - 688 x^{3} + 1720 x^{2} - 496 x + 313$ |
$16$ |
[0,8] |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.64923933252054$ |
$23.64923933252054$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2]$ |
$2$ |
$7$ |
$10980.897985885322$ |
| 16.0.957...944.80 |
$x^{16} - 8 x^{15} + 36 x^{14} - 88 x^{13} + 156 x^{12} - 192 x^{11} + 292 x^{10} - 448 x^{9} + 1140 x^{8} - 1376 x^{7} + 2308 x^{6} - 1680 x^{5} + 1764 x^{4} - 1160 x^{3} + 36 x^{2} - 280 x + 457$ |
$16$ |
[0,8] |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.64923933252054$ |
$23.64923933252054$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2]$ |
$2$ |
$7$ |
$13204.509654362291$ |
| 16.0.149...000.1 |
$x^{16} + 4 x^{12} - 48 x^{10} + 246 x^{8} + 768 x^{6} + 1924 x^{4} + 2352 x^{2} + 2401$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$32.4288037154$ |
$48.49237211223896$ |
✓ |
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2, 6]$ |
$2$ |
$7$ |
$45687.5845647$ |
| 16.16.149...000.1 |
$x^{16} - 24 x^{14} + 220 x^{12} - 984 x^{10} + 2262 x^{8} - 2568 x^{6} + 1180 x^{4} - 72 x^{2} + 1$ |
$16$ |
[16,0] |
$2^{52}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$32.4288037154$ |
$48.49237211223896$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
trivial |
$2$ |
$15$ |
$14732523.2621$ |
| 16.0.149...000.2 |
$x^{16} + 4 x^{12} + 48 x^{10} + 246 x^{8} - 768 x^{6} + 1924 x^{4} - 2352 x^{2} + 2401$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$32.4288037154$ |
$48.49237211223896$ |
✓ |
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2, 2]$ |
$2$ |
$7$ |
$84223.0358383$ |
| 16.0.149...000.3 |
$x^{16} + 24 x^{14} + 220 x^{12} + 984 x^{10} + 2262 x^{8} + 2568 x^{6} + 1180 x^{4} + 72 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{52}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$32.4288037154$ |
$48.49237211223896$ |
✓ |
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2, 6]$ |
$2$ |
$7$ |
$28425.2702638$ |
| 16.16.219...736.1 |
$x^{16} - 20 x^{14} + 140 x^{12} - 440 x^{10} + 679 x^{8} - 520 x^{6} + 188 x^{4} - 28 x^{2} + 1$ |
$16$ |
[16,0] |
$2^{48}\cdot 3^{12}\cdot 11^{4}$ |
$3$ |
$33.2107818055$ |
$60.48215691909035$ |
|
|
? |
$C_2^2:Q_8$ (as 16T31) |
trivial |
$2$ |
$15$ |
$10625489.8901$ |
| 16.0.219...736.1 |
$x^{16} + 20 x^{14} + 140 x^{12} + 440 x^{10} + 679 x^{8} + 520 x^{6} + 188 x^{4} + 28 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}\cdot 11^{4}$ |
$3$ |
$33.2107818055$ |
$60.48215691909035$ |
✓ |
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2, 10]$ |
$2$ |
$7$ |
$9987.74147402$ |
| 16.0.598...000.1 |
$x^{16} - 8 x^{15} + 36 x^{14} - 48 x^{13} + 128 x^{12} + 120 x^{11} + 56 x^{10} + 256 x^{9} + 1026 x^{8} - 232 x^{7} - 304 x^{6} + 432 x^{5} + 764 x^{4} + 1392 x^{3} + 4968 x^{2} + 4592 x + 1438$ |
$16$ |
[0,8] |
$2^{54}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$35.3638612127$ |
$52.881306763677685$ |
✓ |
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2, 8]$ |
$2$ |
$7$ |
$34258.1672484$ |
| 16.0.167...744.1 |
$x^{16} + 16 x^{14} + 248 x^{12} + 1696 x^{10} + 8098 x^{8} + 17744 x^{6} + 32408 x^{4} + 27104 x^{2} + 14641$ |
$16$ |
[0,8] |
$2^{50}\cdot 3^{12}\cdot 23^{4}$ |
$3$ |
$43.5503486816$ |
$95.37259411116924$ |
✓ |
|
? |
$C_2^2:Q_8$ (as 16T31) |
$[2, 2, 2, 10]$ |
$2$ |
$7$ |
$45687.5845647$ |
