| 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 |
| 16.0.7213895789838336.1 |
$x^{16} - 8 x^{15} + 36 x^{14} - 108 x^{13} + 244 x^{12} - 436 x^{11} + 636 x^{10} - 780 x^{9} + 831 x^{8} - 780 x^{7} + 636 x^{6} - 436 x^{5} + 244 x^{4} - 108 x^{3} + 36 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$2^{40}\cdot 3^{8}$ |
$2$ |
$9.79795897113$ |
$9.797958971132712$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$24$ |
$7$ |
$168.461389974$ |
| 16.0.13604889600000000.1 |
$x^{16} + 7 x^{14} + 19 x^{12} + 25 x^{10} + 40 x^{8} + 25 x^{6} + 19 x^{4} + 7 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$10.1942654691$ |
$10.194265469082735$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$12$ |
$7$ |
$114.277788343$ |
| 16.0.42998169600000000.2 |
$x^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} - 20 x^{11} - 7 x^{10} + 31 x^{8} - 7 x^{6} - 20 x^{5} + 6 x^{4} + 2 x^{3} + 5 x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$10.9544511501$ |
$10.954451150103322$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$6$ |
$7$ |
$95.9988129964$ |
| 16.0.584325558976905216.6 |
$x^{16} - 4 x^{15} + 12 x^{14} - 32 x^{13} + 84 x^{12} - 180 x^{11} + 280 x^{10} - 296 x^{9} + 249 x^{8} - 388 x^{7} + 940 x^{6} - 1656 x^{5} + 1914 x^{4} - 1456 x^{3} + 708 x^{2} - 200 x + 25$ |
$16$ |
[0,8] |
$2^{40}\cdot 3^{12}$ |
$2$ |
$12.8948391819$ |
$12.894839181882503$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$24$ |
$7$ |
$2279.43025028$ |
| 16.0.184...016.2 |
$x^{16} - 12 x^{14} + 60 x^{12} - 144 x^{10} + 191 x^{8} - 144 x^{6} + 60 x^{4} - 12 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{8}$ |
$2$ |
$13.8564064606$ |
$13.856406460551018$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$24$ |
$7$ |
$3719.97240803$ |
| 16.0.934...456.10 |
$x^{16} - 4 x^{15} + 16 x^{14} - 40 x^{13} + 96 x^{12} - 172 x^{11} + 268 x^{10} - 396 x^{9} + 595 x^{8} - 948 x^{7} + 1436 x^{6} - 1788 x^{5} + 1736 x^{4} - 1280 x^{3} + 692 x^{2} - 252 x + 49$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{12}$ |
$2$ |
$15.3346345019$ |
$15.33463450191054$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$24$ |
$7$ |
$9197.54888215$ |
| 16.0.110...000.11 |
$x^{16} + 6 x^{14} + 26 x^{12} + 80 x^{10} + 135 x^{8} + 80 x^{6} + 66 x^{4} + 14 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{32}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[2]$ |
$6$ |
$7$ |
$1580.48272444$ |
| 16.0.178...625.1 |
$x^{16} + 5 x^{14} + 29 x^{12} + 10 x^{10} + 82 x^{8} - 30 x^{6} + 261 x^{4} - 135 x^{2} + 81$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{8}\cdot 17^{8}$ |
$3$ |
$15.9687194227$ |
$15.968719422671311$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[3]$ |
$6$ |
$7$ |
$1193.88585358$ |
| 16.0.284...096.1 |
$x^{16} - 13 x^{14} + 67 x^{12} - 247 x^{10} + 640 x^{8} - 247 x^{6} + 67 x^{4} - 13 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{12}\cdot 13^{8}$ |
$3$ |
$16.4377591533$ |
$16.437759153264928$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
$[2]$ |
$12$ |
$7$ |
$4976.56702876$ |
| 16.0.513...056.6 |
$x^{16} - 2 x^{15} + 11 x^{14} - 20 x^{13} + 43 x^{12} - 40 x^{11} + 41 x^{10} + 8 x^{9} - 56 x^{8} + 72 x^{7} - 39 x^{6} - 204 x^{5} + 585 x^{4} - 738 x^{3} + 576 x^{2} - 252 x + 63$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{12}\cdot 7^{8}$ |
$3$ |
$17.0582688357$ |
$17.058268835716344$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[2]$ |
$6$ |
$7$ |
$5348.4217908$ |
| 16.0.109...000.5 |
$x^{16} + 7 x^{8} + 1$ |
$16$ |
[0,8] |
$2^{48}\cdot 5^{8}$ |
$2$ |
$17.88854382$ |
$17.88854381999832$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
trivial |
$8$ |
$7$ |
$18626.6250524$ |
| 16.0.109...000.6 |
$x^{16} - 4 x^{14} + 8 x^{12} + 16 x^{10} + 23 x^{8} - 16 x^{6} + 8 x^{4} + 4 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{48}\cdot 5^{8}$ |
$2$ |
$17.88854382$ |
$17.88854381999832$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$8$ |
$7$ |
$9717.26549391$ |
| 16.0.149...296.15 |
$x^{16} - 12 x^{12} + 135 x^{8} - 108 x^{4} + 81$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}$ |
$2$ |
$18.2360564556$ |
$18.23605645563822$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$24$ |
$7$ |
$35686.7163536$ |
| 16.0.149...296.16 |
$x^{16} - 9 x^{8} + 81$ |
$16$ |
[0,8] |
$2^{48}\cdot 3^{12}$ |
$2$ |
$18.2360564556$ |
$18.23605645563822$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$24$ |
$7$ |
$44535.0027558$ |
| 16.0.235...656.1 |
$x^{16} - 8 x^{15} + 24 x^{14} - 28 x^{13} - 38 x^{12} + 228 x^{11} - 360 x^{10} - 4 x^{9} + 1013 x^{8} - 2092 x^{7} + 2316 x^{6} - 1532 x^{5} + 776 x^{4} - 492 x^{3} + 580 x^{2} - 384 x + 89$ |
$16$ |
[0,8] |
$2^{40}\cdot 11^{8}$ |
$2$ |
$18.7616630393$ |
$18.76166303929372$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$8$ |
$7$ |
$16135.3882167$ |
| 16.0.482...576.2 |
$x^{16} - 2 x^{15} - 13 x^{14} + 28 x^{13} + 67 x^{12} - 160 x^{11} - 142 x^{10} + 350 x^{9} + 457 x^{8} - 1188 x^{7} + 462 x^{6} + 486 x^{5} - 354 x^{4} - 126 x^{3} + 198 x^{2} - 72 x + 9$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{12}\cdot 7^{12}$ |
$3$ |
$19.6197950646$ |
$19.619795064584405$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
$[2]$ |
$12$ |
$7$ |
$15923.474336$ |
| 16.0.747...625.3 |
$x^{16} + 15 x^{14} + 94 x^{12} + 315 x^{10} + 606 x^{8} + 735 x^{6} + 769 x^{4} + 720 x^{2} + 256$ |
$16$ |
[0,8] |
$3^{12}\cdot 5^{12}\cdot 7^{8}$ |
$3$ |
$20.1658932694$ |
$20.165893269373882$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[2]$ |
$6$ |
$7$ |
$56442.6212096$ |
| 16.0.891...000.10 |
$x^{16} + 9 x^{12} + 72 x^{8} + 81 x^{4} + 81$ |
$16$ |
[0,8] |
$2^{32}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$20.3885309382$ |
$20.38853093816547$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[2, 2]$ |
$12$ |
$7$ |
$14306.6698327$ |
| 16.0.968...000.3 |
$x^{16} + 14 x^{14} + 25 x^{12} - 89 x^{10} + 174 x^{8} + 641 x^{6} + 355 x^{4} + 79 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}$ |
$4$ |
$20.4939015319$ |
$20.493901531919196$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
$[4]$ |
$4$ |
$7$ |
$3589.92961547$ |
| 16.0.968...000.12 |
$x^{16} + 15 x^{14} + 83 x^{12} + 185 x^{10} - 54 x^{8} - 925 x^{6} - 675 x^{4} + 1250 x^{2} + 625$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}$ |
$4$ |
$20.4939015319$ |
$20.493901531919196$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[4]$ |
$4$ |
$7$ |
$11981.4998298$ |
| 16.0.130...625.3 |
$x^{16} - x^{15} + 7 x^{14} + 25 x^{12} + 21 x^{11} + 66 x^{10} + 165 x^{9} + 109 x^{8} + 440 x^{7} + 519 x^{6} + 563 x^{5} + 725 x^{4} + 620 x^{3} + 708 x^{2} + 112 x + 16$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{12}\cdot 13^{8}$ |
$3$ |
$20.8814093301$ |
$20.88140933013045$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[4]$ |
$6$ |
$7$ |
$33349.777132$ |
| 16.0.183...625.1 |
$x^{16} - 8 x^{15} + 28 x^{14} - 56 x^{13} + 104 x^{12} - 260 x^{11} + 510 x^{10} - 548 x^{9} + 454 x^{8} - 816 x^{7} + 756 x^{6} + 564 x^{5} - 311 x^{4} - 1312 x^{3} - 1822 x^{2} + 2716 x + 2909$ |
$16$ |
[0,8] |
$5^{8}\cdot 7^{8}\cdot 13^{8}$ |
$3$ |
$21.3307290077$ |
$21.330729007701542$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[5]$ |
$2$ |
$7$ |
$2265.94822301$ |
| 16.0.217...000.7 |
$x^{16} - 6 x^{15} + 13 x^{14} - 12 x^{13} + 18 x^{12} - 150 x^{11} + 604 x^{10} - 1206 x^{9} + 1123 x^{8} + 342 x^{7} - 2094 x^{6} + 1614 x^{5} + 648 x^{4} - 1656 x^{3} + 117 x^{2} + 1134 x + 441$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$21.5582467178$ |
$21.558246717785053$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
$[2]$ |
$6$ |
$7$ |
$26643.8469845$ |
| 16.0.217...000.9 |
$x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} + 38 x^{12} - 46 x^{11} + 24 x^{10} + 18 x^{9} + 223 x^{8} - 174 x^{7} - 24 x^{6} + 1082 x^{5} - 322 x^{4} - 1828 x^{3} + 3698 x^{2} - 2666 x + 961$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$21.5582467178$ |
$21.558246717785053$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[2, 2]$ |
$12$ |
$7$ |
$24155.7451013$ |
| 16.0.281...000.1 |
$x^{16} - 4 x^{15} - 16 x^{14} + 52 x^{13} + 156 x^{12} - 240 x^{11} - 908 x^{10} + 288 x^{9} + 2367 x^{8} + 1912 x^{7} - 1100 x^{6} - 7848 x^{5} - 2996 x^{4} + 6780 x^{3} + 3936 x^{2} - 100 x + 1$ |
$16$ |
[0,8] |
$2^{40}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$21.9089023002$ |
$21.908902300206645$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
$[2, 2]$ |
$24$ |
$7$ |
$31102.0401588$ |
| 16.0.352...625.1 |
$x^{16} - 8 x^{15} + 54 x^{14} - 238 x^{13} + 879 x^{12} - 2544 x^{11} + 6166 x^{10} - 12229 x^{9} + 19974 x^{8} - 26498 x^{7} + 27823 x^{6} - 22494 x^{5} + 13680 x^{4} - 6083 x^{3} + 1944 x^{2} - 427 x + 49$ |
$16$ |
[0,8] |
$3^{12}\cdot 5^{8}\cdot 19^{8}$ |
$3$ |
$22.2178864917$ |
$22.21788649167895$ |
|
✓ |
|
$Q_8 : C_2$ (as 16T11) |
$[4]$ |
$6$ |
$7$ |
$11398.5231056$ |
| 16.16.534...000.1 |
$x^{16} - 4 x^{15} - 20 x^{14} + 100 x^{13} + 44 x^{12} - 624 x^{11} + 362 x^{10} + 1370 x^{9} - 1453 x^{8} - 936 x^{7} + 1580 x^{6} - 82 x^{5} - 459 x^{4} + 86 x^{3} + 41 x^{2} - 6 x - 1$ |
$16$ |
[16,0] |
$2^{24}\cdot 5^{8}\cdot 13^{8}$ |
$3$ |
$22.803508502$ |
$22.80350850198276$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$2$ |
$15$ |
$316695.993468$ |
| 16.16.450...000.1 |
$x^{16} - 24 x^{14} + 198 x^{12} - 684 x^{10} + 1043 x^{8} - 756 x^{6} + 258 x^{4} - 36 x^{2} + 1$ |
$16$ |
[16,0] |
$2^{44}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$26.0542224973$ |
$26.054222497305222$ |
|
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
trivial |
$2$ |
$15$ |
$1201189.95367$ |
| 16.0.450...000.3 |
$x^{16} + 24 x^{14} + 198 x^{12} + 684 x^{10} + 1043 x^{8} + 756 x^{6} + 258 x^{4} + 36 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$26.0542224973$ |
$26.054222497305222$ |
✓ |
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
$[2, 2]$ |
$2$ |
$7$ |
$7598.71222803$ |
| 16.0.228...000.1 |
$x^{16} - 4 x^{15} + 4 x^{14} - 16 x^{13} + 78 x^{12} - 112 x^{11} + 280 x^{10} - 576 x^{9} + 874 x^{8} - 1344 x^{7} + 3056 x^{6} - 2712 x^{5} + 3188 x^{4} - 2288 x^{3} - 1312 x^{2} + 816 x + 1156$ |
$16$ |
[0,8] |
$2^{40}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$28.8337369696$ |
$28.83373696961705$ |
✓ |
✓ |
? |
$Q_8 : C_2$ (as 16T11) |
$[2, 2, 2]$ |
$2$ |
$7$ |
$15197.4244561$ |
