| 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 |
| 16.0.3750900906670801.1 |
$x^{16} - 4 x^{15} + 10 x^{14} - 18 x^{13} + 29 x^{12} - 43 x^{11} + 58 x^{10} - 73 x^{9} + 85 x^{8} - 88 x^{7} + 81 x^{6} - 65 x^{5} + 45 x^{4} - 26 x^{3} + 12 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$13^{2}\cdot 43^{2}\cdot 331^{4}$ |
$3$ |
$9.40553436247$ |
$430.1499738463319$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$8.20527213707$ |
| 16.0.5850424087444225.1 |
$x^{16} - x^{15} - 2 x^{14} + 6 x^{13} + x^{12} - 16 x^{11} + 16 x^{10} + 5 x^{9} - 19 x^{8} + 5 x^{7} + 16 x^{6} - 16 x^{5} + x^{4} + 6 x^{3} - 2 x^{2} - x + 1$ |
$16$ |
[0,8] |
$5^{2}\cdot 37^{2}\cdot 643^{4}$ |
$3$ |
$9.67050623513$ |
$344.8985358043725$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$10.6388599051$ |
| 16.0.6468474822995241.1 |
$x^{16} - 4 x^{15} + 9 x^{14} - 14 x^{13} + 16 x^{12} - 9 x^{11} - 8 x^{10} + 27 x^{9} - 35 x^{8} + 27 x^{7} - 8 x^{6} - 9 x^{5} + 16 x^{4} - 14 x^{3} + 9 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$3^{2}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4}$ |
$4$ |
$9.73139538561$ |
$202.7239502377556$ |
|
|
✓ |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$11.6239832087$ |
| 16.0.15224515627376896.1 |
$x^{16} - 3 x^{15} + 4 x^{14} - 7 x^{12} + 10 x^{11} - 3 x^{10} - 7 x^{9} + 12 x^{8} - 7 x^{7} - 3 x^{6} + 10 x^{5} - 7 x^{4} + 4 x^{2} - 3 x + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 2777^{4}$ |
$2$ |
$10.2661822023$ |
$210.78899402008636$ |
|
|
✓ |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$31.042083439$ |
| 16.0.56513372936922225.1 |
$x^{16} - 4 x^{15} + 10 x^{14} - 15 x^{13} + 16 x^{12} - 12 x^{11} + 11 x^{10} - 9 x^{9} + 13 x^{8} - 9 x^{7} + 11 x^{6} - 12 x^{5} + 16 x^{4} - 15 x^{3} + 10 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$3^{6}\cdot 5^{2}\cdot 1327^{4}$ |
$3$ |
$11.143187848304358$ |
$185.6784083426463$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$50.71857743068159$ |
| 16.0.121485239855939584.4 |
$x^{16} - 4 x^{14} + 8 x^{12} - 8 x^{10} + 3 x^{8} + 2 x^{6} - x^{4} - x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 17^{2}\cdot 283^{4}$ |
$3$ |
$11.689144294$ |
$254.4186362288933$ |
|
|
✓ |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$56.5032173873$ |
| 16.4.382030401053594241.1 |
$x^{16} - x^{15} - 4 x^{14} + 4 x^{13} + 10 x^{12} - 3 x^{11} - 18 x^{10} - 5 x^{9} + 2 x^{8} + x^{7} + 8 x^{6} + 16 x^{5} + 3 x^{4} + 16 x^{3} + 3 x^{2} + 3 x + 1$ |
$16$ |
[4,6] |
$3^{6}\cdot 13^{2}\cdot 1327^{4}$ |
$3$ |
$12.5568619681$ |
$299.39743727044845$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$222.519410564$ |
| 16.4.503360547930148624.1 |
$x^{16} + 6 x^{14} + 6 x^{12} - 3 x^{10} + 22 x^{8} + 42 x^{6} - 7 x^{4} - 21 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{4}\cdot 23^{2}\cdot 2777^{4}$ |
$3$ |
$12.7751923657$ |
$505.4542511444532$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$291.344930357$ |
| 16.0.858064711060094976.1 |
$x^{16} + x^{12} + 7 x^{8} + x^{6} + 3 x^{4} + 3 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{2}\cdot 23^{2}\cdot 229^{4}$ |
$4$ |
$13.2082415489$ |
|
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$190.345542449$ |
| 16.0.858064711060094976.2 |
$x^{16} + 6 x^{12} - x^{10} + 11 x^{8} - x^{6} + 6 x^{4} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{2}\cdot 23^{2}\cdot 229^{4}$ |
$4$ |
$13.2082415489$ |
|
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$157.749405876$ |
| 16.0.124...481.1 |
$x^{16} - 5 x^{15} + 12 x^{14} - 17 x^{13} + 20 x^{12} - 33 x^{11} + 62 x^{10} - 81 x^{9} + 77 x^{8} - 70 x^{7} + 93 x^{6} - 112 x^{5} + 92 x^{4} - 61 x^{3} + 46 x^{2} - 30 x + 9$ |
$16$ |
[0,8] |
$3^{2}\cdot 19^{4}\cdot 97^{2}\cdot 103^{4}$ |
$4$ |
$13.5171250023$ |
$754.6436245009959$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$381.907701445$ |
| 16.4.132...401.1 |
$x^{16} - x^{15} - 7 x^{14} + 2 x^{13} + 11 x^{12} + x^{11} - 11 x^{10} - 2 x^{9} + 11 x^{8} - 2 x^{7} - 11 x^{6} + x^{5} + 11 x^{4} + 2 x^{3} - 7 x^{2} - x + 1$ |
$16$ |
[4,6] |
$7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 103^{4}$ |
$4$ |
$13.5743336077$ |
$767.500488599193$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$539.112493485$ |
| 16.4.140...281.1 |
$x^{16} - x^{15} - 2 x^{14} + 5 x^{13} - 7 x^{12} - 5 x^{11} + 21 x^{10} + 9 x^{9} - 23 x^{8} + 19 x^{7} + 7 x^{6} - 72 x^{5} + 28 x^{4} + 59 x^{3} - 32 x^{2} - 15 x + 9$ |
$16$ |
[4,6] |
$3^{2}\cdot 19^{4}\cdot 103^{6}$ |
$3$ |
$13.6189152203$ |
$244.09863248010305$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$767.372560815$ |
| 16.4.145...144.1 |
$x^{16} - 3 x^{14} + 5 x^{12} - 8 x^{10} + 9 x^{8} - 8 x^{6} + 5 x^{4} - 3 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{16}\cdot 43^{2}\cdot 331^{4}$ |
$3$ |
$13.6511912497$ |
|
|
|
✓ |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$470.848623252$ |
| 16.4.145...144.2 |
$x^{16} - 4 x^{14} + 9 x^{12} - 19 x^{10} + 27 x^{8} - 28 x^{6} + 18 x^{4} - 6 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{16}\cdot 43^{2}\cdot 331^{4}$ |
$3$ |
$13.6511912497$ |
|
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$445.363754488$ |
| 16.0.220...521.1 |
$x^{16} - x^{14} + 8 x^{12} - 2 x^{10} + 20 x^{8} + 7 x^{6} + 30 x^{4} + 15 x^{2} + 49$ |
$16$ |
[0,8] |
$37^{2}\cdot 97^{2}\cdot 643^{4}$ |
$3$ |
$14.0095577408$ |
$1519.120469218949$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$262.281294865$ |
| 16.8.457...225.1 |
$x^{16} - 20 x^{12} + 46 x^{10} - 10 x^{8} - 76 x^{6} + 93 x^{4} - 34 x^{2} + 1$ |
$16$ |
[8,4] |
$3^{10}\cdot 5^{2}\cdot 1327^{4}$ |
$3$ |
$14.6652599486$ |
$185.6784083426463$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$1681.65919709$ |
| 16.8.471...689.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 18 x^{13} - 45 x^{12} + 10 x^{11} + 102 x^{10} - 112 x^{9} - 64 x^{8} + 156 x^{7} - 16 x^{6} - 89 x^{5} + 31 x^{4} + 24 x^{3} - 11 x^{2} - 3 x + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4}$ |
$4$ |
$14.692496258$ |
$202.7239502377556$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$1706.05390163$ |
| 16.0.865...024.1 |
$x^{16} + x^{10} - x^{8} + x^{6} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{2}\cdot 19^{4}\cdot 103^{4}$ |
$4$ |
$15.2604682242$ |
|
|
|
✓ |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$926.825871335$ |
| 16.4.865...024.1 |
$x^{16} - x^{10} - x^{8} - x^{6} + 1$ |
$16$ |
[4,6] |
$2^{16}\cdot 3^{2}\cdot 19^{4}\cdot 103^{4}$ |
$4$ |
$15.260468224211051$ |
|
|
|
✓ |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$1274.7393091275173$ |
| 16.8.119...609.1 |
$x^{16} - 4 x^{15} - x^{14} + 13 x^{13} + 2 x^{12} - 8 x^{11} - 13 x^{10} + x^{9} + 27 x^{8} + x^{7} - 13 x^{6} - 8 x^{5} + 2 x^{4} + 13 x^{3} - x^{2} - 4 x + 1$ |
$16$ |
[8,4] |
$3^{2}\cdot 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 103^{4}$ |
$5$ |
$15.5725120357$ |
$1329.34984108774$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$2853.11388035$ |
| 16.8.269...904.1 |
$x^{16} - 8 x^{14} + 26 x^{12} - 41 x^{10} + 24 x^{8} + 9 x^{6} - 10 x^{4} - x^{2} + 1$ |
$16$ |
[8,4] |
$2^{16}\cdot 11^{2}\cdot 23^{2}\cdot 283^{4}$ |
$4$ |
$16.3819904979$ |
|
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$4639.55424287$ |
| 16.8.281...704.1 |
$x^{16} - 4 x^{14} - 11 x^{12} + 25 x^{10} + 64 x^{8} + 25 x^{6} - 11 x^{4} - 4 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{8}\cdot 43^{2}\cdot 2777^{4}$ |
$3$ |
$16.4282962073$ |
$1382.2358698861783$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$7694.89620613$ |
| 16.0.358...616.1 |
$x^{16} + 5 x^{14} + 17 x^{12} + 34 x^{10} + 60 x^{8} + 19 x^{6} + 68 x^{4} - 32 x^{2} + 64$ |
$16$ |
[0,8] |
$2^{6}\cdot 97^{2}\cdot 2777^{4}$ |
$3$ |
$16.6773362486$ |
$1467.9754766344022$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$7$ |
$1192.8395084$ |
| 16.8.341...456.1 |
$x^{16} - 9 x^{12} - x^{10} + 59 x^{8} - 102 x^{6} + 68 x^{4} - 16 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{16}\cdot 17^{2}\cdot 53^{2}\cdot 283^{4}$ |
$4$ |
$19.2007062492$ |
|
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$20260.1764433$ |
| 16.12.700...944.1 |
$x^{16} - 9 x^{14} + 19 x^{12} + 2 x^{10} - 27 x^{8} + 2 x^{6} + 19 x^{4} - 9 x^{2} + 1$ |
$16$ |
[12,2] |
$2^{16}\cdot 3^{6}\cdot 19^{4}\cdot 103^{4}$ |
$4$ |
$20.0839056554$ |
|
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$13$ |
$56100.6192446$ |
| 16.12.905...649.1 |
$x^{16} - 8 x^{15} + 24 x^{14} - 28 x^{13} - 39 x^{12} + 234 x^{11} - 381 x^{10} + 46 x^{9} + 654 x^{8} - 890 x^{7} + 425 x^{6} + 78 x^{5} - 176 x^{4} + 64 x^{3} + 2 x^{2} - 6 x + 1$ |
$16$ |
[12,2] |
$3^{8}\cdot 19^{4}\cdot 97^{2}\cdot 103^{4}$ |
$4$ |
$20.4082046454$ |
$754.6436245009959$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$13$ |
$61811.3534598$ |
| 16.0.312...664.1 |
$x^{16} + 9 x^{14} + 39 x^{12} + 122 x^{10} + 225 x^{8} + 180 x^{6} + 68 x^{4} + 14 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{2}\cdot 19^{6}\cdot 103^{4}$ |
$4$ |
$22.0501759376$ |
$586.7805127570678$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
$[2]$ |
$2$ |
$7$ |
$5234.91606702$ |
| 16.4.370...600.1 |
$x^{16} - 7 x^{14} + 19 x^{12} - 12 x^{10} - 29 x^{8} + 3 x^{6} + 3 x^{4} + 18 x^{2} + 9$ |
$16$ |
[4,6] |
$2^{16}\cdot 3^{6}\cdot 5^{2}\cdot 1327^{4}$ |
$4$ |
$22.2863756966$ |
|
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$35349.2308093$ |
| 16.4.370...600.2 |
$x^{16} + 7 x^{14} + 19 x^{12} + 12 x^{10} - 29 x^{8} - 3 x^{6} + 3 x^{4} - 18 x^{2} + 9$ |
$16$ |
[4,6] |
$2^{16}\cdot 3^{6}\cdot 5^{2}\cdot 1327^{4}$ |
$4$ |
$22.2863756966$ |
|
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$9$ |
$35087.261258$ |
| 16.0.125...009.1 |
$x^{16} - x^{15} + 4 x^{14} + 7 x^{13} + 33 x^{12} + 53 x^{11} + 209 x^{10} + 406 x^{9} + 877 x^{8} + 1350 x^{7} + 1742 x^{6} + 1763 x^{5} + 1473 x^{4} + 840 x^{3} + 317 x^{2} + 66 x + 9$ |
$16$ |
[0,8] |
$7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 97^{2}\cdot 103^{4}$ |
$5$ |
$24.0472260094$ |
$7559.003175022484$ |
✓ |
|
? |
$C_2^8.S_4$ (as 16T1664) |
$[2, 2]$ |
$2$ |
$7$ |
$7168.52068171$ |
| 16.0.814...816.1 |
$x^{16} - 5 x^{14} + 26 x^{12} - 36 x^{10} + 180 x^{8} - 127 x^{6} + 256 x^{4} - 264 x^{2} + 81$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{2}\cdot 19^{4}\cdot 97^{2}\cdot 103^{4}$ |
$5$ |
$27.0342500047$ |
$2768.0450193841634$ |
✓ |
|
? |
$C_2^8.S_4$ (as 16T1664) |
$[2]$ |
$2$ |
$7$ |
$101705.265084$ |
| 16.16.917...616.1 |
$x^{16} - 15 x^{14} + 89 x^{12} - 267 x^{10} + 428 x^{8} - 356 x^{6} + 139 x^{4} - 21 x^{2} + 1$ |
$16$ |
[16,0] |
$2^{16}\cdot 3^{2}\cdot 19^{4}\cdot 103^{6}$ |
$4$ |
$27.2378304406$ |
|
|
|
✓ |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$15$ |
$1461834.16499$ |
| 16.16.115...584.1 |
$x^{16} - 19 x^{14} + 129 x^{12} - 390 x^{10} + 567 x^{8} - 409 x^{6} + 144 x^{4} - 22 x^{2} + 1$ |
$16$ |
[16,0] |
$2^{20}\cdot 43^{2}\cdot 2777^{4}$ |
$3$ |
$27.6289907789$ |
$1792.5381499258424$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$15$ |
$2923397.64798$ |
