| 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 |
| 16.0.3692461181640625.1 |
$x^{16} - 2 x^{15} - 2 x^{14} + 9 x^{13} - 3 x^{12} - 15 x^{11} + 17 x^{10} + 8 x^{9} - 25 x^{8} + 8 x^{7} + 17 x^{6} - 15 x^{5} - 3 x^{4} + 9 x^{3} - 2 x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 3889^{2}$ |
$2$ |
$9.39630804632$ |
$208.51940394717084$ |
|
|
✓ |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$40.8735633138$ |
| 16.0.6472705322265625.1 |
$x^{16} - x^{15} + x^{14} + x^{13} + 3 x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{8} + 9 x^{7} + 6 x^{6} + 8 x^{5} + 8 x^{4} + 3 x^{3} + 4 x^{2} + 3 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 19^{2}\cdot 271^{2}$ |
$3$ |
$9.73179304548$ |
$239.93242815578742$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$56.3298547938$ |
| 16.0.6741949462890625.1 |
$x^{16} + x^{14} - 5 x^{13} + 2 x^{12} - 5 x^{11} + 13 x^{10} - 10 x^{9} + 15 x^{8} - 20 x^{7} + 17 x^{6} - 20 x^{5} + 17 x^{4} - 10 x^{3} + 9 x^{2} - 5 x + 1$ |
$16$ |
[0,8] |
$5^{14}\cdot 1051^{2}$ |
$2$ |
$9.75661332423$ |
$132.55622019828223$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$58.1502195758$ |
| 16.0.11610062500000000.1 |
$x^{16} - 5 x^{15} + 15 x^{14} - 30 x^{13} + 43 x^{12} - 40 x^{11} + 15 x^{10} + 20 x^{9} - 36 x^{8} + 20 x^{7} + 15 x^{6} - 35 x^{5} + 27 x^{4} - 15 x^{3} + 10 x^{2} - 5 x + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{12}\cdot 431^{2}$ |
$3$ |
$10.0937410715$ |
$110.19269431629391$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$80.5768870744$ |
| 16.0.14584336181640625.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 2 x^{13} - 2 x^{12} + 2 x^{11} + 2 x^{10} - 12 x^{9} + 19 x^{8} - 15 x^{7} + 5 x^{6} + 6 x^{5} - 8 x^{4} + 5 x^{3} - 2 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 59^{2}\cdot 131^{2}$ |
$3$ |
$10.2386551729$ |
$293.9606214962803$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$95.2086244076$ |
| 16.0.15010078369140625.1 |
$x^{16} - x^{15} + 3 x^{14} - 6 x^{13} + 9 x^{12} - 14 x^{11} + 21 x^{10} - 24 x^{9} + 29 x^{8} - 32 x^{7} + 33 x^{6} - 25 x^{5} + 22 x^{4} - 17 x^{3} + 9 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 7841^{2}$ |
$2$ |
$10.2570845388$ |
$296.0828347910079$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$103.338172859$ |
| 16.0.24068613525390625.1 |
$x^{16} - 2 x^{15} + 4 x^{14} - 9 x^{13} + 11 x^{12} - 16 x^{11} + 20 x^{10} - 15 x^{9} + 17 x^{8} - 10 x^{7} - 2 x^{5} - 4 x^{4} + 3 x^{3} + x^{2} + x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 9929^{2}$ |
$2$ |
$10.5642991848$ |
$333.1810239839254$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$127.826318151$ |
| 16.0.28323838134765625.1 |
$x^{16} - 2 x^{15} - x^{14} + 5 x^{13} - 2 x^{12} - 5 x^{11} + 6 x^{10} + 2 x^{9} - 7 x^{8} + 2 x^{7} + 6 x^{6} - 5 x^{5} - 2 x^{4} + 5 x^{3} - x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 10771^{2}$ |
$2$ |
$10.6723364102$ |
$347.0208076301062$ |
|
|
✓ |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$145.46809548$ |
| 16.0.31334531494140625.1 |
$x^{16} - 2 x^{15} + 5 x^{14} - 3 x^{13} + 4 x^{12} + 4 x^{11} + 4 x^{10} - x^{9} + 21 x^{8} - 13 x^{7} + 26 x^{6} - 7 x^{5} + 14 x^{4} + x^{3} + 5 x^{2} + x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 11329^{2}$ |
$2$ |
$10.73992999$ |
$355.89615140582174$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$148.252775341$ |
| 16.0.119878242431640625.1 |
$x^{16} - x^{15} - 2 x^{14} - x^{13} + 2 x^{12} + 5 x^{11} + 2 x^{10} - 3 x^{9} - 5 x^{8} - 3 x^{7} + 2 x^{6} + 5 x^{5} + 2 x^{4} - x^{3} - 2 x^{2} - x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 22159^{2}$ |
$2$ |
$11.679419911$ |
$497.74004416672085$ |
|
|
✓ |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$306.510717396$ |
| 16.4.114...625.1 |
$x^{16} - 3 x^{15} + x^{14} + 6 x^{12} + x^{11} - 20 x^{10} + 16 x^{9} + 12 x^{8} + 2 x^{7} - 40 x^{6} - 7 x^{5} + 51 x^{4} - 20 x^{3} + 4 x^{2} - 4 x + 1$ |
$16$ |
[4,6] |
$3^{8}\cdot 5^{12}\cdot 2671^{2}$ |
$3$ |
$15.5282447144$ |
$299.31265178493385$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$9$ |
$1346.34048894$ |
| 16.4.132...561.1 |
$x^{16} - 2 x^{15} - x^{14} + x^{13} + x^{12} + 3 x^{11} - 6 x^{10} - 5 x^{9} + 6 x^{8} + 5 x^{7} - 6 x^{6} - 3 x^{5} + x^{4} - x^{3} - x^{2} + 2 x + 1$ |
$16$ |
[4,6] |
$17^{12}\cdot 151^{2}$ |
$2$ |
$15.6750454752$ |
$102.87862820314302$ |
|
|
|
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$9$ |
$2367.99461691$ |
| 16.8.241...625.1 |
$x^{16} - 4 x^{15} + 16 x^{13} - 9 x^{12} - 28 x^{11} + 28 x^{10} + 11 x^{9} - 60 x^{8} + 126 x^{7} - 102 x^{6} - 20 x^{5} + 69 x^{4} - 57 x^{3} + 43 x^{2} - 14 x + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 5^{12}\cdot 3881^{2}$ |
$3$ |
$16.2706943184$ |
$360.7945361423178$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$11$ |
$4697.01767862$ |
| 16.8.354...625.1 |
$x^{16} - 4 x^{14} - 8 x^{12} + 13 x^{10} + 30 x^{8} - 58 x^{6} + 37 x^{4} - 11 x^{2} + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 5^{14}\cdot 941^{2}$ |
$3$ |
$16.6670248939$ |
$217.24720256820567$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$11$ |
$5010.77021277$ |
| 16.0.732...625.1 |
$x^{16} - 7 x^{15} + 24 x^{14} - 54 x^{13} + 84 x^{12} - 73 x^{11} - 34 x^{10} + 243 x^{9} - 457 x^{8} + 486 x^{7} - 136 x^{6} - 584 x^{5} + 1344 x^{4} - 1728 x^{3} + 1536 x^{2} - 896 x + 256$ |
$16$ |
[0,8] |
$5^{12}\cdot 547889^{2}$ |
$2$ |
$17.4407065903$ |
$2474.9919677893727$ |
✓ |
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$10$ |
$7$ |
$9516.84702281$ |
| 16.8.823...000.1 |
$x^{16} - 6 x^{15} + 15 x^{14} - 26 x^{13} + 34 x^{12} - 18 x^{11} - 24 x^{10} + 78 x^{9} - 119 x^{8} + 96 x^{7} - 31 x^{6} - 34 x^{5} + 69 x^{4} - 52 x^{3} + 25 x^{2} - 8 x + 1$ |
$16$ |
[8,4] |
$2^{16}\cdot 5^{12}\cdot 2269^{2}$ |
$3$ |
$17.568586081$ |
|
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$11$ |
$7839.46452897$ |
| 16.0.936...625.1 |
$x^{16} - 3 x^{15} + 5 x^{14} - 5 x^{13} + 6 x^{11} + 2 x^{10} + 2 x^{6} - 6 x^{5} + 5 x^{3} + 5 x^{2} + 3 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{14}\cdot 11^{2}\cdot 139^{2}$ |
$4$ |
$17.7096638082$ |
$296.1330461861123$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
$[2]$ |
$2$ |
$7$ |
$1557.45003189$ |
| 16.0.112...616.1 |
$x^{16} - 4 x^{15} + 14 x^{14} - 44 x^{13} + 93 x^{12} - 168 x^{11} + 252 x^{10} - 304 x^{9} + 329 x^{8} - 276 x^{7} + 246 x^{6} - 140 x^{5} + 95 x^{4} - 48 x^{3} + 24 x^{2} - 8 x + 2$ |
$16$ |
[0,8] |
$2^{48}\cdot 631^{2}$ |
$2$ |
$17.9099204516$ |
$260.6099032408631$ |
|
|
|
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$7$ |
$14485.3357952$ |
| 16.0.273...625.1 |
$x^{16} - 3 x^{15} + 7 x^{14} - 9 x^{13} + 19 x^{12} - 16 x^{11} + 49 x^{10} - 32 x^{9} + 98 x^{8} - 110 x^{7} + 145 x^{6} - 40 x^{5} + 52 x^{4} + 24 x^{3} + 19 x^{2} + 6 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 439^{2}\cdot 2411^{2}$ |
$3$ |
$18.9369581578$ |
$3439.9994137769304$ |
✓ |
|
? |
$S_4^2:C_4$ (as 16T1497) |
$[3]$ |
$10$ |
$7$ |
$4846.77455506$ |
| 16.8.688...625.1 |
$x^{16} - 3 x^{15} - x^{14} + 5 x^{13} + 8 x^{12} + 10 x^{11} - 59 x^{10} - 12 x^{9} + 103 x^{8} - 12 x^{7} - 59 x^{6} + 10 x^{5} + 8 x^{4} + 5 x^{3} - x^{2} - 3 x + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 5^{12}\cdot 19^{2}\cdot 1091^{2}$ |
$4$ |
$20.0613624563$ |
$833.8295968505179$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$11$ |
$23439.0271585$ |
| 16.12.287...000.1 |
$x^{16} - 4 x^{15} - 4 x^{14} + 34 x^{13} - 30 x^{12} - 70 x^{11} + 155 x^{10} - 18 x^{9} - 203 x^{8} + 232 x^{7} + 23 x^{6} - 340 x^{5} + 27 x^{4} + 142 x^{3} - 9 x^{2} - 16 x + 1$ |
$16$ |
[12,2] |
$2^{16}\cdot 5^{12}\cdot 13411^{2}$ |
$3$ |
$21.9376520658$ |
|
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$13$ |
$110255.201908$ |
| 16.12.461...000.1 |
$x^{16} - 18 x^{14} - 14 x^{13} + 82 x^{12} + 114 x^{11} + 26 x^{10} + 8 x^{9} - 243 x^{8} - 466 x^{7} - 82 x^{6} - 36 x^{5} - 244 x^{4} + 138 x^{3} + 260 x^{2} + 18 x - 19$ |
$16$ |
[12,2] |
$2^{28}\cdot 5^{12}\cdot 839^{2}$ |
$3$ |
$26.091571695$ |
|
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$13$ |
$734291.99165$ |
| 16.16.896...625.1 |
$x^{16} - x^{15} - 26 x^{14} + 26 x^{13} + 251 x^{12} - 243 x^{11} - 1134 x^{10} + 1021 x^{9} + 2526 x^{8} - 1934 x^{7} - 2850 x^{6} + 1554 x^{5} + 1607 x^{4} - 412 x^{3} - 370 x^{2} - 11 x + 11$ |
$16$ |
[16,0] |
$5^{12}\cdot 11^{8}\cdot 4139^{2}$ |
$3$ |
$31.4076739759$ |
$713.4631698538752$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$15$ |
$5700531.29159$ |
| 16.16.480...000.1 |
$x^{16} - 26 x^{14} + 241 x^{12} - 1011 x^{10} + 2196 x^{8} - 2565 x^{6} + 1540 x^{4} - 400 x^{2} + 25$ |
$16$ |
[16,0] |
$2^{16}\cdot 5^{12}\cdot 547889^{2}$ |
$3$ |
$34.8814131806$ |
|
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
$2$ |
$15$ |
$16873694.5909$ |
