| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 16.8.551...744.2 |
$x^{16} - 60 x^{12} - 96 x^{10} + 270 x^{8} + 288 x^{6} - 396 x^{4} + 9$ |
$16$ |
(8, 4) |
$2^{60}\cdot 3^{14}$ |
$2$ |
$35.183867915$ |
$49.75750318214772$ |
|
|
? |
$C_2^6.Q_8$ (as 16T968) |
trivial |
$[2]$ |
$2$ |
$11$ |
$4229590.55699$ |
$7$ |
$3$ |
| 16.10.140...568.1 |
$x^{16} - 8 x^{15} + 8 x^{14} + 56 x^{13} - 52 x^{12} - 256 x^{11} + 72 x^{10} + 768 x^{9} + 82 x^{8} - 1248 x^{7} - 288 x^{6} + 1136 x^{5} + 212 x^{4} - 592 x^{3} - 88 x^{2} + 160 x + 46$ |
$16$ |
(10, 3) |
$-\,2^{60}\cdot 3^{12}\cdot 23$ |
$3$ |
$37.3088115038$ |
|
|
|
? |
$C_2\wr Q_8$ (as 16T1484) |
trivial |
$[2]$ |
$2$ |
$12$ |
$13951549.7965$ |
$9$ |
$23$ |
| 16.0.291...576.1 |
$x^{16} + 48 x^{14} + 768 x^{12} + 5712 x^{10} + 21690 x^{8} + 42768 x^{6} + 44496 x^{4} + 23184 x^{2} + 4761$ |
$16$ |
(0, 8) |
$2^{60}\cdot 3^{14}\cdot 23^{2}$ |
$3$ |
$52.0666410466$ |
$238.628602282277$ |
✓ |
|
? |
$C_2^6.Q_8$ (as 16T968) |
$[2, 2, 120]$ |
$[2, 2, 120]$ |
$2$ |
$7$ |
$45687.5845647$ |
$0$ |
$23$ |
| 16.8.291...576.2 |
$x^{16} - 108 x^{12} + 192 x^{10} + 2430 x^{8} - 4320 x^{6} - 12636 x^{4} + 6624 x^{2} + 4761$ |
$16$ |
(8, 4) |
$2^{60}\cdot 3^{14}\cdot 23^{2}$ |
$3$ |
$52.0666410466$ |
$238.628602282277$ |
|
|
? |
$C_2^6.Q_8$ (as 16T968) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$136873679.556$ |
$5$ |
$23$ |
| 16.12.291...576.2 |
$x^{16} - 24 x^{14} - 48 x^{12} + 3960 x^{10} - 19782 x^{8} + 13032 x^{6} + 15552 x^{4} - 18216 x^{2} + 4761$ |
$16$ |
(12, 2) |
$2^{60}\cdot 3^{14}\cdot 23^{2}$ |
$3$ |
$52.0666410466$ |
$238.628602282277$ |
|
|
? |
$C_2^6.Q_8$ (as 16T968) |
trivial |
$[2, 2, 2]$ |
$2$ |
$13$ |
$298269079.419$ |
$9$ |
$23$ |
| 18.6.170...664.1 |
$x^{18} - 8 x^{16} + 36 x^{14} - 120 x^{12} + 288 x^{10} - 512 x^{8} + 648 x^{6} - 560 x^{4} + 292 x^{2} - 64$ |
$18$ |
(6, 6) |
$2^{60}\cdot 23^{6}$ |
$2$ |
$28.6643829681$ |
|
|
|
|
$C_2^8.F_9:C_2$ (as 18T692) |
trivial |
trivial |
$2$ |
$11$ |
$11513997.2723$ |
$6$ |
$23$ |
| 18.6.136...312.1 |
$x^{18} - 2 x^{16} + 12 x^{14} - 136 x^{12} + 350 x^{10} - 28 x^{8} - 644 x^{6} + 120 x^{4} + 377 x^{2} - 18$ |
$18$ |
(6, 6) |
$2^{63}\cdot 23^{6}$ |
$2$ |
$32.1746820199$ |
|
|
|
? |
$C_2^8.F_9:C_2$ (as 18T695) |
$[2]$ |
$[2]$ |
$2$ |
$11$ |
$24055270.1624$ |
$6$ |
$23$ |
| 20.0.240...384.1 |
$x^{20} - 5 x^{18} - 8 x^{16} - 4 x^{14} + 182 x^{12} + 34 x^{10} + 620 x^{8} + 1180 x^{6} + 321 x^{4} - 21 x^{2} + 4$ |
$20$ |
(0, 10) |
$2^{60}\cdot 113^{6}$ |
$2$ |
$33.0379825943$ |
|
|
|
|
$C_2^9.S_6:C_2$ (as 20T952) |
trivial |
trivial |
$2$ |
$9$ |
$1061995867.61$ |
$0$ |
$113$ |
