| 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 |
| 14.0.8817149082834027.1 |
$x^{14} - x^{13} + 4 x^{12} + x^{11} + 6 x^{10} + 4 x^{9} + 10 x^{8} + 12 x^{6} - 5 x^{5} + 4 x^{4} - 7 x^{3} + 2 x^{2} - x + 1$ |
$14$ |
[0,7] |
$-\,3^{7}\cdot 13^{4}\cdot 109^{4}$ |
$3$ |
$13.7705730417$ |
$65.19969325081216$ |
|
|
? |
$\GL(3,2) \times C_2$ (as 14T19) |
trivial |
$6$ |
$6$ |
$415.648287609$ |
| 14.0.8817149082834027.2 |
$x^{14} - 2 x^{13} + 5 x^{12} - 6 x^{11} + 9 x^{10} - 7 x^{9} + 8 x^{8} - 3 x^{7} + 7 x^{6} + 7 x^{5} + 5 x^{4} + 3 x^{3} + 4 x^{2} - x + 1$ |
$14$ |
[0,7] |
$-\,3^{7}\cdot 13^{4}\cdot 109^{4}$ |
$3$ |
$13.7705730417$ |
$65.19969325081216$ |
|
|
? |
$\GL(3,2) \times C_2$ (as 14T19) |
trivial |
$6$ |
$6$ |
$415.648287609$ |
| 14.6.8857465265197237.1 |
$x^{14} - x^{13} - 5 x^{12} + 6 x^{11} + 6 x^{10} - 9 x^{9} - x^{8} + 7 x^{7} + x^{6} - 9 x^{5} - 6 x^{4} + 6 x^{3} + 5 x^{2} - x - 1$ |
$14$ |
[6,4] |
$13^{7}\cdot 109^{4}$ |
$2$ |
$13.7750610633$ |
$37.64306044943742$ |
|
|
? |
$\GL(3,2) \times C_2$ (as 14T19) |
trivial |
$2$ |
$9$ |
$341.120812559$ |
| 14.6.8857465265197237.2 |
$x^{14} - 6 x^{12} - 3 x^{11} + 9 x^{10} + 16 x^{9} + 8 x^{8} - 23 x^{7} - 31 x^{6} - 14 x^{5} - x^{4} + 12 x^{3} + 10 x^{2} + 4 x + 1$ |
$14$ |
[6,4] |
$13^{7}\cdot 109^{4}$ |
$2$ |
$13.7750610633$ |
$37.64306044943742$ |
|
|
? |
$\GL(3,2) \times C_2$ (as 14T19) |
trivial |
$2$ |
$9$ |
$341.120812559$ |
| 14.0.287...904.1 |
$x^{14} + 16 x^{12} + 94 x^{10} + 256 x^{8} + 337 x^{6} + 204 x^{4} + 52 x^{2} + 4$ |
$14$ |
[0,7] |
$-\,2^{26}\cdot 809^{4}$ |
$2$ |
$24.5413325807$ |
$143.34336125777284$ |
✓ |
|
? |
$\GL(3,2) \times C_2$ (as 14T19) |
$[2]$ |
$4$ |
$6$ |
$19291.3072044$ |
| 14.0.287...904.2 |
$x^{14} + 17 x^{12} + 108 x^{10} + 328 x^{8} + 492 x^{6} + 328 x^{4} + 68 x^{2} + 4$ |
$14$ |
[0,7] |
$-\,2^{26}\cdot 809^{4}$ |
$2$ |
$24.5413325807$ |
$143.34336125777284$ |
✓ |
|
? |
$\GL(3,2) \times C_2$ (as 14T19) |
$[2]$ |
$4$ |
$6$ |
$19291.3072044$ |
| 14.14.919...928.1 |
$x^{14} - 24 x^{12} + 219 x^{10} - 978 x^{8} + 2263 x^{6} - 2628 x^{4} + 1357 x^{2} - 242$ |
$14$ |
[14,0] |
$2^{31}\cdot 809^{4}$ |
$2$ |
$31.4346662517$ |
$170.46494509614888$ |
|
|
? |
$\GL(3,2) \times C_2$ (as 14T19) |
trivial |
$2$ |
$13$ |
$2287951.21075$ |
| 14.14.919...928.2 |
$x^{14} - 20 x^{12} + 144 x^{10} - 466 x^{8} + 740 x^{6} - 568 x^{4} + 176 x^{2} - 8$ |
$14$ |
[14,0] |
$2^{31}\cdot 809^{4}$ |
$2$ |
$31.4346662517$ |
$170.46494509614888$ |
|
|
? |
$\GL(3,2) \times C_2$ (as 14T19) |
trivial |
$2$ |
$13$ |
$2287951.21075$ |
