| 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 |
| 14.2.686...584.1 |
$x^{14} - 7 x^{13} - 14 x^{12} + 175 x^{11} + 35 x^{10} - 1946 x^{9} + 357 x^{8} + 11091 x^{7} + 3003 x^{6} - 206654 x^{5} + 378665 x^{4} - 1590365 x^{3} + 2212714 x^{2} - 2532103 x + 1252255$ |
$14$ |
[2,6] |
$2^{12}\cdot 3^{13}\cdot 7^{15}\cdot 19^{12}$ |
$4$ |
$504.2008534916931$ |
$553.1543605461457$ |
|
|
? |
$F_7 \times C_2$ (as 14T7) |
$[7]$ |
$2$ |
$7$ |
$6487140389784.11$ |
| 14.0.836...024.1 |
$x^{14} + 467856$ |
$14$ |
[0,7] |
$-\,2^{20}\cdot 3^{12}\cdot 7^{14}\cdot 19^{12}$ |
$4$ |
$602.804494212$ |
$759.9471507764919$ |
|
|
? |
$F_7 \times C_2$ (as 14T7) |
$[7, 7]$ |
$4$ |
$6$ |
$7961638499839.606$ |
| 14.0.298...488.1 |
$x^{14} - 7 x^{13} + 35 x^{12} - 119 x^{11} + 329 x^{10} - 721 x^{9} + 1337 x^{8} + 1284559 x^{7} - 4500440 x^{6} - 40530910 x^{5} + 112580482 x^{4} + 22513666 x^{3} - 148601642 x^{2} + 40527578 x + 413845826258$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 3^{12}\cdot 7^{11}\cdot 11^{12}\cdot 19^{12}$ |
$5$ |
$2087.80150147$ |
$2290.508824994667$ |
|
|
? |
$F_7$ (as 14T4) |
not computed |
$2$ |
$6$ |
|
| 14.2.896...464.1 |
$x^{14} - 3311814 x^{7} - 189226092$ |
$14$ |
[2,6] |
$2^{12}\cdot 3^{13}\cdot 7^{11}\cdot 11^{12}\cdot 19^{12}$ |
$5$ |
$2258.2358373$ |
$2477.4908489170007$ |
|
|
? |
$F_7 \times C_2$ (as 14T7) |
not computed |
$2$ |
$7$ |
|
