| 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 |
| 14.6.156...504.1 |
$x^{14} - 7 x^{13} + 7 x^{12} + 28 x^{11} - 28 x^{10} - 140 x^{9} - 252 x^{8} + 3024 x^{7} - 7560 x^{6} + 8848 x^{5} - 4480 x^{4} - 560 x^{3} + 1792 x^{2} - 784 x + 112$ |
$14$ |
[6,4] |
$2^{8}\cdot 3^{17}\cdot 7^{15}$ |
$3$ |
$45.3775296991$ |
$92.91812571124727$ |
|
|
|
$S_7$ (as 14T46) |
trivial |
$2$ |
$9$ |
$13981319.4928$ |
| 14.0.678...728.1 |
$x^{14} - 7 x^{13} + 35 x^{12} - 119 x^{11} + 329 x^{10} - 721 x^{9} + 1379 x^{8} - 2177 x^{7} + 1813 x^{6} - 1225 x^{5} + 2107 x^{4} + 1225 x^{3} - 392 x^{2} - 1960 x + 1568$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 3^{20}\cdot 7^{15}$ |
$3$ |
$69.998653949$ |
$246.17988078259026$ |
|
|
|
$S_7$ (as 14T46) |
trivial |
$2$ |
$6$ |
$309460557.501$ |
| 14.0.846...816.1 |
$x^{14} - 28 x^{12} + 231 x^{10} + 742 x^{8} - 6517 x^{6} - 59136 x^{4} + 295141 x^{2} + 142814$ |
$14$ |
[0,7] |
$-\,2^{25}\cdot 3^{12}\cdot 7^{15}$ |
$3$ |
$71.1175562418$ |
$162.34291888251445$ |
|
|
|
$S_7$ (as 14T46) |
$[4]$ |
$2$ |
$6$ |
$91866342.5122$ |
| 14.6.169...632.1 |
$x^{14} - 28 x^{12} + 168 x^{10} + 504 x^{8} - 3024 x^{6} - 6048 x^{4} - 9072 x^{2} - 36288$ |
$14$ |
[6,4] |
$2^{26}\cdot 3^{12}\cdot 7^{15}$ |
$3$ |
$74.7272443458$ |
$204.53926080145584$ |
|
|
? |
$S_7$ (as 14T46) |
trivial |
$2$ |
$9$ |
$554978941.697$ |
