| 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 |
| 14.0.136...712.1 |
$x^{14} - 172 x^{7} + 7424$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 7^{21}\cdot 29^{6}$ |
$3$ |
$142.041342931$ |
$714.3208556078927$ |
|
|
? |
$C_7:F_7$ (as 14T14) |
$[7]$ |
$2$ |
$6$ |
$975926453.281$ |
| 14.14.544...848.1 |
$x^{14} - 84 x^{12} + 2625 x^{10} - 38892 x^{8} - 926 x^{7} + 287042 x^{6} + 16646 x^{5} - 989016 x^{4} - 23548 x^{3} + 1195061 x^{2} - 341446 x - 146334$ |
$14$ |
[14,0] |
$2^{14}\cdot 7^{21}\cdot 29^{6}$ |
$3$ |
$156.826357238$ |
$788.6741660751798$ |
|
|
? |
$C_7:F_7$ (as 14T14) |
trivial |
$2$ |
$13$ |
$447182556479$ |
| 14.14.221...512.1 |
$x^{14} - 6 x^{13} - 59 x^{12} + 380 x^{11} + 631 x^{10} - 6114 x^{9} + 6477 x^{8} + 12096 x^{7} - 21795 x^{6} - 1290 x^{5} + 16631 x^{4} - 6556 x^{3} - 835 x^{2} + 426 x + 47$ |
$14$ |
[14,0] |
$2^{27}\cdot 7^{14}\cdot 79^{6}$ |
$3$ |
$173.350317811$ |
$3125.099126761678$ |
|
|
? |
$C_7:F_7$ (as 14T14) |
trivial |
$2$ |
$13$ |
$493281649946$ |
| 14.0.126...368.1 |
$x^{14} - 551 x^{7} + 195112$ |
$14$ |
[0,7] |
$-\,2^{6}\cdot 7^{21}\cdot 29^{12}$ |
$3$ |
$446.831635601$ |
$714.3208556078927$ |
|
|
? |
$C_7:F_7$ (as 14T14) |
$[7, 14]$ |
$2$ |
$6$ |
$275657054732$ |
