| 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 |
| 14.0.372...936.1 |
$x^{14} - 6 x^{13} + 20 x^{12} - 52 x^{11} + 113 x^{10} - 214 x^{9} + 393 x^{8} - 660 x^{7} + 973 x^{6} - 1226 x^{5} + 1245 x^{4} - 952 x^{3} + 500 x^{2} - 84 x + 13$ |
$14$ |
[0,7] |
$-\,2^{14}\cdot 13^{6}\cdot 19^{6}$ |
$3$ |
$21.2066245267$ |
$78.56251606399157$ |
|
|
|
$D_7^2$ (as 14T13) |
trivial |
$4$ |
$6$ |
$20225.9097244$ |
| 14.2.506...000.1 |
$x^{14} - 4 x^{13} + 2 x^{12} + 24 x^{11} - 50 x^{10} + 8 x^{9} + 106 x^{8} - 176 x^{7} + 89 x^{6} + 28 x^{5} - 72 x^{4} + 24 x^{3} + 68 x^{2} - 96 x + 64$ |
$14$ |
[2,6] |
$2^{27}\cdot 5^{7}\cdot 13^{6}$ |
$3$ |
$25.5533088915$ |
$80.60344076699752$ |
|
|
|
$D_7^2$ (as 14T13) |
$[2]$ |
$2$ |
$7$ |
$114268.201269$ |
| 14.2.197...528.1 |
$x^{14} - 4 x^{13} + 6 x^{11} + 40 x^{10} - 88 x^{9} + 11 x^{8} - 64 x^{7} + 396 x^{6} - 472 x^{5} + 492 x^{4} - 688 x^{3} + 512 x^{2} - 160 x + 16$ |
$14$ |
[2,6] |
$2^{21}\cdot 11^{7}\cdot 13^{6}$ |
$3$ |
$28.1608416105$ |
$84.5376018693857$ |
|
|
|
$D_7^2$ (as 14T13) |
trivial |
$2$ |
$7$ |
$140194.233151$ |
| 14.0.179...224.1 |
$x^{14} + 15 x^{12} - 78 x^{11} + 232 x^{10} - 832 x^{9} + 3072 x^{8} - 7046 x^{7} + 18996 x^{6} - 39026 x^{5} + 71164 x^{4} - 122460 x^{3} + 151847 x^{2} - 114686 x + 47545$ |
$14$ |
[0,7] |
$-\,2^{14}\cdot 13^{12}\cdot 19^{6}$ |
$3$ |
$63.6613495446$ |
$78.56251606399157$ |
|
|
|
$D_7^2$ (as 14T13) |
$[7]$ |
$4$ |
$6$ |
$27147114.557$ |
| 14.14.226...057.1 |
$x^{14} - 2 x^{13} - 349 x^{12} - 72 x^{11} + 36188 x^{10} + 56049 x^{9} - 1444514 x^{8} - 2857477 x^{7} + 25343855 x^{6} + 48357153 x^{5} - 195969927 x^{4} - 272636914 x^{3} + 701452818 x^{2} + 485583417 x - 963639599$ |
$14$ |
[14,0] |
$577^{7}\cdot 1009^{7}$ |
$2$ |
$763.01572723$ |
$763.0157272297865$ |
|
|
? |
$D_7^2$ (as 14T13) |
$[2]$ |
$2$ |
$13$ |
$1734662984620000$ |
| 14.14.226...057.2 |
$x^{14} - 6 x^{13} - 333 x^{12} + 2458 x^{11} + 27489 x^{10} - 244901 x^{9} - 545963 x^{8} + 7571477 x^{7} - 3173277 x^{6} - 73124614 x^{5} + 118055451 x^{4} + 27685502 x^{3} - 168908516 x^{2} + 118708648 x - 26099424$ |
$14$ |
[14,0] |
$577^{7}\cdot 1009^{7}$ |
$2$ |
$763.01572723$ |
$763.0157272297865$ |
|
|
|
$D_7^2$ (as 14T13) |
$[2]$ |
$2$ |
$13$ |
$3505494749950000000$ |
