| 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 |
| 14.6.528...416.2 |
$x^{14} + 13 x^{12} + 45 x^{10} + 17 x^{8} - 105 x^{6} - 85 x^{4} + 23 x^{2} - 1$ |
$14$ |
[6,4] |
$2^{16}\cdot 73^{8}$ |
$2$ |
$25.6324548361$ |
$44.74617826366183$ |
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
trivial |
$2$ |
$9$ |
$102723.518439$ |
| 14.6.921...521.1 |
$x^{14} - 7 x^{13} + 23 x^{12} - 47 x^{11} + 50 x^{10} + 14 x^{9} - 157 x^{8} + 313 x^{7} - 355 x^{6} + 245 x^{5} - 72 x^{4} - 34 x^{3} + 41 x^{2} - 15 x + 2$ |
$14$ |
[6,4] |
$313^{8}$ |
$1$ |
$26.6701424746$ |
$46.09950106351405$ |
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
trivial |
$2$ |
$9$ |
$210120.670926$ |
| 14.10.338...624.1 |
$x^{14} - 2 x^{12} - 44 x^{10} + 164 x^{8} - 4 x^{6} - 356 x^{4} + 232 x^{2} - 4$ |
$14$ |
[10,2] |
$2^{22}\cdot 73^{8}$ |
$2$ |
$34.4987259015$ |
|
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
trivial |
$2$ |
$11$ |
$1260748.74442$ |
| 14.2.338...624.1 |
$x^{14} + 13 x^{12} + 53 x^{10} + 45 x^{8} - 141 x^{6} - 217 x^{4} - 57 x^{2} - 1$ |
$14$ |
[2,6] |
$2^{22}\cdot 73^{8}$ |
$2$ |
$34.4987259015$ |
|
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
$[2]$ |
$2$ |
$7$ |
$102337.853546$ |
| 14.10.338...624.2 |
$x^{14} - 11 x^{12} - 15 x^{10} + 109 x^{8} + 19 x^{6} - 97 x^{4} + 27 x^{2} - 1$ |
$14$ |
[10,2] |
$2^{22}\cdot 73^{8}$ |
$2$ |
$34.4987259015$ |
|
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
trivial |
$2$ |
$11$ |
$1375060.27173$ |
| 14.2.589...344.1 |
$x^{14} + 15 x^{12} + 80 x^{10} + 177 x^{8} + 133 x^{6} - 7 x^{4} - 14 x^{2} - 1$ |
$14$ |
[2,6] |
$2^{6}\cdot 313^{8}$ |
$2$ |
$35.8953498941$ |
$130.38907924530898$ |
|
|
|
$C_2^3:F_8:C_3$ (as 14T35) |
$[2, 6]$ |
$2$ |
$7$ |
$146720.997209$ |
| 14.6.330...000.1 |
$x^{14} - 6 x^{13} + 14 x^{12} + 12 x^{11} - 90 x^{10} + 80 x^{9} + 152 x^{8} - 248 x^{7} - 368 x^{6} + 1024 x^{5} - 2616 x^{3} + 2840 x^{2} + 200 x - 1000$ |
$14$ |
[6,4] |
$2^{16}\cdot 5^{4}\cdot 73^{8}$ |
$3$ |
$40.5971845902$ |
$100.05549633087136$ |
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
$[2]$ |
$2$ |
$9$ |
$1050836.65101$ |
| 14.6.541...984.1 |
$x^{14} + x^{12} - 33 x^{10} - 73 x^{8} + 45 x^{6} + 61 x^{4} + x^{2} - 1$ |
$14$ |
[6,4] |
$2^{26}\cdot 73^{8}$ |
$2$ |
$42.0544179266$ |
|
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
trivial |
$2$ |
$9$ |
$2376689.90087$ |
| 14.14.377...016.1 |
$x^{14} - 28 x^{12} + 289 x^{10} - 1328 x^{8} + 2632 x^{6} - 2194 x^{4} + 661 x^{2} - 16$ |
$14$ |
[14,0] |
$2^{12}\cdot 313^{8}$ |
$2$ |
$48.311558337$ |
$155.05962075717505$ |
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
trivial |
$2$ |
$13$ |
$30192708.8808$ |
| 14.14.147...824.1 |
$x^{14} - 51 x^{12} + 893 x^{10} - 7231 x^{8} + 29919 x^{6} - 64453 x^{4} + 68303 x^{2} - 27889$ |
$14$ |
[14,0] |
$2^{16}\cdot 73^{8}\cdot 167^{2}$ |
$3$ |
$53.2501855337$ |
|
|
|
? |
$C_2^3:F_8:C_3$ (as 14T35) |
trivial |
$2$ |
$13$ |
$102247594.83$ |
