| 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 |
| 14.8.705...375.1 |
$x^{14} - 14 x^{12} + 77 x^{10} - 210 x^{8} - 3 x^{7} + 294 x^{6} + 21 x^{5} - 196 x^{4} - 42 x^{3} + 49 x^{2} + 21 x + 1$ |
$14$ |
[8,3] |
$-\,5^{7}\cdot 7^{14}\cdot 11^{3}$ |
$3$ |
$26.1660771505$ |
$70.85656453559409$ |
|
|
✓ |
$D_7^2:C_6$ (as 14T32) |
trivial |
$2$ |
$10$ |
$101194.152832$ |
| 14.0.888...000.1 |
$x^{14} - 14 x^{12} + 77 x^{10} - 210 x^{8} - 2 x^{7} + 294 x^{6} + 14 x^{5} - 196 x^{4} - 28 x^{3} + 49 x^{2} + 14 x + 2$ |
$14$ |
[0,7] |
$-\,2^{20}\cdot 5^{3}\cdot 7^{14}$ |
$3$ |
$26.6023606918$ |
$60.4266812699448$ |
|
|
✓ |
$D_7^2:C_6$ (as 14T32) |
trivial |
$4$ |
$6$ |
$74262.3951103$ |
| 14.2.131...489.1 |
$x^{14} - x^{13} - 5 x^{12} + 7 x^{11} - 14 x^{10} - 28 x^{9} + 42 x^{8} - 49 x^{7} - 42 x^{6} + 84 x^{5} - 91 x^{4} - 63 x^{3} + 35 x^{2} - 42 x - 35$ |
$14$ |
[2,6] |
$3^{7}\cdot 7^{12}\cdot 163^{3}$ |
$3$ |
$27.3508342026$ |
$131.62174156482672$ |
|
|
? |
$D_7^2:C_6$ (as 14T32) |
trivial |
$2$ |
$7$ |
$76923.8109577$ |
| 14.8.217...000.1 |
$x^{14} - 14 x^{12} + 77 x^{10} - 210 x^{8} - 2 x^{7} + 294 x^{6} + 14 x^{5} - 196 x^{4} - 28 x^{3} + 49 x^{2} + 14 x - 4$ |
$14$ |
[8,3] |
$-\,2^{12}\cdot 5^{7}\cdot 7^{14}$ |
$3$ |
$28.3536355497$ |
$60.4266812699448$ |
|
|
? |
$D_7^2:C_6$ (as 14T32) |
trivial |
$2$ |
$10$ |
$175787.219415$ |
| 14.0.285...584.1 |
$x^{14} + 14 x^{12} + 77 x^{10} + 210 x^{8} - x^{7} + 294 x^{6} - 7 x^{5} + 196 x^{4} - 14 x^{3} + 49 x^{2} - 7 x + 2$ |
$14$ |
[0,7] |
$-\,2^{9}\cdot 7^{21}$ |
$2$ |
$28.9178727915$ |
$62.219800588126716$ |
|
|
✓ |
$D_7^2:C_6$ (as 14T32) |
trivial |
$2$ |
$6$ |
$112348.0847$ |
| 14.2.129...625.1 |
$x^{14} - 14 x^{12} + 77 x^{10} - 210 x^{8} - 7 x^{7} + 294 x^{6} + 49 x^{5} - 196 x^{4} - 98 x^{3} + 49 x^{2} + 49 x - 19$ |
$14$ |
[2,6] |
$5^{7}\cdot 7^{14}\cdot 29^{3}$ |
$3$ |
$32.2072794673$ |
$115.04897352306399$ |
|
|
? |
$D_7^2:C_6$ (as 14T32) |
trivial |
$2$ |
$7$ |
$137320.853297$ |
| 14.2.146...625.1 |
$x^{14} + 14 x^{12} + 77 x^{10} + 210 x^{8} - x^{7} + 294 x^{6} - 7 x^{5} + 196 x^{4} - 14 x^{3} + 49 x^{2} - 7 x - 7$ |
$14$ |
[2,6] |
$5^{3}\cdot 7^{14}\cdot 29^{7}$ |
$3$ |
$53.22017834921804$ |
$115.04897352306399$ |
|
|
? |
$D_7^2:C_6$ (as 14T32) |
trivial |
$2$ |
$7$ |
$6126468.273892359$ |
| 14.14.271...984.1 |
$x^{14} - 42 x^{12} - 56 x^{11} + 553 x^{10} + 1344 x^{9} - 1764 x^{8} - 7788 x^{7} - 2744 x^{6} + 12628 x^{5} + 12348 x^{4} - 3528 x^{3} - 8673 x^{2} - 3136 x - 224$ |
$14$ |
[14,0] |
$2^{21}\cdot 7^{16}\cdot 73^{3}$ |
$3$ |
$65.56239273$ |
$648.3724288912375$ |
|
|
? |
$D_7^2:C_6$ (as 14T32) |
trivial |
$2$ |
$13$ |
$432123032.888$ |
| 14.14.138...125.1 |
$x^{14} - 28 x^{12} + 308 x^{10} - 1680 x^{8} - 9 x^{7} + 4704 x^{6} + 126 x^{5} - 6272 x^{4} - 504 x^{3} + 3136 x^{2} + 504 x + 19$ |
$14$ |
[14,0] |
$5^{7}\cdot 7^{14}\cdot 2969^{3}$ |
$3$ |
$86.8387970756$ |
$1164.0961370205969$ |
|
|
? |
$D_7^2:C_6$ (as 14T32) |
trivial |
$2$ |
$13$ |
$2005457332.46$ |
