| 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 |
| 14.0.56316949686099.1 |
$x^{14} - 2 x^{13} + 6 x^{12} - 11 x^{11} + 19 x^{10} - 26 x^{9} + 33 x^{8} - 35 x^{7} + 33 x^{6} - 26 x^{5} + 19 x^{4} - 10 x^{3} + 6 x^{2} - x + 1$ |
$14$ |
[0,7] |
$-\,3^{7}\cdot 2953^{3}$ |
$2$ |
$9.59817157113$ |
$94.12226091632095$ |
|
|
✓ |
$D_7 \wr C_2$ (as 14T20) |
trivial |
$6$ |
$6$ |
$24.3506832156$ |
| 14.2.9242067299140625.1 |
$x^{14} - 2 x^{13} + 5 x^{12} - 5 x^{11} + 8 x^{10} - 10 x^{9} + x^{8} - 2 x^{7} - 5 x^{6} + 8 x^{5} + 10 x^{4} + 2 x^{3} - 6 x^{2} - x + 1$ |
$14$ |
[2,6] |
$5^{7}\cdot 4909^{3}$ |
$2$ |
$13.816946643$ |
$156.66843970627906$ |
|
|
? |
$D_7 \wr C_2$ (as 14T20) |
trivial |
$2$ |
$7$ |
$263.069092309$ |
| 14.0.55750667696881664.1 |
$x^{14} - 2 x^{12} - 4 x^{11} - 4 x^{10} + 6 x^{9} + 22 x^{8} + 10 x^{7} - 4 x^{6} - 52 x^{5} - 16 x^{4} - 2 x^{3} + 41 x^{2} + 18 x + 2$ |
$14$ |
[0,7] |
$-\,2^{14}\cdot 13^{6}\cdot 89^{3}$ |
$3$ |
$15.7094405657$ |
$170.0331445703484$ |
|
|
|
$D_7 \wr C_2$ (as 14T20) |
trivial |
$4$ |
$6$ |
$2314.96730681$ |
| 14.2.346634844681273344.1 |
$x^{14} - 2 x^{13} + 9 x^{12} - 8 x^{11} + 18 x^{10} + 12 x^{9} - 14 x^{8} + 64 x^{7} - 31 x^{6} + 94 x^{5} - 103 x^{4} + 104 x^{3} - 24 x^{2} + 8$ |
$14$ |
[2,6] |
$2^{33}\cdot 7^{9}$ |
$2$ |
$17.8997932819$ |
$94.3520317696364$ |
|
|
|
$D_7 \wr C_2$ (as 14T20) |
trivial |
$2$ |
$7$ |
$13565.9141384$ |
| 14.8.182...375.1 |
$x^{14} - 5 x^{13} + 5 x^{12} + 11 x^{11} - 26 x^{10} + 17 x^{9} - 4 x^{8} - x^{7} + 50 x^{6} - 95 x^{5} + x^{4} + 76 x^{3} + 3 x^{2} - 18 x - 4$ |
$14$ |
[8,3] |
$-\,5^{7}\cdot 28579^{3}$ |
$2$ |
$20.1535808776$ |
$378.0145499845211$ |
|
|
? |
$D_7 \wr C_2$ (as 14T20) |
trivial |
$2$ |
$10$ |
$12063.7005717$ |
| 14.14.263...832.1 |
$x^{14} - 6 x^{13} - 5 x^{12} + 88 x^{11} - 80 x^{10} - 412 x^{9} + 638 x^{8} + 744 x^{7} - 1558 x^{6} - 496 x^{5} + 1504 x^{4} + 116 x^{3} - 491 x^{2} - 58 x - 1$ |
$14$ |
[14,0] |
$2^{21}\cdot 107881^{3}$ |
$2$ |
$33.8870060316$ |
$929.0037674842874$ |
|
|
|
$D_7 \wr C_2$ (as 14T20) |
trivial |
$2$ |
$13$ |
$4194838.84544$ |
| 14.8.522...792.1 |
$x^{14} - 4 x^{13} + 7 x^{12} - 14 x^{11} - 38 x^{10} + 132 x^{9} - 109 x^{8} + 230 x^{7} + 394 x^{6} - 580 x^{5} - 769 x^{4} + 474 x^{3} + 325 x^{2} - 52 x - 8$ |
$14$ |
[8,3] |
$-\,2^{14}\cdot 3^{7}\cdot 11^{3}\cdot 13^{6}\cdot 61^{3}$ |
$5$ |
$41.9489573859$ |
$808.6497764045625$ |
|
|
|
$D_7 \wr C_2$ (as 14T20) |
trivial |
$2$ |
$10$ |
$9117806.23781$ |
| 14.14.823...625.1 |
$x^{14} - 2 x^{13} - 34 x^{12} + 47 x^{11} + 441 x^{10} - 324 x^{9} - 2618 x^{8} + 332 x^{7} + 6281 x^{6} + 2236 x^{5} - 2272 x^{4} - 299 x^{3} + 373 x^{2} - 70 x + 4$ |
$14$ |
[14,0] |
$5^{7}\cdot 11^{3}\cdot 311^{3}\cdot 641^{3}$ |
$4$ |
$51.0826119931$ |
$3311.2391940178527$ |
|
|
? |
$D_7 \wr C_2$ (as 14T20) |
trivial |
$2$ |
$13$ |
$45374712.1437$ |
