| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 7.14.18.13 |
$14$ |
$x^{14} - 28 x^{11} + 28 x^{10} - 98 x^{8} - 378 x^{7} + 196 x^{6} - 196 x^{4} + 196 x^{3} + 49$ |
$7$ |
$7$ |
$2$ |
$18$ |
$D_{14}$ (as 14T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(7 t + 7\right) x^{4} + 14 x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.18.23 |
$14$ |
$x^{14} + 42 x^{13} + 777 x^{12} + 8372 x^{11} + 58807 x^{10} + 289170 x^{9} + 1074619 x^{8} + 3344382 x^{7} + 9376654 x^{6} + 22416786 x^{5} + 39663806 x^{4} + 45629668 x^{3} + 31016412 x^{2} + 11931696 x + 2670097$ |
$7$ |
$7$ |
$2$ |
$18$ |
$D_{14}$ (as 14T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 28 x^{4} + 35 x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.19.11 |
$14$ |
$x^{14} + 14 x^{7} + 14 x^{6} + 7$ |
$7$ |
$14$ |
$1$ |
$19$ |
$D_{14}$ (as 14T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 14 x^{7} + 14 x^{6} + 7$ |
$[6, 0]$ |
$[2, 1]$ |
| 7.14.19.4 |
$14$ |
$x^{14} + 21 x^{7} + 42 x^{6} + 21$ |
$7$ |
$14$ |
$1$ |
$19$ |
$D_{14}$ (as 14T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 21 x^{7} + 42 x^{6} + 21$ |
$[6, 0]$ |
$[2, 1]$ |
| 7.14.25.35 |
$14$ |
$x^{14} + 7 x^{12} + 252$ |
$7$ |
$14$ |
$1$ |
$25$ |
$D_{14}$ (as 14T3) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 7 x^{12} + 252$ |
$[12, 0]$ |
$[2, 1]$ |
| 7.14.25.56 |
$14$ |
$x^{14} + 21 x^{12} + 217$ |
$7$ |
$14$ |
$1$ |
$25$ |
$D_{14}$ (as 14T3) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 21 x^{12} + 217$ |
$[12, 0]$ |
$[2, 1]$ |
