| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 7.14.18.10 |
$14$ |
$x^{14} - 98 x^{11} - 154 x^{10} - 245 x^{8} + 504 x^{7} + 1225 x^{6} - 686 x^{4} - 1078 x^{3} + 49$ |
$7$ |
$7$ |
$2$ |
$18$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(21 t + 14\right) x^{4} + \left(28 t + 7\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.18.16 |
$14$ |
$x^{14} - 140 x^{10} - 1176 x^{8} - 4690 x^{7} + 196 x^{6} - 980 x^{3} + 49$ |
$7$ |
$7$ |
$2$ |
$18$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(14 t + 42\right) x^{4} + \left(28 t + 14\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.18.19 |
$14$ |
$x^{14} + 14 x^{11} + 49 x^{8} + 14 x^{7} - 1176 x^{6} + 98 x^{4} + 49$ |
$7$ |
$7$ |
$2$ |
$18$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 7 x^{4} + \left(14 t + 42\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.25.22 |
$14$ |
$x^{14} + 7 x^{13} + 21 x^{12} + 168$ |
$7$ |
$14$ |
$1$ |
$25$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 7 x^{13} + 21 x^{12} + 168$ |
$[12, 0]$ |
$[2, 1]$ |
| 7.14.25.3 |
$14$ |
$x^{14} + 7 x^{12} + 35 x^{7} + 252$ |
$7$ |
$14$ |
$1$ |
$25$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 7 x^{12} + 35 x^{7} + 252$ |
$[12, 0]$ |
$[2, 1]$ |
| 7.14.25.30 |
$14$ |
$x^{14} + 14 x^{13} + 21 x^{12} + 266$ |
$7$ |
$14$ |
$1$ |
$25$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 14 x^{13} + 21 x^{12} + 266$ |
$[12, 0]$ |
$[2, 1]$ |
| 7.14.25.47 |
$14$ |
$x^{14} + 14 x^{13} + 21 x^{12} + 35 x^{7} + 168$ |
$7$ |
$14$ |
$1$ |
$25$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 14 x^{13} + 21 x^{12} + 35 x^{7} + 168$ |
$[12, 0]$ |
$[2, 1]$ |
| 7.14.25.8 |
$14$ |
$x^{14} + 21 x^{13} + 7 x^{12} + 42 x^{7} + 105$ |
$7$ |
$14$ |
$1$ |
$25$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 21 x^{13} + 7 x^{12} + 42 x^{7} + 105$ |
$[12, 0]$ |
$[2, 1]$ |
| 7.14.25.9 |
$14$ |
$x^{14} + 21 x^{13} + 7 x^{12} + 28 x^{7} + 252$ |
$7$ |
$14$ |
$1$ |
$25$ |
$D_7^2$ (as 14T13) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 4$ |
$x^{14} + 21 x^{13} + 7 x^{12} + 28 x^{7} + 252$ |
$[12, 0]$ |
$[2, 1]$ |
