| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 7.14.18.12 |
$14$ |
$x^{14} - 252 x^{11} - 238 x^{10} + 5292 x^{8} + 8834 x^{7} + 3577 x^{6} - 1764 x^{4} - 1666 x^{3} + 49$ |
$7$ |
$7$ |
$2$ |
$18$ |
$C_7^2:C_4$ (as 14T12) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 t x^{4} + \left(42 t + 7\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.18.20 |
$14$ |
$x^{14} - 126 x^{11} - 112 x^{10} - 3381 x^{8} - 4690 x^{7} - 1568 x^{6} - 882 x^{4} - 784 x^{3} + 49$ |
$7$ |
$7$ |
$2$ |
$18$ |
$C_7^2:C_4$ (as 14T12) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(35 t + 42\right) x^{4} + \left(28 t + 28\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.18.5 |
$14$ |
$x^{14} - 168 x^{11} - 84 x^{10} - 3528 x^{8} - 7042 x^{7} - 2940 x^{6} - 1176 x^{4} - 588 x^{3} + 49$ |
$7$ |
$7$ |
$2$ |
$18$ |
$C_7^2:C_4$ (as 14T12) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(42 t + 42\right) x^{4} + \left(28 t + 42\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.18.6 |
$14$ |
$x^{14} - 154 x^{11} + 42 x^{10} - 1421 x^{8} - 6160 x^{7} + 147 x^{6} - 1078 x^{4} + 294 x^{3} + 49$ |
$7$ |
$7$ |
$2$ |
$18$ |
$C_7^2:C_4$ (as 14T12) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(35 t + 28\right) x^{4} + \left(7 t + 42\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
| 7.14.24.14 |
$14$ |
$x^{14} - 42 x^{13} - 735 x^{12} - 574 x^{7} - 20874 x^{6} - 148127$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_7^2:C_4$ (as 14T12) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(14 t + 21\right) x^{6} + 196 t + 301$ |
$[6, 0]$ |
$[2]$ |
| 7.14.24.16 |
$14$ |
$x^{14} - 56 x^{13} - 392 x^{12} - 868 x^{7} - 16856 x^{6} - 171794$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_7^2:C_4$ (as 14T12) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(14 t + 14\right) x^{6} + 245 t + 301$ |
$[6, 0]$ |
$[2]$ |
| 7.14.24.17 |
$14$ |
$x^{14} - 70 x^{13} - 1421 x^{12} - 1456 x^{7} - 23128 x^{6} + 11368$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_7^2:C_4$ (as 14T12) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(21 t + 28\right) x^{6} + 294 t + 154$ |
$[6, 0]$ |
$[2]$ |
| 7.14.24.30 |
$14$ |
$x^{14} - 126 x^{13} + 1323 x^{12} - 476 x^{7} - 7056 x^{6} - 73010$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_7^2:C_4$ (as 14T12) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 21 t x^{6} + 147 t + 203$ |
$[6, 0]$ |
$[2]$ |
