| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 17.14.0.1 |
$14$ |
$x^{14} + x^{8} + 11 x^{7} + x^{6} + 8 x^{5} + 16 x^{4} + 13 x^{3} + 9 x^{2} + 3 x + 3$ |
$17$ |
$1$ |
$14$ |
$0$ |
$C_{14}$ (as 14T1) |
$14$ |
$1$ |
$[\ ]$ |
$[\ ]^{14}$ |
$t^{14} + t^{8} + 11 t^{7} + t^{6} + 8 t^{5} + 16 t^{4} + 13 t^{3} + 9 t^{2} + 3 t + 3$ |
$x - 17$ |
$[0]$ |
$[]$ |
| 17.14.7.1 |
$14$ |
$x^{14} + 1071 x^{13} + 491708 x^{12} + 125464437 x^{11} + 19221135969 x^{10} + 1769192651898 x^{9} + 90773424099277 x^{8} + 2022717194718445 x^{7} + 1543148215595651 x^{6} + 511298184911304 x^{5} + 94664842882197 x^{4} + 31823467716383 x^{3} + 1100435035211950 x^{2} + 24803053432496659 x + 29942903574449667$ |
$17$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 12 t + 14$ |
$x^{2} + 153 x + 17$ |
$[0]$ |
$[1]$ |
| 17.14.7.2 |
$14$ |
$x^{14} + 289650828 x^{2} - 5744741422$ |
$17$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 12 t + 14$ |
$x^{2} + 17 t$ |
$[0]$ |
$[1]$ |
| 17.14.12.1 |
$14$ |
$x^{14} + 112 x^{13} + 5397 x^{12} + 145376 x^{11} + 2374589 x^{10} + 23755536 x^{9} + 138569137 x^{8} + 408357986 x^{7} + 415709315 x^{6} + 213889074 x^{5} + 66465343 x^{4} + 48952246 x^{3} + 353976063 x^{2} + 1858653398 x + 4197785820$ |
$17$ |
$7$ |
$2$ |
$12$ |
$F_7$ (as 14T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$t^{2} + 16 t + 3$ |
$x^{7} + 17$ |
$[0]$ |
$[3]$ |
| 17.14.13.1 |
$14$ |
$x^{14} + 17$ |
$17$ |
$14$ |
$1$ |
$13$ |
$F_7 \times C_2$ (as 14T7) |
$6$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{6}$ |
$t + 14$ |
$x^{14} + 17$ |
$[0]$ |
$[6]$ |
| 17.14.13.2 |
$14$ |
$x^{14} + 51$ |
$17$ |
$14$ |
$1$ |
$13$ |
$F_7 \times C_2$ (as 14T7) |
$6$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{6}$ |
$t + 14$ |
$x^{14} + 51$ |
$[0]$ |
$[6]$ |
