| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.14.0.1 |
$14$ |
$x^{14} + x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{4} + 3 x^{3} + x + 2$ |
$5$ |
$1$ |
$14$ |
$0$ |
$C_{14}$ (as 14T1) |
$14$ |
$1$ |
$[\ ]$ |
$[\ ]^{14}$ |
$t^{14} + t^{8} + 4 t^{6} + 4 t^{5} + 2 t^{4} + 3 t^{3} + t + 2$ |
$x - 5$ |
$[0]$ |
$[]$ |
| 5.14.7.1 |
$14$ |
$x^{14} + 140 x^{13} + 8435 x^{12} + 284200 x^{11} + 5810525 x^{10} + 72852500 x^{9} + 534104381 x^{8} + 1994350486 x^{7} + 2670547075 x^{6} + 1822151870 x^{5} + 743294125 x^{4} + 386790250 x^{3} + 1508497384 x^{2} + 5074882448 x + 4401772109$ |
$5$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 3 t + 3$ |
$x^{2} + 20 x + 5$ |
$[0]$ |
$[1]$ |
| 5.14.7.2 |
$14$ |
$x^{14} + 46875 x^{2} - 234375$ |
$5$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 3 t + 3$ |
$x^{2} + 5 t$ |
$[0]$ |
$[1]$ |
| 5.14.12.1 |
$14$ |
$x^{14} + 28 x^{13} + 350 x^{12} + 2576 x^{11} + 12404 x^{10} + 41104 x^{9} + 96152 x^{8} + 160650 x^{7} + 192444 x^{6} + 165676 x^{5} + 106232 x^{4} + 65016 x^{3} + 59920 x^{2} + 57232 x + 27193$ |
$5$ |
$7$ |
$2$ |
$12$ |
$F_7$ (as 14T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$t^{2} + 4 t + 2$ |
$x^{7} + 5$ |
$[0]$ |
$[3]$ |
| 5.14.13.1 |
$14$ |
$x^{14} + 5$ |
$5$ |
$14$ |
$1$ |
$13$ |
$F_7 \times C_2$ (as 14T7) |
$6$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{6}$ |
$t + 3$ |
$x^{14} + 5$ |
$[0]$ |
$[6]$ |
| 5.14.13.2 |
$14$ |
$x^{14} + 10$ |
$5$ |
$14$ |
$1$ |
$13$ |
$F_7 \times C_2$ (as 14T7) |
$6$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{6}$ |
$t + 3$ |
$x^{14} + 10$ |
$[0]$ |
$[6]$ |
