Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.14.0.1 |
$14$ |
$x^{14} + 2 x^{9} + x^{8} + x^{7} + 2 x^{6} + x^{5} + 2 x^{3} + x^{2} + 2$ |
$3$ |
$1$ |
$14$ |
$0$ |
$C_{14}$ (as 14T1) |
$14$ |
$1$ |
$[\ ]$ |
$[\ ]^{14}$ |
$t^{14} + 2 t^{9} + t^{8} + t^{7} + 2 t^{6} + t^{5} + 2 t^{3} + t^{2} + 2$ |
$x - 3$ |
$[0]$ |
$[]$ |
3.14.7.1 |
$14$ |
$x^{14} - 486 x^{4} - 2187$ |
$3$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 2 t^{2} + 1$ |
$x^{2} + 3 t$ |
$[0]$ |
$[1]$ |
3.14.7.2 |
$14$ |
$x^{14} + 21 x^{12} + 189 x^{10} + 4 x^{9} + 945 x^{8} - 94 x^{7} + 2835 x^{6} - 630 x^{5} + 5107 x^{4} + 630 x^{3} + 5131 x^{2} + 1242 x + 2212$ |
$3$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 2 t^{2} + 1$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
3.14.12.1 |
$14$ |
$x^{14} + 14 x^{13} + 98 x^{12} + 448 x^{11} + 1484 x^{10} + 3752 x^{9} + 7448 x^{8} + 11782 x^{7} + 14938 x^{6} + 15008 x^{5} + 11452 x^{4} + 6328 x^{3} + 2632 x^{2} + 896 x + 185$ |
$3$ |
$7$ |
$2$ |
$12$ |
$F_7$ (as 14T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{7} + 3$ |
$[0]$ |
$[3]$ |
3.14.13.1 |
$14$ |
$x^{14} + 6$ |
$3$ |
$14$ |
$1$ |
$13$ |
$F_7 \times C_2$ (as 14T7) |
$6$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{6}$ |
$t + 1$ |
$x^{14} + 6$ |
$[0]$ |
$[6]$ |
3.14.13.2 |
$14$ |
$x^{14} + 3$ |
$3$ |
$14$ |
$1$ |
$13$ |
$F_7 \times C_2$ (as 14T7) |
$6$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{6}$ |
$t + 1$ |
$x^{14} + 3$ |
$[0]$ |
$[6]$ |