| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 13.14.0.1 |
$14$ |
$x^{14} + 4 x^{7} + 6 x^{5} + 11 x^{4} + 7 x^{3} + 10 x^{2} + 10 x + 2$ |
$13$ |
$1$ |
$14$ |
$0$ |
$C_{14}$ (as 14T1) |
$14$ |
$1$ |
$[\ ]$ |
$[\ ]^{14}$ |
$t^{14} + 4 t^{7} + 6 t^{5} + 11 t^{4} + 7 t^{3} + 10 t^{2} + 10 t + 2$ |
$x - 13$ |
$[0]$ |
$[\ ]$ |
| 13.14.7.1 |
$14$ |
$x^{14} + 910 x^{13} + 354991 x^{12} + 76965980 x^{11} + 10019422049 x^{10} + 783716146850 x^{9} + 34178120507901 x^{8} + 647835779318542 x^{7} + 444315567676253 x^{6} + 132448262974664 x^{5} + 22043433979203 x^{4} + 4640995086910 x^{3} + 109804606053970 x^{2} + 2252387433208628 x + 7052605388282809$ |
$13$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 3 t + 11$ |
$x^{2} + 130 x + 13$ |
$[0]$ |
$[1]$ |
| 13.14.7.2 |
$14$ |
$x^{14} + 14480427 x^{2} - 690233687$ |
$13$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 3 t + 11$ |
$x^{2} + 13 t$ |
$[0]$ |
$[1]$ |
| 13.14.12.1 |
$14$ |
$x^{14} + 84 x^{13} + 3038 x^{12} + 61488 x^{11} + 756084 x^{10} + 5714352 x^{9} + 25377688 x^{8} + 58198682 x^{7} + 50756468 x^{6} + 22895628 x^{5} + 6802152 x^{4} + 9898168 x^{3} + 63376432 x^{2} + 249556496 x + 421775625$ |
$13$ |
$7$ |
$2$ |
$12$ |
$D_{7}$ (as 14T2) |
$2$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{2}$ |
$t^{2} + 12 t + 2$ |
$x^{7} + 13$ |
$[0]$ |
$[1]$ |
| 13.14.12.2 |
$14$ |
$x^{14} - 728 x^{7} - 11154$ |
$13$ |
$7$ |
$2$ |
$12$ |
$C_7 \wr C_2$ (as 14T8) |
$14$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{14}$ |
$t^{2} + 12 t + 2$ |
$x^{7} + 65 t + 26$ |
$[0]$ |
$[1]$ |
| 13.14.12.3 |
$14$ |
$x^{14} - 1716 x^{7} - 91260$ |
$13$ |
$7$ |
$2$ |
$12$ |
$C_7 \wr C_2$ (as 14T8) |
$14$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{14}$ |
$t^{2} + 12 t + 2$ |
$x^{7} + 156 t + 78$ |
$[0]$ |
$[1]$ |
| 13.14.12.4 |
$14$ |
$x^{14} - 1586 x^{7} - 198575$ |
$13$ |
$7$ |
$2$ |
$12$ |
$C_7 \wr C_2$ (as 14T8) |
$14$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{14}$ |
$t^{2} + 12 t + 2$ |
$x^{7} + 156 t + 143$ |
$[0]$ |
$[1]$ |
| 13.14.13.1 |
$14$ |
$x^{14} + 13$ |
$13$ |
$14$ |
$1$ |
$13$ |
$D_{14}$ (as 14T3) |
$2$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{2}$ |
$t + 11$ |
$x^{14} + 13$ |
$[0]$ |
$[2]$ |
| 13.14.13.2 |
$14$ |
$x^{14} + 26$ |
$13$ |
$14$ |
$1$ |
$13$ |
$D_{14}$ (as 14T3) |
$2$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{2}$ |
$t + 11$ |
$x^{14} + 26$ |
$[0]$ |
$[2]$ |
