| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 19.14.0.1 |
$14$ |
$x^{14} + 11 x^{7} + 11 x^{6} + 11 x^{5} + x^{4} + 5 x^{3} + 16 x^{2} + 7 x + 2$ |
$19$ |
$1$ |
$14$ |
$0$ |
$C_{14}$ (as 14T1) |
$14$ |
$1$ |
$[\ ]$ |
$[\ ]^{14}$ |
$t^{14} + 11 t^{7} + 11 t^{6} + 11 t^{5} + t^{4} + 5 t^{3} + 16 t^{2} + 7 t + 2$ |
$x - 19$ |
$[0]$ |
$[]$ |
| 19.14.7.1 |
$14$ |
$x^{14} - 836 x^{13} + 11529618 x^{12} + 40153059632 x^{11} + 45701018933715 x^{10} - 27199543314328911 x^{9} - 122971941784309357645 x^{8} - 171679318980585845579840 x^{7} - 4585575958956710706912 x^{6} + 50052189831457642637 x^{5} + 1651410192170735556 x^{4} - 8261685479759434 x^{3} - 232742465638578 x^{2} - 829512973792 x - 15195819563$ |
$19$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 6 t + 17$ |
$x^{2} + \left(38 t^{6} + 266 t^{5} + 19 t^{4} + 304 t^{3} + 209 t^{2} + 152 t + 76\right) x + 19 t$ |
$[0]$ |
$[1]$ |
| 19.14.7.2 |
$14$ |
$x^{14} - 9082 x^{13} + 74145923 x^{12} + 132432948192 x^{11} + 1786839611560128 x^{10} + 5067376315465156928 x^{9} + 9248554083250091316158 x^{8} + 5246110013130072565373868 x^{7} + 175722527581751735007002 x^{6} + 1829322849882921651008 x^{5} + 12255932895690917952 x^{4} + 17258794241329632 x^{3} + 183592645794377 x^{2} - 427270691242 x + 893871739$ |
$19$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 6 t + 17$ |
$x^{2} + \left(304 t^{6} + 342 t^{5} + 285 t^{4} + 304 t^{3} + 247 t^{2} + 323 t + 266\right) x + 19$ |
$[0]$ |
$[1]$ |
| 19.14.12.1 |
$14$ |
$x^{14} + 126 x^{13} + 6818 x^{12} + 205632 x^{11} + 3742284 x^{10} + 41321448 x^{9} + 260402968 x^{8} + 775862822 x^{7} + 520808330 x^{6} + 165413472 x^{5} + 33744732 x^{4} + 71380792 x^{3} + 731029768 x^{2} + 4357641344 x + 11135742105$ |
$19$ |
$7$ |
$2$ |
$12$ |
$F_7$ (as 14T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$t^{2} + 18 t + 2$ |
$x^{7} + 19$ |
$[0]$ |
$[3]$ |
| 19.14.13.1 |
$14$ |
$x^{14} + 38$ |
$19$ |
$14$ |
$1$ |
$13$ |
$F_7 \times C_2$ (as 14T7) |
$6$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{6}$ |
$t + 17$ |
$x^{14} + 38$ |
$[0]$ |
$[6]$ |
| 19.14.13.2 |
$14$ |
$x^{14} + 19$ |
$19$ |
$14$ |
$1$ |
$13$ |
$F_7 \times C_2$ (as 14T7) |
$6$ |
$14$ |
$[\ ]$ |
$[\ ]_{14}^{6}$ |
$t + 17$ |
$x^{14} + 19$ |
$[0]$ |
$[6]$ |
