| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 7.14.0.1 |
$14$ |
$x^{14} + 5 x^{7} + 6 x^{5} + 2 x^{4} + 3 x^{2} + 6 x + 3$ |
$7$ |
$1$ |
$14$ |
$0$ |
$C_{14}$ (as 14T1) |
$14$ |
$1$ |
$[\ ]$ |
$[\ ]^{14}$ |
$t^{14} + 5 t^{7} + 6 t^{5} + 2 t^{4} + 3 t^{2} + 6 t + 3$ |
$x - 7$ |
$[0]$ |
$[]$ |
| 7.14.7.1 |
$14$ |
$x^{14} + 49 x^{12} + 1029 x^{10} + 12017 x^{8} + 8 x^{7} + 82859 x^{6} - 1176 x^{5} + 352947 x^{4} + 13720 x^{3} + 881203 x^{2} - 19160 x + 794999$ |
$7$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 6 t + 4$ |
$x^{2} + 7$ |
$[0]$ |
$[1]$ |
| 7.14.7.2 |
$14$ |
$x^{14} - 756 x^{13} + 407484 x^{12} - 120759324 x^{11} + 18245133144 x^{10} - 1371646043208 x^{9} + 45234910589400 x^{8} - 365498518846944 x^{7} - 160150981540032 x^{6} - 9636001680480 x^{5} - 1806831694584 x^{4} - 187090145760 x^{3} - 8419197738 x^{2} - 138355224 x - 3294172$ |
$7$ |
$2$ |
$7$ |
$7$ |
$C_{14}$ (as 14T1) |
$7$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{7}$ |
$t^{7} + 6 t + 4$ |
$x^{2} + \left(21 t^{6} + 42 t^{4} + 42 t^{3} + 42 t^{2} + 42 t\right) x + 7 t$ |
$[0]$ |
$[1]$ |
| 7.14.24.25 |
$14$ |
$x^{14} + 126 x^{13} + 5817 x^{12} + 127764 x^{11} + 1590057 x^{10} + 12246066 x^{9} + 60787881 x^{8} + 196875020 x^{7} + 413882343 x^{6} + 559281870 x^{5} + 489084183 x^{4} + 294720048 x^{3} + 193157055 x^{2} + 232471890 x + 192871675$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_{14}$ (as 14T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 x^{6} + 154$ |
$[6, 0]$ |
$[1]$ |
| 7.14.24.44 |
$14$ |
$x^{14} + 84 x^{13} + 1764 x^{12} - 1260 x^{7} - 52920 x^{6} - 121716$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_{14}$ (as 14T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 x^{6} + 294 t + 252$ |
$[6, 0]$ |
$[1]$ |
| 7.14.24.45 |
$14$ |
$x^{14} + 84 x^{13} + 1764 x^{12} - 182 x^{7} - 7644 x^{6} - 49343$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_{14}$ (as 14T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 x^{6} + 98 t + 203$ |
$[6, 0]$ |
$[1]$ |
| 7.14.24.51 |
$14$ |
$x^{14} + 84 x^{13} + 1764 x^{12} - 1162 x^{7} - 48804 x^{6} - 22589$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_{14}$ (as 14T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 x^{6} + 245 t + 154$ |
$[6, 0]$ |
$[1]$ |
| 7.14.24.52 |
$14$ |
$x^{14} + 126 x^{13} + 5817 x^{12} + 127764 x^{11} + 1590057 x^{10} + 12246066 x^{9} + 60787881 x^{8} + 196875314 x^{7} + 413900865 x^{6} + 559596744 x^{5} + 492695973 x^{4} + 319261698 x^{3} + 289675197 x^{2} + 437454864 x + 375615754$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_{14}$ (as 14T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 x^{6} + 301$ |
$[6, 0]$ |
$[1]$ |
| 7.14.24.53 |
$14$ |
$x^{14} + 84 x^{13} + 1764 x^{12} + 14 x^{7} + 588 x^{6} - 14357$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_{14}$ (as 14T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 x^{6} + 49 t + 154$ |
$[6, 0]$ |
$[1]$ |
| 7.14.24.54 |
$14$ |
$x^{14} + 84 x^{13} + 1764 x^{12} - 1652 x^{7} - 69384 x^{6} + 163660$ |
$7$ |
$7$ |
$2$ |
$24$ |
$C_{14}$ (as 14T1) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 x^{6} + 294 t + 56$ |
$[6, 0]$ |
$[1]$ |
| 7.14.25.52 |
$14$ |
$x^{14} + 7 x^{13} + 42 x^{12} + 42 x^{7} + 203$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 7 x^{13} + 42 x^{12} + 42 x^{7} + 203$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.54 |
$14$ |
$x^{14} + 21 x^{13} + 42 x^{12} + 28 x^{7} + 301$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 21 x^{13} + 42 x^{12} + 28 x^{7} + 301$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.59 |
$14$ |
$x^{14} + 42 x^{12} + 7$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 42 x^{12} + 7$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.60 |
$14$ |
$x^{14} + 28 x^{13} + 28 x^{12} + 21 x^{7} + 21$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 28 x^{13} + 28 x^{12} + 21 x^{7} + 21$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.62 |
$14$ |
$x^{14} + 28 x^{12} + 266$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 28 x^{12} + 266$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.63 |
$14$ |
$x^{14} + 28 x^{13} + 28 x^{12} + 21 x^{7} + 119$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 28 x^{13} + 28 x^{12} + 21 x^{7} + 119$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.72 |
$14$ |
$x^{14} + 35 x^{13} + 42 x^{12} + 14 x^{7} + 105$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 35 x^{13} + 42 x^{12} + 14 x^{7} + 105$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.73 |
$14$ |
$x^{14} + 42 x^{12} + 154$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 42 x^{12} + 154$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.75 |
$14$ |
$x^{14} + 14 x^{13} + 28 x^{12} + 35 x^{7} + 217$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 14 x^{13} + 28 x^{12} + 35 x^{7} + 217$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.89 |
$14$ |
$x^{14} + 42 x^{12} + 56$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 42 x^{12} + 56$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.91 |
$14$ |
$x^{14} + 14 x^{13} + 28 x^{12} + 35 x^{7} + 168$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 14 x^{13} + 28 x^{12} + 35 x^{7} + 168$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.93 |
$14$ |
$x^{14} + 28 x^{12} + 70$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 28 x^{12} + 70$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.95 |
$14$ |
$x^{14} + 14 x^{13} + 42 x^{12} + 35 x^{7} + 252$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 14 x^{13} + 42 x^{12} + 35 x^{7} + 252$ |
$[12, 0]$ |
$[1, 1]$ |
| 7.14.25.96 |
$14$ |
$x^{14} + 7 x^{13} + 28 x^{12} + 42 x^{7} + 315$ |
$7$ |
$14$ |
$1$ |
$25$ |
$C_{14}$ (as 14T1) |
$1$ |
$2$ |
$[2]$ |
$[2]_{2}$ |
$t + 4$ |
$x^{14} + 7 x^{13} + 28 x^{12} + 42 x^{7} + 315$ |
$[12, 0]$ |
$[1, 1]$ |
