| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 7.14.16.17 |
$14$ |
$x^{14} + 14 x^{9} + 14 x^{7} - 294 x^{6} + 49 x^{4} + 98 x^{2} + 49$ |
$7$ |
$7$ |
$2$ |
$16$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$2$ |
$3$ |
$[4/3]$ |
$[4/3]_{3}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(7 t + 21\right) x^{3} + 7 x^{2} + 7$ |
$[2, 0]$ |
$[1]$ |
| 7.14.16.18 |
$14$ |
$x^{14} + 14 x^{10} + 56 x^{9} + 14 x^{7} - 245 x^{6} + 392 x^{5} + 784 x^{4} + 98 x^{3} + 392 x^{2} + 49$ |
$7$ |
$7$ |
$2$ |
$16$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$2$ |
$3$ |
$[4/3]$ |
$[4/3]_{3}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(7 t + 28\right) x^{3} + 28 x^{2} + 7$ |
$[2, 0]$ |
$[1]$ |
| 7.14.16.27 |
$14$ |
$x^{14} + 42 x^{13} + 777 x^{12} + 8316 x^{11} + 56889 x^{10} + 259714 x^{9} + 804573 x^{8} + 1701062 x^{7} + 2503473 x^{6} + 2867256 x^{5} + 3491593 x^{4} + 5146806 x^{3} + 6156409 x^{2} + 4300044 x + 1611550$ |
$7$ |
$7$ |
$2$ |
$16$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$2$ |
$3$ |
$[4/3]$ |
$[4/3]_{3}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 14 x^{2} + 7$ |
$[2, 0]$ |
$[1]$ |
| 7.14.17.10 |
$14$ |
$x^{14} + 7 x^{5} + 21 x^{4} + 21$ |
$7$ |
$14$ |
$1$ |
$17$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[4/3]$ |
$[4/3]_{6}$ |
$t + 4$ |
$x^{14} + 7 x^{5} + 21 x^{4} + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 7.14.17.2 |
$14$ |
$x^{14} + 7 x^{5} + 14 x^{4} + 7$ |
$7$ |
$14$ |
$1$ |
$17$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[4/3]$ |
$[4/3]_{6}$ |
$t + 4$ |
$x^{14} + 7 x^{5} + 14 x^{4} + 7$ |
$[4, 0]$ |
$[1, 1]$ |
| 7.14.17.5 |
$14$ |
$x^{14} + 14 x^{5} + 42 x^{4} + 21$ |
$7$ |
$14$ |
$1$ |
$17$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[4/3]$ |
$[4/3]_{6}$ |
$t + 4$ |
$x^{14} + 14 x^{5} + 42 x^{4} + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 7.14.17.6 |
$14$ |
$x^{14} + 7 x^{5} + 35 x^{4} + 21$ |
$7$ |
$14$ |
$1$ |
$17$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[4/3]$ |
$[4/3]_{6}$ |
$t + 4$ |
$x^{14} + 7 x^{5} + 35 x^{4} + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 7.14.17.7 |
$14$ |
$x^{14} + 14 x^{5} + 7 x^{4} + 7$ |
$7$ |
$14$ |
$1$ |
$17$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[4/3]$ |
$[4/3]_{6}$ |
$t + 4$ |
$x^{14} + 14 x^{5} + 7 x^{4} + 7$ |
$[4, 0]$ |
$[1, 1]$ |
| 7.14.17.9 |
$14$ |
$x^{14} + 14 x^{5} + 28 x^{4} + 7$ |
$7$ |
$14$ |
$1$ |
$17$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[4/3]$ |
$[4/3]_{6}$ |
$t + 4$ |
$x^{14} + 14 x^{5} + 28 x^{4} + 7$ |
$[4, 0]$ |
$[1, 1]$ |
| 7.14.20.12 |
$14$ |
$x^{14} - 84 x^{12} + 14 x^{11} - 882 x^{10} - 588 x^{9} + 49 x^{8} + 14 x^{7} - 588 x^{5} + 98 x^{4} + 49$ |
$7$ |
$7$ |
$2$ |
$20$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$2$ |
$3$ |
$[5/3]$ |
$[5/3]_{3}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(21 t + 21\right) x^{5} + 7 x^{4} + 7$ |
$[4, 0]$ |
$[1]$ |
| 7.14.20.18 |
$14$ |
$x^{14} + 42 x^{13} + 805 x^{12} + 9380 x^{11} + 74893 x^{10} + 439894 x^{9} + 1995217 x^{8} + 7146950 x^{7} + 19867113 x^{6} + 40468372 x^{5} + 55877213 x^{4} + 48631926 x^{3} + 25666137 x^{2} + 8649900 x + 2416270$ |
$7$ |
$7$ |
$2$ |
$20$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$2$ |
$3$ |
$[5/3]$ |
$[5/3]_{3}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 14 x^{5} + 28 x^{4} + 7$ |
$[4, 0]$ |
$[1]$ |
| 7.14.20.22 |
$14$ |
$x^{14} + 42 x^{13} + 861 x^{12} + 11368 x^{11} + 107457 x^{10} + 765954 x^{9} + 4184089 x^{8} + 17178734 x^{7} + 50571297 x^{6} + 100475508 x^{5} + 127144969 x^{4} + 99449994 x^{3} + 47146869 x^{2} + 14224896 x + 3720874$ |
$7$ |
$7$ |
$2$ |
$20$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$2$ |
$3$ |
$[5/3]$ |
$[5/3]_{3}^{2}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 42 x^{5} + 14 x^{4} + 7$ |
$[4, 0]$ |
$[1]$ |
| 7.14.21.17 |
$14$ |
$x^{14} + 42 x^{9} + 42 x^{8} + 7 x^{7} + 21$ |
$7$ |
$14$ |
$1$ |
$21$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[5/3]$ |
$[5/3]_{6}$ |
$t + 4$ |
$x^{14} + 42 x^{9} + 42 x^{8} + 7 x^{7} + 21$ |
$[8, 0]$ |
$[1, 1]$ |
| 7.14.21.29 |
$14$ |
$x^{14} + 7 x^{10} + 14 x^{9} + 28 x^{8} + 42 x^{7} + 7$ |
$7$ |
$14$ |
$1$ |
$21$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[5/3]$ |
$[5/3]_{6}$ |
$t + 4$ |
$x^{14} + 7 x^{10} + 14 x^{9} + 28 x^{8} + 42 x^{7} + 7$ |
$[8, 0]$ |
$[1, 1]$ |
| 7.14.21.35 |
$14$ |
$x^{14} + 14 x^{10} + 21 x^{9} + 21 x^{8} + 7 x^{7} + 21$ |
$7$ |
$14$ |
$1$ |
$21$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[5/3]$ |
$[5/3]_{6}$ |
$t + 4$ |
$x^{14} + 14 x^{10} + 21 x^{9} + 21 x^{8} + 7 x^{7} + 21$ |
$[8, 0]$ |
$[1, 1]$ |
| 7.14.21.37 |
$14$ |
$x^{14} + 7 x^{10} + 42 x^{9} + 14 x^{8} + 7 x^{7} + 7$ |
$7$ |
$14$ |
$1$ |
$21$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[5/3]$ |
$[5/3]_{6}$ |
$t + 4$ |
$x^{14} + 7 x^{10} + 42 x^{9} + 14 x^{8} + 7 x^{7} + 7$ |
$[8, 0]$ |
$[1, 1]$ |
| 7.14.21.44 |
$14$ |
$x^{14} + 35 x^{10} + 35 x^{9} + 35 x^{8} + 7 x^{7} + 21$ |
$7$ |
$14$ |
$1$ |
$21$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[5/3]$ |
$[5/3]_{6}$ |
$t + 4$ |
$x^{14} + 35 x^{10} + 35 x^{9} + 35 x^{8} + 7 x^{7} + 21$ |
$[8, 0]$ |
$[1, 1]$ |
| 7.14.21.47 |
$14$ |
$x^{14} + 7 x^{8} + 7$ |
$7$ |
$14$ |
$1$ |
$21$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$1$ |
$6$ |
$[5/3]$ |
$[5/3]_{6}$ |
$t + 4$ |
$x^{14} + 7 x^{8} + 7$ |
$[8, 0]$ |
$[1, 1]$ |
| 7.14.24.37 |
$14$ |
$x^{14} + 70 x^{13} + 1225 x^{12} - 378 x^{7} - 13230 x^{6} - 93933$ |
$7$ |
$7$ |
$2$ |
$24$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 35 x^{6} + 147 t + 252$ |
$[6, 0]$ |
$[3]$ |
| 7.14.24.8 |
$14$ |
$x^{14} + 42 x^{13} + 441 x^{12} - 182 x^{7} - 3822 x^{6} - 49343$ |
$7$ |
$7$ |
$2$ |
$24$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 21 x^{6} + 98 t + 203$ |
$[6, 0]$ |
$[3]$ |
| 7.14.25.38 |
$14$ |
$x^{14} + 7 x^{13} + 21 x^{12} + 35 x^{7} + 203$ |
$7$ |
$14$ |
$1$ |
$25$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$2$ |
$[2]$ |
$[2]_{2}^{3}$ |
$t + 4$ |
$x^{14} + 7 x^{13} + 21 x^{12} + 35 x^{7} + 203$ |
$[12, 0]$ |
$[3, 1]$ |
| 7.14.25.45 |
$14$ |
$x^{14} + 7 x^{13} + 35 x^{12} + 21 x^{7} + 203$ |
$7$ |
$14$ |
$1$ |
$25$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$2$ |
$[2]$ |
$[2]_{2}^{3}$ |
$t + 4$ |
$x^{14} + 7 x^{13} + 35 x^{12} + 21 x^{7} + 203$ |
$[12, 0]$ |
$[3, 1]$ |
| 7.14.25.49 |
$14$ |
$x^{14} + 7 x^{12} + 21$ |
$7$ |
$14$ |
$1$ |
$25$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$2$ |
$[2]$ |
$[2]_{2}^{3}$ |
$t + 4$ |
$x^{14} + 7 x^{12} + 21$ |
$[12, 0]$ |
$[3, 1]$ |
| 7.14.25.53 |
$14$ |
$x^{14} + 14 x^{13} + 14 x^{12} + 21 x^{7} + 119$ |
$7$ |
$14$ |
$1$ |
$25$ |
$(C_7:C_3) \times C_2$ (as 14T5) |
$3$ |
$2$ |
$[2]$ |
$[2]_{2}^{3}$ |
$t + 4$ |
$x^{14} + 14 x^{13} + 14 x^{12} + 21 x^{7} + 119$ |
$[12, 0]$ |
$[3, 1]$ |
