| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.14.14.19 |
$14$ |
$x^{14} + 14 x^{13} + 98 x^{12} + 400 x^{11} + 956 x^{10} + 1160 x^{9} + 152 x^{8} - 320 x^{7} + 5296 x^{6} + 6432 x^{5} - 11936 x^{4} + 21504 x^{3} + 2368 x^{2} - 13440 x + 16512$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{6} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.20 |
$14$ |
$x^{14} + 14 x^{13} + 126 x^{12} + 1168 x^{11} + 9868 x^{10} + 64520 x^{9} + 317384 x^{8} + 1190080 x^{7} + 3447536 x^{6} + 7751584 x^{5} + 13448736 x^{4} + 17658368 x^{3} + 16807744 x^{2} + 10589568 x + 3453824$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.31 |
$14$ |
$x^{14} - 12 x^{13} + 50 x^{12} + 120 x^{11} - 820 x^{10} - 144 x^{9} + 8472 x^{8} + 9920 x^{7} - 30672 x^{6} - 59456 x^{5} + 106336 x^{4} + 342912 x^{3} + 180800 x^{2} - 207616 x - 301952$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4}\right) x + 4 t^{6} + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.32 |
$14$ |
$x^{14} + 54 x^{12} + 120 x^{11} + 820 x^{10} + 2720 x^{9} + 6776 x^{8} + 25024 x^{7} + 26992 x^{6} + 10880 x^{5} - 106848 x^{4} - 260736 x^{3} + 163520 x^{2} - 376832 x + 67712$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.34 |
$14$ |
$x^{14} + 14 x^{13} + 98 x^{12} + 680 x^{11} + 4124 x^{10} + 16872 x^{9} + 59992 x^{8} + 168192 x^{7} + 397680 x^{6} + 807456 x^{5} + 1341920 x^{4} + 1886592 x^{3} + 2248768 x^{2} + 1722752 x + 1571456$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.36 |
$14$ |
$x^{14} + 14 x^{13} + 178 x^{12} + 1408 x^{11} + 9124 x^{10} + 39752 x^{9} + 139912 x^{8} + 354816 x^{7} + 759216 x^{6} + 1347488 x^{5} + 2155616 x^{4} + 3190784 x^{3} + 3149504 x^{2} + 1996160 x + 1327488$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 4 t^{6} + 4 t^{4} + 4 t^{3} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.37 |
$14$ |
$x^{14} + 78 x^{12} + 80 x^{11} + 532 x^{10} + 192 x^{9} - 1160 x^{8} + 640 x^{7} + 496 x^{6} - 13824 x^{5} - 11744 x^{4} + 30464 x^{3} + 65216 x^{2} + 35840 x + 119936$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
