Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.12.18.32 |
$12$ |
$x^{12} + 6 x^{11} + 8 x^{10} - 8 x^{9} + 10 x^{8} + 64 x^{7} + 40 x^{6} + 48 x^{5} + 4 x^{4} + 56 x^{3} - 32 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[3]$ |
2.12.18.35 |
$12$ |
$x^{12} + 6 x^{11} + 12 x^{10} + 12 x^{9} + 26 x^{8} + 48 x^{7} + 32 x^{6} - 8 x^{5} + 4 x^{4} - 8 x^{3} - 32 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t + 2\right) x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[3]$ |
2.12.18.37 |
$12$ |
$x^{12} + 12 x^{9} + 2 x^{8} - 32 x^{7} - 16 x^{6} + 40 x^{5} + 52 x^{4} - 16 x^{2} + 8$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 2$ |
$[3, 2, 0]$ |
$[3]$ |
2.12.18.38 |
$12$ |
$x^{12} - 4 x^{11} + 10 x^{10} - 8 x^{9} + 26 x^{8} - 8 x^{7} + 24 x^{6} + 16 x^{5} + 52 x^{4} + 32 x^{3} + 56 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[3]$ |
2.12.18.44 |
$12$ |
$x^{12} - 4 x^{11} + 22 x^{10} - 4 x^{9} + 54 x^{8} + 64 x^{7} + 16 x^{6} + 56 x^{5} + 60 x^{4} - 32 x^{3} + 88 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{3} + \left(2 t^{2} + 2\right) x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[3]$ |
2.12.18.46 |
$12$ |
$x^{12} + 2 x^{11} + 22 x^{10} + 52 x^{9} + 74 x^{8} + 56 x^{7} + 176 x^{6} + 168 x^{5} + 204 x^{4} + 72 x^{3} + 216 x^{2} + 216$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + \left(2 t + 2\right) x^{2} + 6$ |
$[3, 2, 0]$ |
$[3]$ |
2.12.18.53 |
$12$ |
$x^{12} + 2 x^{11} + 18 x^{10} + 56 x^{9} + 86 x^{8} + 88 x^{7} + 136 x^{6} + 192 x^{5} + 92 x^{4} + 120 x^{3} + 120 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + \left(2 t^{2} + 2 t + 2\right) x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[3]$ |