Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.12.6.2 |
$12$ |
$x^{12} + 22 x^{10} + 177 x^{8} + 4 x^{7} + 644 x^{6} - 100 x^{5} + 876 x^{4} - 224 x^{3} + 1076 x^{2} + 344 x + 112$ |
$3$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
3.12.18.51 |
$12$ |
$x^{12} + 48 x^{10} + 108 x^{8} + 24 x^{6} + 108 x^{5} - 72 x^{4} + 108 x^{3} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{5} + 6 x^{4} + \left(6 t + 6\right) x^{3} + 9 t + 3$ |
$[4, 0]$ |
$[1, 1]$ |
3.12.18.75 |
$12$ |
$x^{12} + 12 x^{10} + 36 x^{8} - 30 x^{6} - 180 x^{4} + 549$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{4} + 18 t + 3$ |
$[4, 0]$ |
$[1, 1]$ |
3.12.18.82 |
$12$ |
$x^{12} + 24 x^{11} + 252 x^{10} + 1558 x^{9} + 6450 x^{8} + 19068 x^{7} + 41627 x^{6} + 68094 x^{5} + 83298 x^{4} + 74306 x^{3} + 45618 x^{2} + 17400 x + 3277$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 6 x^{4} + 3 x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |