Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.12.14.1 |
$12$ |
$x^{12} - 6 x^{8} - 6 x^{6} + 18 x^{4} + 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
3.12.14.14 |
$12$ |
$x^{12} - 6 x^{8} - 6 x^{6} + 45 x^{4} + 54 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
3.12.16.22 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 192 x^{9} + 324 x^{8} + 432 x^{7} + 2808 x^{6} - 3240 x^{5} + 12312 x^{4} - 12528 x^{3} + 121824 x^{2} + 517428$ |
$3$ |
$3$ |
$4$ |
$16$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6\right) x^{2} + 9 t^{3} + 9 t^{2} + 18 t + 12$ |
$[2, 0]$ |
$[1]$ |
3.12.16.37 |
$12$ |
$x^{12} - 6 x^{11} + 60 x^{10} - 10 x^{9} + 603 x^{8} + 3924 x^{7} + 16740 x^{6} + 36078 x^{5} + 108120 x^{4} + 201600 x^{3} + 381102 x^{2} + 225588 x + 200729$ |
$3$ |
$3$ |
$4$ |
$16$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3\right) x^{2} + 18 t^{3} + 18 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |