Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.12.16.27 |
$12$ |
$x^{12} + 24 x^{11} + 198 x^{10} + 624 x^{9} + 837 x^{8} + 1512 x^{7} + 12690 x^{6} + 13608 x^{5} + 49410 x^{4} - 22248 x^{3} - 219024 x^{2} + 185733$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^3:C_4$ (as 12T72) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{2} + 3\right) x^{2} + 9 t^{3} + 18 t^{2} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
3.12.16.46 |
$12$ |
$x^{12} - 24 x^{11} + 216 x^{10} + 804 x^{9} + 1944 x^{8} + 11664 x^{7} + 33912 x^{6} + 37584 x^{5} + 295488 x^{4} + 32184 x^{3} + 981072 x^{2} + 1122984$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^3:C_4$ (as 12T72) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6\right) x^{2} + 9 t^{3} + 18 t + 12$ |
$[2, 0]$ |
$[1]$ |
3.12.18.43 |
$12$ |
$x^{12} - 6 x^{11} + 12 x^{10} + 48 x^{9} + 81 x^{8} + 54 x^{7} + 48 x^{6} - 72 x^{5} - 54 x^{4} - 72 x^{3} + 234$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^3:C_4$ (as 12T72) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{5} + \left(6 t + 3\right) x^{4} + 3 t x^{3} + 3 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
3.12.18.70 |
$12$ |
$x^{12} - 6 x^{10} + 6 x^{9} + 45 x^{8} + 18 x^{7} + 12 x^{6} + 270 x^{4} + 108 x^{3} + 450$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^3:C_4$ (as 12T72) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{4} + \left(3 t + 6\right) x^{3} + 21 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |