Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.12.18.12 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} - 18 x^{9} + 18 x^{8} + 18 x^{7} - 3 x^{6} - 36 x^{5} + 90 x^{4} + 54 x^{3} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 3 t x^{4} + \left(3 t + 3\right) x^{3} + 9 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |
3.12.18.16 |
$12$ |
$x^{12} + 6 x^{11} + 12 x^{10} + 18 x^{8} + 42 x^{6} + 126 x^{5} - 126 x^{4} + 441$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{5} + 3 t x^{4} + 21$ |
$[4, 0]$ |
$[2, 1]$ |
3.12.18.18 |
$12$ |
$x^{12} + 6 x^{11} + 24 x^{10} + 36 x^{9} + 18 x^{8} + 6 x^{6} + 72 x^{5} + 72 x^{4} + 90$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{5} + \left(3 t + 6\right) x^{4} + 9 t + 12$ |
$[4, 0]$ |
$[2, 1]$ |
3.12.18.24 |
$12$ |
$x^{12} + 6 x^{10} - 6 x^{9} + 18 x^{8} + 18 x^{7} + 69 x^{6} + 126 x^{4} + 36 x^{3} + 225$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{4} + \left(6 t + 3\right) x^{3} + 9 t + 21$ |
$[4, 0]$ |
$[2, 1]$ |
3.12.18.25 |
$12$ |
$x^{12} + 12 x^{11} + 30 x^{10} - 36 x^{9} + 45 x^{8} - 12 x^{6} - 72 x^{5} + 144 x^{4} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(6 t + 3\right) x^{4} + 9 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |
3.12.18.3 |
$12$ |
$x^{12} - 6 x^{11} + 39 x^{10} + 90 x^{9} + 45 x^{8} - 12 x^{6} + 144 x^{5} + 144 x^{4} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + \left(6 t + 3\right) x^{4} + 9 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |
3.12.18.34 |
$12$ |
$x^{12} + 6 x^{10} + 18 x^{8} + 36 x^{7} + 6 x^{6} + 18 x^{4} + 216 x^{3} + 549$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{4} + \left(6 t + 6\right) x^{3} + 18 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |
3.12.18.50 |
$12$ |
$x^{12} + 12 x^{11} + 24 x^{10} - 60 x^{9} + 144 x^{8} - 72 x^{7} + 6 x^{6} - 180 x^{5} + 396 x^{4} - 180 x^{3} + 549$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 6 t x^{4} + 6 x^{3} + 18 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |