Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.12.18.83 |
$12$ |
$x^{12} - 6 x^{11} + 51 x^{10} - 30 x^{9} + 117 x^{8} - 36 x^{7} + 60 x^{6} + 252 x^{5} - 36 x^{4} + 288 x^{3} + 360$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3:S_3^2$ (as 12T71) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + 3 x^{4} + 6 t x^{3} + 18 t + 12$ |
$[4, 0]$ |
$[1, 1]$ |
3.12.22.17 |
$12$ |
$x^{12} - 12 x^{9} + 18 x^{7} + 366 x^{6} + 324 x^{5} + 297 x^{4} + 774 x^{3} + 486 x^{2} + 378 x + 333$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3:S_3^2$ (as 12T71) |
$2$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 12\right) x^{3} + \left(9 t + 9\right) x^{2} + \left(9 t + 18\right) x + 18 t + 21$ |
$[6, 0]$ |
$[1, 1]$ |
3.12.22.20 |
$12$ |
$x^{12} + 36 x^{9} - 18 x^{8} + 366 x^{6} - 108 x^{5} + 621 x^{4} + 864 x^{3} + 594 x^{2} + 324 x + 90$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3:S_3^2$ (as 12T71) |
$2$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 24\right) x^{3} + \left(18 t + 9\right) x^{2} + \left(18 t + 18\right) x + 9 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
3.12.22.75 |
$12$ |
$x^{12} - 48 x^{9} + 18 x^{7} + 1122 x^{6} + 864 x^{5} - 108 x^{4} + 1584 x^{3} + 729 x^{2} - 270 x + 549$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3:S_3^2$ (as 12T71) |
$2$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 24 t x^{3} + \left(18 t + 18\right) x^{2} + 9 x + 18 t + 3$ |
$[6, 0]$ |
$[1, 1]$ |