| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.16.33 |
$12$ |
$x^{12} + 6 x^{11} + 72 x^{10} + 308 x^{9} + 1476 x^{8} + 4692 x^{7} + 6054 x^{6} + 5154 x^{5} + 14988 x^{4} + 27588 x^{3} + 20238 x^{2} + 2280 x + 1145$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.35 |
$12$ |
$x^{12} + 18 x^{10} - 60 x^{9} + 405 x^{8} - 540 x^{7} + 3942 x^{6} - 7776 x^{5} + 59454 x^{4} + 13716 x^{3} + 568620 x^{2} + 2365929$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3\right) x^{2} + 18 t^{3} + 9 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.38 |
$12$ |
$x^{12} + 12 x^{11} + 54 x^{10} + 174 x^{9} + 675 x^{8} + 1782 x^{7} + 3618 x^{6} + 11016 x^{5} + 16524 x^{4} + 32670 x^{3} + 98010 x^{2} + 463725$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$1$ |
$[2]$ |
$[2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 x^{2} + 18 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.39 |
$12$ |
$x^{12} + 18 x^{10} + 12 x^{9} + 189 x^{8} + 108 x^{7} + 1350 x^{6} - 1296 x^{5} + 3078 x^{4} - 3780 x^{3} - 4860 x^{2} + 11745$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3\right) x^{2} + 9 t^{2} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.18.1 |
$12$ |
$x^{12} + 30 x^{10} + 42 x^{9} + 18 x^{8} - 18 x^{7} + 39 x^{6} + 36 x^{5} - 72 x^{4} + 90 x^{3} + 234$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{5} + 3 t x^{4} + 3 x^{3} + 3 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.46 |
$12$ |
$x^{12} + 12 x^{11} + 30 x^{10} - 36 x^{9} + 18 x^{8} + 18 x^{7} + 3 x^{6} - 36 x^{5} + 90 x^{4} + 72 x^{3} + 153$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 3 t x^{4} + \left(3 t + 3\right) x^{3} + 12 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.71 |
$12$ |
$x^{12} - 12 x^{11} + 66 x^{10} + 60 x^{9} + 162 x^{8} + 72 x^{7} + 30 x^{6} + 504 x^{5} + 252 x^{4} + 504 x^{3} + 882$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{5} + 3 t x^{4} + 6 t x^{3} + 21 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.72 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} - 12 x^{9} + 63 x^{8} - 18 x^{7} + 39 x^{6} + 90 x^{5} - 54 x^{4} + 90 x^{3} + 234$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$2$ |
$[2]$ |
$[2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + \left(6 t + 3\right) x^{4} + 3 x^{3} + 3 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
