| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.15.1 |
$12$ |
$x^{12} + 3 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{4} + 3$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.10 |
$12$ |
$x^{12} + 3 x^{4} + 3 x^{3} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[3/2]$ |
$[5/4, 5/4, 3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{4} + 3 x^{3} + 6$ |
$[4, 0]$ |
$[2, 2]$ |
| 3.12.15.11 |
$12$ |
$x^{12} + 3 x^{6} + 6 x^{4} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 6 x^{4} + 6$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.12 |
$12$ |
$x^{12} + 6 x^{6} + 6 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 6 x^{4} + 3$ |
$[4, 0]$ |
$[2, 2]$ |
| 3.12.15.13 |
$12$ |
$x^{12} + 6 x^{4} + 3 x^{3} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[3/2]$ |
$[5/4, 5/4, 3/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{4} + 3 x^{3} + 6$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.14 |
$12$ |
$x^{12} + 3 x^{5} + 3 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[3/2]$ |
$[5/4, 5/4, 3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{5} + 3 x^{4} + 3$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.15 |
$12$ |
$x^{12} + 6 x^{4} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{4} + 6$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.16 |
$12$ |
$x^{12} + 3 x^{6} + 3 x^{5} + 3 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[3/2]$ |
$[5/4, 5/4, 3/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 3 x^{5} + 3 x^{4} + 3$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.2 |
$12$ |
$x^{12} + 3 x^{6} + 3 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 3 x^{4} + 3$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.3 |
$12$ |
$x^{12} + 6 x^{6} + 6 x^{4} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 6 x^{4} + 6$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.4 |
$12$ |
$x^{12} + 6 x^{5} + 6 x^{4} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[3/2]$ |
$[5/4, 5/4, 3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{5} + 6 x^{4} + 6$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.5 |
$12$ |
$x^{12} + 6 x^{6} + 3 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 3 x^{4} + 3$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.6 |
$12$ |
$x^{12} + 6 x^{6} + 3 x^{5} + 3 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[3/2]$ |
$[5/4, 5/4, 3/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 3 x^{5} + 3 x^{4} + 3$ |
$[4, 0]$ |
$[1, 2]$ |
| 3.12.15.7 |
$12$ |
$x^{12} + 6 x^{6} + 3 x^{4} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 3 x^{4} + 6$ |
$[4, 0]$ |
$[2, 2]$ |
| 3.12.15.8 |
$12$ |
$x^{12} + 3 x^{5} + 6 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[3/2]$ |
$[5/4, 5/4, 3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{5} + 6 x^{4} + 3$ |
$[4, 0]$ |
$[2, 2]$ |
| 3.12.15.9 |
$12$ |
$x^{12} + 3 x^{6} + 3 x^{5} + 6 x^{4} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[3/2]$ |
$[5/4, 5/4, 3/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 3 x^{5} + 6 x^{4} + 6$ |
$[4, 0]$ |
$[1, 2]$ |
