| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.15.12 |
$12$ |
$x^{12} + 6 x^{6} + 6 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$15$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 6 x^{4} + 3$ |
$[4, 0]$ |
$[2, 2]$ |
| 3.12.15.7 |
$12$ |
$x^{12} + 6 x^{6} + 3 x^{4} + 6$ |
$3$ |
$12$ |
$1$ |
$15$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[3/2]$ |
$[3/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 3 x^{4} + 6$ |
$[4, 0]$ |
$[2, 2]$ |
| 3.12.23.122 |
$12$ |
$x^{12} + 6 x^{9} + 6 x^{6} + 24 x^{3} + 9 x^{2} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[5/2]$ |
$[5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 6 x^{6} + 24 x^{3} + 9 x^{2} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.14 |
$12$ |
$x^{12} + 3 x^{9} + 15 x^{6} + 9 x^{5} + 9 x^{4} + 18 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[5/2]$ |
$[5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 15 x^{6} + 9 x^{5} + 9 x^{4} + 18 x^{2} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.20 |
$12$ |
$x^{12} + 21 x^{6} + 9 x^{4} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[5/2]$ |
$[5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 21 x^{6} + 9 x^{4} + 9 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
