| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.35.30 |
$12$ |
$x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 4 x^{8} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[4/3, 4/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 4 x^{8} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.417 |
$12$ |
$x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{7} + 8 x^{4} + 8 x^{3} + 10$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[8/3, 8/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{10} + 8 x^{8} + 8 x^{7} + 8 x^{4} + 8 x^{3} + 10$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.606 |
$12$ |
$x^{12} + 8 x^{11} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[8/3, 8/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.666 |
$12$ |
$x^{12} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[8/3, 8/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.699 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 18$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[4/3, 4/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 18$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.700 |
$12$ |
$x^{12} + 8 x^{11} + 8 x^{3} + 10$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[4/3, 4/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 8 x^{3} + 10$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.768 |
$12$ |
$x^{12} + 8 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 18$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[8/3, 8/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 18$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.780 |
$12$ |
$x^{12} + 8 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{4} + 8 x^{3} + 26$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[8/3, 8/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{4} + 8 x^{3} + 26$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.827 |
$12$ |
$x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{3} + 26$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[4/3, 4/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{3} + 26$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.833 |
$12$ |
$x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{8} + 8 x^{7} + 8 x^{4} + 8 x^{3} + 10$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[8/3, 8/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{8} + 8 x^{7} + 8 x^{4} + 8 x^{3} + 10$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.843 |
$12$ |
$x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 18$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[8/3, 8/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 18$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.942 |
$12$ |
$x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{4} + 8 x^{3} + 26$ |
$2$ |
$12$ |
$1$ |
$35$ |
$C_4:S_4$ (as 12T54) |
$2$ |
$3$ |
$[3, 4]$ |
$[8/3, 8/3, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{4} + 8 x^{3} + 26$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
