Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.12.16.15 |
$12$ |
$x^{12} + 2 x^{10} - 2 x^{9} + 8 x^{8} + 4 x^{7} + 12 x^{6} - 4 x^{5} + 8 x^{4} - 4 x^{3} + 8 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{4} + 2 t x^{3} + 2 x^{2} + 2$ |
$[3, 0]$ |
$[1, 1]$ |
2.12.16.5 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{10} - 2 x^{9} + 8 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 12 x^{3} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 2 t x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
2.12.20.27 |
$12$ |
$x^{12} - 2 x^{11} - 2 x^{10} + 28 x^{9} + 56 x^{8} + 12 x^{7} - 12 x^{6} + 28 x^{5} + 48 x^{4} + 40 x^{3} + 48 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 t x^{4} + \left(4 t + 4\right) x^{3} + 6 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
2.12.20.29 |
$12$ |
$x^{12} - 2 x^{11} + 10 x^{10} + 8 x^{9} + 4 x^{8} + 36 x^{7} + 36 x^{6} + 4 x^{5} + 48 x^{4} + 32 x^{3} + 24 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 4\right) x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
2.12.20.3 |
$12$ |
$x^{12} - 2 x^{11} + 2 x^{10} + 16 x^{9} - 4 x^{8} + 4 x^{7} + 36 x^{6} + 4 x^{5} + 16 x^{4} + 32 x^{3} + 24 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
2.12.20.41 |
$12$ |
$x^{12} - 2 x^{11} + 2 x^{10} + 12 x^{9} + 24 x^{8} - 4 x^{7} + 12 x^{6} + 28 x^{5} + 40 x^{4} + 40 x^{3} + 48 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{3} + 6 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
2.12.22.38 |
$12$ |
$x^{12} + 8 x^{11} + 28 x^{10} + 44 x^{9} + 18 x^{8} - 32 x^{7} + 16 x^{6} + 64 x^{5} + 76 x^{4} - 24 x^{3} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$22$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 6 x^{4} + 4 t x^{3} + 2 t x^{2} + 6$ |
$[6, 0]$ |
$[1, 1]$ |
2.12.22.40 |
$12$ |
$x^{12} + 4 x^{10} - 4 x^{9} + 6 x^{8} - 8 x^{7} + 40 x^{6} + 32 x^{5} + 68 x^{4} + 8 x^{3} + 92 x^{2} + 148$ |
$2$ |
$6$ |
$2$ |
$22$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 4 t x^{3} + \left(6 t + 4\right) x^{2} + 8 t + 14$ |
$[6, 0]$ |
$[1, 1]$ |
2.12.22.45 |
$12$ |
$x^{12} + 8 x^{11} + 28 x^{10} + 44 x^{9} + 18 x^{8} - 32 x^{7} + 8 x^{6} + 32 x^{5} + 28 x^{4} + 40 x^{3} + 20 x^{2} + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 6 x^{4} + 4 t x^{3} + 2 t x^{2} + 8 t + 6$ |
$[6, 0]$ |
$[1, 1]$ |
2.12.22.6 |
$12$ |
$x^{12} + 12 x^{10} - 4 x^{9} + 40 x^{8} - 16 x^{7} + 52 x^{6} + 40 x^{5} + 60 x^{4} + 40 x^{3} + 40 x^{2} + 48 x + 84$ |
$2$ |
$6$ |
$2$ |
$22$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 6 x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 8 t + 10$ |
$[6, 0]$ |
$[1, 1]$ |
2.12.22.70 |
$12$ |
$x^{12} + 12 x^{10} - 4 x^{9} + 40 x^{8} - 16 x^{7} + 44 x^{6} + 40 x^{5} + 12 x^{4} + 8 x^{3} + 24 x^{2} + 16 x + 4$ |
$2$ |
$6$ |
$2$ |
$22$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 6 x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 2$ |
$[6, 0]$ |
$[1, 1]$ |
2.12.22.73 |
$12$ |
$x^{12} - 4 x^{9} + 12 x^{8} + 24 x^{7} + 60 x^{6} + 24 x^{5} + 60 x^{4} + 8 x^{3} + 48 x^{2} + 148$ |
$2$ |
$6$ |
$2$ |
$22$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 2\right) x^{4} + 4 t x^{3} + \left(4 t + 2\right) x^{2} + 8 t + 14$ |
$[6, 0]$ |
$[1, 1]$ |