| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.16.1 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} + 4 x^{9} - 4 x^{7} + 10 x^{6} + 8 x^{5} + 4 x^{4} + 12 x^{3} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.10 |
$12$ |
$x^{12} - 2 x^{11} + 8 x^{10} - 2 x^{9} + 8 x^{8} + 4 x^{7} + 2 x^{6} + 8 x^{5} - 4 x^{4} + 4 x^{3} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:C_2^2$ (as 12T158) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{4} + \left(2 t + 2\right) x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.11 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{9} + 8 x^{8} + 8 x^{7} + 6 x^{6} + 8 x^{5} + 4 x^{4} + 20 x^{3} + 4 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$3$ |
$[2]$ |
$[2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(2 t + 2\right) x^{3} + 2 x^{2} + 6 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.12 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} + 2 x^{9} + 8 x^{8} - 4 x^{7} + 10 x^{6} + 4 x^{5} + 4 x^{4} + 12 x^{3} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 2\right) x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.13 |
$12$ |
$x^{12} + 10 x^{11} + 47 x^{10} + 144 x^{9} + 330 x^{8} + 578 x^{7} + 785 x^{6} + 830 x^{5} + 530 x^{4} - 64 x^{3} - 189 x^{2} - 30 x + 25$ |
$2$ |
$6$ |
$2$ |
$16$ |
$D_6$ (as 12T3) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2} + 6$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.14 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} - 2 x^{9} + 12 x^{8} - 4 x^{7} + 10 x^{6} - 4 x^{5} + 4 x^{4} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 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) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{4} + 2 t x^{3} + 2 x^{2} + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.16 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{9} + 16 x^{8} + 16 x^{7} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.17 |
$12$ |
$x^{12} - 2 x^{10} - 2 x^{9} + 8 x^{8} + 8 x^{7} - 2 x^{6} - 4 x^{5} + 12 x^{4} + 8 x^{3} - 4 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{4} + 2 t x^{3} + 2 x^{2} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.18 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.19 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 14 x^{8} + 8 x^{6} + 4 x^{5} + 16 x^{4} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t x^{4} + 2 x^{3} + \left(2 t + 2\right) x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.2 |
$12$ |
$x^{12} - 2 x^{11} + 6 x^{10} + 2 x^{9} + 16 x^{8} + 16 x^{6} + 24 x^{4} + 4 x^{3} + 16 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 2\right) x^{4} + 2 t x^{3} + 2 x^{2} + 4 t + 6$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.20 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 12 x^{8} + 8 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} - 4 x^{3} - 4 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.21 |
$12$ |
$x^{12} + 2 x^{5} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[14/9, 14/9]$ |
$[14/9, 14/9, 14/9, 14/9, 14/9, 14/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{5} + 2$ |
$[5, 5, 0]$ |
$[1, 2]$ |
| 2.12.16.22 |
$12$ |
$x^{12} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_2^3.S_4$ (as 12T98) |
$4$ |
$3$ |
$[4/3, 5/3]$ |
$[4/3, 4/3, 5/3, 5/3]_{3}^{4}$ |
$t + 1$ |
$x^{12} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.16.23 |
$12$ |
$x^{12} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_4^2:S_3$ (as 12T65) |
$2$ |
$3$ |
$[4/3, 5/3]$ |
$[4/3, 4/3, 5/3, 5/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.16.24 |
$12$ |
$x^{12} + 2 x^{6} + 2 x^{5} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[14/9, 14/9]$ |
$[14/9, 14/9, 14/9, 14/9, 14/9, 14/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{6} + 2 x^{5} + 2$ |
$[5, 5, 0]$ |
$[1, 2]$ |
| 2.12.16.25 |
$12$ |
$x^{12} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_2^3.S_4$ (as 12T98) |
$4$ |
$3$ |
$[4/3, 5/3]$ |
$[4/3, 4/3, 5/3, 5/3]_{3}^{4}$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.16.26 |
$12$ |
$x^{12} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_4^2:S_3$ (as 12T63) |
$2$ |
$3$ |
$[4/3, 5/3]$ |
$[4/3, 4/3, 5/3, 5/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.16.27 |
$12$ |
$x^{12} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_4^2:S_3$ (as 12T64) |
$2$ |
$3$ |
$[4/3, 5/3]$ |
$[4/3, 4/3, 5/3, 5/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.16.28 |
$12$ |
$x^{12} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_4^2:S_3$ (as 12T62) |
$2$ |
$3$ |
$[4/3, 5/3]$ |
$[4/3, 4/3, 5/3, 5/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.16.3 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 10 x^{9} + 8 x^{8} + 4 x^{7} + 2 x^{6} - 4 x^{5} - 4 x^{4} + 4 x^{3} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$3$ |
$[2]$ |
$[2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + \left(2 t + 2\right) x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.4 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 14 x^{6} + 8 x^{5} + 8 x^{4} + 4 x^{3} + 4 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 6 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 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) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 2 t x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.6 |
$12$ |
$x^{12} - 2 x^{9} - 2 x^{6} + 24 x^{3} + 36$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{3} + 6 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.7 |
$12$ |
$x^{12} + 2 x^{11} + 6 x^{10} + 12 x^{9} + 8 x^{8} + 4 x^{7} + 6 x^{6} + 20 x^{5} + 20 x^{4} + 4 x^{3} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t + 2\right) x^{4} + 2 x^{3} + 6 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.8 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{10} - 2 x^{9} + 6 x^{8} + 8 x^{7} + 6 x^{6} + 24 x^{5} + 4 x^{4} + 16 x^{3} + 20 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 2 t x^{3} + \left(2 t + 2\right) x^{2} + 6 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.9 |
$12$ |
$x^{12} - 2 x^{9} + 16 x^{6} - 12 x^{3} + 36$ |
$2$ |
$6$ |
$2$ |
$16$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{3} + 6$ |
$[3, 0]$ |
$[1, 1]$ |
