| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.31 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 6 x^{8} + 12 x^{7} + 32 x^{6} + 48 x^{5} + 76 x^{4} + 48 x^{3} + 40 x^{2} + 8 x + 8$ |
$2$ |
$4$ |
$3$ |
$12$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3, 4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{2} + \left(2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
| 2.12.24.1 |
$12$ |
$x^{12} + 12 x^{10} + 62 x^{8} + 32 x^{7} + 144 x^{6} + 16 x^{5} + 60 x^{4} - 64 x^{3} - 16 x^{2} - 96 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{2} + 4 t x + 4 t^{2} + 4 t + 2$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.10 |
$12$ |
$x^{12} + 12 x^{11} + 64 x^{10} + 76 x^{9} + 146 x^{8} + 336 x^{7} + 448 x^{6} + 336 x^{5} + 876 x^{4} + 496 x^{3} + 384 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 4\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.113 |
$12$ |
$x^{12} - 8 x^{11} + 84 x^{10} - 36 x^{9} + 418 x^{8} + 368 x^{7} + 912 x^{6} + 368 x^{5} + 524 x^{4} + 256 x^{3} + 528 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4\right) x^{2} + \left(4 t + 4\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.119 |
$12$ |
$x^{12} - 8 x^{11} + 84 x^{10} - 48 x^{9} + 462 x^{8} + 160 x^{7} + 480 x^{6} + 592 x^{5} + 284 x^{4} + 352 x^{3} + 240 x^{2} + 32 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4\right) x^{2} + 4 t x + 4 t^{2} + 2$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.131 |
$12$ |
$x^{12} + 8 x^{10} - 4 x^{9} + 66 x^{8} - 208 x^{7} + 320 x^{6} + 368 x^{5} + 460 x^{4} - 32 x^{3} + 96 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 t^{2} x^{2} + \left(4 t + 4\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.148 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 116 x^{9} + 394 x^{8} + 816 x^{7} + 1296 x^{6} + 1888 x^{5} + 1756 x^{4} + 1808 x^{3} + 1168 x^{2} + 624 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(4 t^{2} + 4 t + 4\right) x^{2} + \left(4 t^{2} + 4\right) x + 4 t^{2} + 4 t + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.194 |
$12$ |
$x^{12} + 28 x^{10} - 20 x^{9} - 66 x^{8} + 176 x^{7} + 144 x^{6} + 240 x^{5} + 700 x^{4} + 224 x^{3} + 112 x^{2} + 240 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 4/3, 4/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 4\right) x^{2} + 4 x + 4 t^{2} + 4 t + 2$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.20 |
$12$ |
$x^{12} + 20 x^{10} - 4 x^{9} + 106 x^{8} + 160 x^{7} + 416 x^{6} + 704 x^{5} + 860 x^{4} + 1024 x^{3} + 1008 x^{2} + 592 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 4\right) x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 4 t + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.226 |
$12$ |
$x^{12} - 8 x^{11} + 80 x^{10} - 60 x^{9} + 106 x^{8} + 192 x^{7} + 352 x^{6} + 464 x^{5} + 924 x^{4} + 672 x^{3} + 704 x^{2} + 848 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4 t + 4\right) x + 4 t^{2} + 4 t + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.248 |
$12$ |
$x^{12} - 8 x^{11} + 72 x^{10} + 8 x^{9} + 178 x^{8} + 128 x^{7} + 720 x^{6} + 704 x^{5} + 876 x^{4} - 32 x^{3} - 192 x^{2} - 288 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + 4 t^{2} x^{2} + 4 t^{2} x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.31 |
$12$ |
$x^{12} + 4 x^{11} + 56 x^{10} + 212 x^{9} + 338 x^{8} + 720 x^{7} + 800 x^{6} + 720 x^{5} + 684 x^{4} + 16 x^{3} - 288 x^{2} + 144 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 4 t^{2} x^{2} + \left(4 t^{2} + 4\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.50 |
$12$ |
$x^{12} - 8 x^{11} + 8 x^{10} + 108 x^{9} + 142 x^{8} + 240 x^{7} + 448 x^{6} + 240 x^{5} + 284 x^{4} + 448 x^{3} + 160 x^{2} + 240 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 4/3, 4/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + 4 t^{2} x^{2} + 4 x + 4 t^{2} + 4 t + 2$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.57 |
$12$ |
$x^{12} + 12 x^{11} + 60 x^{10} + 152 x^{9} + 194 x^{8} + 144 x^{7} + 320 x^{6} + 672 x^{5} + 332 x^{4} - 16 x^{3} + 912 x^{2} - 288 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 4 x^{2} + \left(4 t^{2} + 4 t\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.58 |
$12$ |
$x^{12} - 8 x^{11} + 20 x^{10} + 84 x^{9} + 270 x^{8} + 576 x^{7} + 1024 x^{6} + 1280 x^{5} + 1372 x^{4} + 1184 x^{3} + 624 x^{2} + 240 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(4 t^{2} + 4 t + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 4 t^{2} + 2$ |
$[5, 4, 0]$ |
$[1]$ |
