| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.24.146 |
$12$ |
$x^{12} + 12 x^{11} + 52 x^{10} + 64 x^{9} + 162 x^{8} + 376 x^{7} + 712 x^{6} + 496 x^{5} + 996 x^{4} + 832 x^{3} + 1520 x^{2} + 800 x + 584$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t^{2} + 4 t\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 8 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.155 |
$12$ |
$x^{12} - 4 x^{10} + 30 x^{8} + 40 x^{7} + 40 x^{6} + 16 x^{5} + 68 x^{4} - 80 x^{3} + 144 x^{2} + 224 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t x + 4 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.192 |
$12$ |
$x^{12} + 8 x^{10} + 24 x^{9} - 90 x^{8} - 296 x^{7} - 152 x^{6} + 864 x^{5} + 2452 x^{4} + 2992 x^{3} + 2336 x^{2} + 96 x + 1016$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 6 t\right) x^{2} + 4 t^{2} x + 8 t^{2} + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.204 |
$12$ |
$x^{12} + 12 x^{11} + 40 x^{10} - 8 x^{9} - 26 x^{8} + 808 x^{7} + 824 x^{6} - 192 x^{5} + 980 x^{4} + 3872 x^{3} + 64 x^{2} - 224 x + 3128$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 6 t\right) x^{2} + 4 t^{2} x + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.239 |
$12$ |
$x^{12} + 22 x^{10} - 4 x^{9} - 158 x^{8} - 160 x^{7} - 168 x^{6} + 80 x^{5} + 1292 x^{4} + 3104 x^{3} + 4136 x^{2} + 3216 x + 5048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T60) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t + 2\right) x^{2} + \left(4 t + 4\right) x + 12 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.283 |
$12$ |
$x^{12} + 10 x^{10} + 28 x^{9} + 74 x^{8} + 80 x^{7} + 616 x^{6} + 1760 x^{5} + 3820 x^{4} + 4672 x^{3} + 4760 x^{2} + 3184 x + 1784$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T60) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 2 t + 2\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{2} + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.30.158 |
$12$ |
$x^{12} + 4 x^{11} + 92 x^{10} + 368 x^{9} + 1458 x^{8} + 2464 x^{7} + 5216 x^{6} + 6592 x^{5} + 10204 x^{4} + 8304 x^{3} + 11280 x^{2} + 4160 x + 5048$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 4 t + 12\right) x^{2} + 8 t^{2} x + 12 t^{2} + 8 t + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.221 |
$12$ |
$x^{12} + 4 x^{11} + 40 x^{10} + 400 x^{9} + 1418 x^{8} + 1744 x^{7} + 1184 x^{6} + 5472 x^{5} + 9068 x^{4} + 2000 x^{3} + 2464 x^{2} + 1016$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 8 t\right) x^{2} + 8 t^{2} + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.24 |
$12$ |
$x^{12} + 4 x^{11} + 80 x^{10} + 440 x^{9} + 1394 x^{8} + 3184 x^{7} + 5760 x^{6} + 8128 x^{5} + 9484 x^{4} + 8080 x^{3} + 4928 x^{2} + 2208 x + 536$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 8 t + 8\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{2} + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.269 |
$12$ |
$x^{12} + 4 x^{11} + 56 x^{10} + 352 x^{9} + 754 x^{8} + 1008 x^{7} + 928 x^{6} + 928 x^{5} + 2060 x^{4} + 3472 x^{3} + 3936 x^{2} + 2368 x + 536$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 8 t\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{2} + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.282 |
$12$ |
$x^{12} + 4 x^{11} + 76 x^{10} + 600 x^{9} + 2522 x^{8} + 6752 x^{7} + 11328 x^{6} + 14784 x^{5} + 17276 x^{4} + 10608 x^{3} + 10768 x^{2} + 2336 x + 2392$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 12 t + 12\right) x^{2} + \left(8 t + 8\right) x + 12 t^{2} + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.32 |
$12$ |
$x^{12} + 4 x^{11} + 92 x^{10} + 392 x^{9} + 1522 x^{8} + 3424 x^{7} + 6688 x^{6} + 9952 x^{5} + 12764 x^{4} + 13168 x^{3} + 11920 x^{2} + 7456 x + 5048$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 4 t + 12\right) x^{2} + \left(8 t^{2} + 8\right) x + 12 t^{2} + 8 t + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.36 |
$12$ |
$x^{12} + 4 x^{11} + 68 x^{10} + 480 x^{9} + 986 x^{8} + 416 x^{7} + 832 x^{6} + 3648 x^{5} + 2844 x^{4} + 2160 x^{3} + 2736 x^{2} + 1944$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 12 t + 4\right) x^{2} + 12 t^{2} + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.82 |
$12$ |
$x^{12} + 4 x^{11} + 64 x^{10} + 488 x^{9} + 1802 x^{8} + 4176 x^{7} + 6912 x^{6} + 9728 x^{5} + 9580 x^{4} + 3536 x^{3} + 5760 x^{2} + 1632 x + 1016$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_4^2:C_6$ (as 12T60) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 8 t + 8\right) x^{2} + 8 x + 8 t^{2} + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
