| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.12 |
$12$ |
$x^{12} + 84 x^{10} - 88 x^{9} + 1660 x^{8} - 1568 x^{7} + 13920 x^{6} - 4928 x^{5} + 47280 x^{4} + 23936 x^{3} + 63552 x^{2} + 32896 x + 51520$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_4\times A_4$ (as 12T29) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t\right) x + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.17 |
$12$ |
$x^{12} + 12 x^{10} + 32 x^{9} + 84 x^{8} + 32 x^{7} + 544 x^{6} - 704 x^{5} - 4176 x^{4} - 5248 x^{3} + 16064 x^{2} + 21248 x + 6592$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_4\times A_4$ (as 12T29) |
$12$ |
$1$ |
$[2]$ |
$[2, 2]^{12}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t^{5} + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.18.10 |
$12$ |
$x^{12} + 24 x^{11} + 220 x^{10} + 80 x^{9} - 6036 x^{8} + 1216 x^{7} + 178592 x^{6} + 665728 x^{5} + 2382448 x^{4} - 2608256 x^{3} + 716736 x^{2} - 243456 x + 182080$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_4\times A_4$ (as 12T29) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{2} + 4\right) x + 8 t^{3} + 8 t^{2} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.6 |
$12$ |
$x^{12} + 12 x^{10} - 1568 x^{9} + 556 x^{8} + 23552 x^{7} + 197664 x^{6} + 569088 x^{5} + 1498736 x^{4} + 3086336 x^{3} + 4459200 x^{2} + 4036096 x + 1813312$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_4\times A_4$ (as 12T29) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{2}\right) x + 8 t^{4} + 8 t^{3} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.33.162 |
$12$ |
$x^{12} - 16 x^{11} + 356 x^{10} - 896 x^{9} + 4350 x^{8} - 2496 x^{7} + 7824 x^{6} - 2304 x^{5} + 13516 x^{4} - 320 x^{3} + 27408 x^{2} + 20136$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_4\times A_4$ (as 12T29) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 12 x^{2} + 16 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.21 |
$12$ |
$x^{12} + 24 x^{11} + 168 x^{10} + 152 x^{9} - 622 x^{8} + 6080 x^{7} + 3728 x^{6} + 12224 x^{5} + 8956 x^{4} + 14624 x^{3} - 640 x^{2} + 672 x - 5256$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_4\times A_4$ (as 12T29) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t^{2} + 8 t\right) x^{2} + \left(8 t + 8\right) x + 4 t^{2} + 28 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.246 |
$12$ |
$x^{12} + 24 x^{11} + 192 x^{10} + 536 x^{9} + 322 x^{8} + 1216 x^{7} + 4304 x^{6} + 9984 x^{5} + 30172 x^{4} + 37920 x^{3} + 55328 x^{2} + 14112 x + 24696$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_4\times A_4$ (as 12T29) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t^{2} + 8\right) x^{2} + \left(8 t + 8\right) x + 28 t^{2} + 28 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.306 |
$12$ |
$x^{12} - 16 x^{11} + 356 x^{10} - 896 x^{9} + 4270 x^{8} - 1344 x^{7} + 1808 x^{6} + 11520 x^{5} + 652 x^{4} + 5056 x^{3} + 11280 x^{2} + 6504$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_4\times A_4$ (as 12T29) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 12 x^{2} + 16 t^{2} + 16 t + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.317 |
$12$ |
$x^{12} + 8 x^{11} + 36 x^{10} + 896 x^{9} + 1566 x^{8} + 4512 x^{7} + 8848 x^{6} + 14592 x^{5} + 14540 x^{4} + 21024 x^{3} + 28176 x^{2} + 25128$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_4\times A_4$ (as 12T29) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + \left(8 t + 12\right) x^{2} + 16 t^{2} + 16 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.322 |
$12$ |
$x^{12} + 24 x^{11} + 192 x^{10} + 536 x^{9} + 402 x^{8} + 2496 x^{7} + 8976 x^{6} + 7040 x^{5} + 23324 x^{4} + 29216 x^{3} + 25248 x^{2} + 25632 x + 25272$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_4\times A_4$ (as 12T29) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t^{2} + 8\right) x^{2} + \left(8 t + 8\right) x + 12 t^{2} + 12 t + 30$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.347 |
$12$ |
$x^{12} + 24 x^{11} + 268 x^{10} + 704 x^{9} + 1046 x^{8} + 352 x^{7} + 1392 x^{6} - 128 x^{5} - 276 x^{4} - 160 x^{3} + 560 x^{2} + 4488$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_4\times A_4$ (as 12T29) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 16 t^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.38 |
$12$ |
$x^{12} + 8 x^{11} + 36 x^{10} + 896 x^{9} + 1550 x^{8} + 4512 x^{7} + 5008 x^{6} + 10496 x^{5} + 5516 x^{4} + 6688 x^{3} + 3088 x^{2} - 536$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_4\times A_4$ (as 12T29) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + \left(8 t + 12\right) x^{2} + 16 t + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
