| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.14.10 |
$12$ |
$x^{12} - 6 x^{9} + 12 x^{8} + 51 x^{6} - 36 x^{5} + 36 x^{4} - 18 x^{3} + 36 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.15 |
$12$ |
$x^{12} - 6 x^{9} + 6 x^{8} + 24 x^{6} - 18 x^{5} + 9 x^{4} - 18 x^{3} + 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.18.31 |
$12$ |
$x^{12} - 12 x^{11} + 84 x^{10} - 72 x^{9} + 108 x^{8} + 42 x^{6} - 36 x^{5} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{5} + 6 x^{4} + \left(6 t + 6\right) x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.35 |
$12$ |
$x^{12} + 6 x^{11} + 21 x^{10} + 30 x^{9} + 18 x^{8} - 36 x^{7} + 6 x^{6} - 36 x^{5} - 72 x^{4} + 144 x^{3} + 360$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 6 x^{4} + 3 t x^{3} + 18 t + 12$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.36 |
$12$ |
$x^{12} - 6 x^{11} + 57 x^{10} - 42 x^{9} + 126 x^{8} - 36 x^{7} + 51 x^{6} - 18 x^{5} + 36 x^{4} - 18 x^{3} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + 6 x^{4} + \left(6 t + 3\right) x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.66 |
$12$ |
$x^{12} + 9 x^{8} + 6 x^{6} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{4} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.73 |
$12$ |
$x^{12} + 6 x^{11} + 15 x^{10} + 24 x^{9} + 27 x^{8} + 18 x^{7} - 3 x^{6} - 36 x^{5} - 36 x^{4} - 36 x^{3} + 360$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[2]$ |
$[2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 3 x^{4} + 3 x^{3} + 18 t + 12$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.76 |
$12$ |
$x^{12} + 6 x^{11} + 21 x^{10} + 36 x^{9} + 36 x^{8} - 12 x^{6} - 36 x^{5} - 72 x^{4} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 6 x^{4} + 9 t + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.79 |
$12$ |
$x^{12} - 6 x^{11} + 57 x^{10} - 30 x^{9} + 54 x^{8} + 36 x^{7} + 60 x^{6} - 126 x^{5} + 252 x^{4} + 126 x^{3} + 441$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + 6 x^{4} + \left(3 t + 6\right) x^{3} + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.84 |
$12$ |
$x^{12} - 6 x^{11} + 18 x^{10} + 6 x^{9} + 81 x^{8} + 36 x^{7} + 114 x^{6} - 126 x^{5} - 252 x^{3} + 441$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{5} + \left(3 t + 3\right) x^{4} + 6 t x^{3} + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.86 |
$12$ |
$x^{12} + 12 x^{10} + 36 x^{8} + 33 x^{6} + 144 x^{4} + 54 x^{3} + 225$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{4} + \left(3 t + 3\right) x^{3} + 9 t + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.87 |
$12$ |
$x^{12} - 6 x^{11} + 45 x^{10} + 30 x^{9} + 99 x^{8} + 36 x^{7} + 51 x^{6} + 198 x^{5} + 108 x^{4} + 198 x^{3} + 333$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + \left(3 t + 3\right) x^{4} + \left(6 t + 3\right) x^{3} + 18 t + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.22.25 |
$12$ |
$x^{12} - 30 x^{9} - 18 x^{8} + 36 x^{7} + 573 x^{6} + 594 x^{5} - 378 x^{4} - 360 x^{3} + 270 x^{2} + 432 x + 225$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 3\right) x^{3} + 9 t x^{2} + 18 x + 9 t + 21$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.48 |
$12$ |
$x^{12} + 6 x^{9} + 18 x^{8} - 36 x^{7} + 6 x^{6} + 54 x^{5} + 81 x^{4} - 252 x^{3} + 540 x^{2} + 864 x + 360$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{3} + 9 x^{2} + 18 t x + 18 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.63 |
$12$ |
$x^{12} + 12 x^{9} + 18 x^{8} + 96 x^{6} + 108 x^{5} + 189 x^{4} + 252 x^{3} + 297 x^{2} + 162 x + 225$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 12\right) x^{3} + 9 x^{2} + \left(9 t + 9\right) x + 9 t + 21$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.65 |
$12$ |
$x^{12} - 42 x^{9} + 18 x^{8} - 18 x^{7} + 1023 x^{6} + 54 x^{5} + 972 x^{4} - 126 x^{3} + 216 x^{2} - 54 x + 9$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(24 t + 3\right) x^{3} + \left(9 t + 18\right) x^{2} + 9 t x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.66 |
$12$ |
$x^{12} + 18 x^{9} + 18 x^{7} + 312 x^{6} + 540 x^{5} + 756 x^{4} + 648 x^{3} + 486 x^{2} + 216 x + 90$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(15 t + 24\right) x^{3} + \left(18 t + 18\right) x^{2} + \left(9 t + 18\right) x + 9 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.77 |
$12$ |
$x^{12} + 36 x^{7} - 12 x^{6} + 81 x^{4} + 486 x^{2} - 216 x + 117$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(9 t + 9\right) x^{2} + 18 x + 9 t + 3$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.82 |
$12$ |
$x^{12} - 18 x^{7} + 465 x^{6} + 378 x^{5} + 837 x^{4} + 324 x^{3} + 405 x^{2} - 216 x + 144$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(21 t + 21\right) x^{3} + \left(9 t + 9\right) x^{2} + \left(18 t + 9\right) x + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.83 |
$12$ |
$x^{12} - 30 x^{9} - 18 x^{8} + 18 x^{7} + 519 x^{6} + 918 x^{5} + 135 x^{4} + 936 x^{3} + 999 x^{2} - 270 x + 549$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 3\right) x^{3} + \left(18 t + 9\right) x^{2} + 9 x + 18 t + 3$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.85 |
$12$ |
$x^{12} + 12 x^{9} + 18 x^{8} + 42 x^{6} + 108 x^{5} + 162 x^{4} + 36 x^{3} + 216 x^{2} + 90$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{3} + \left(9 t + 18\right) x^{2} + 9 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.88 |
$12$ |
$x^{12} + 6 x^{9} + 18 x^{8} + 132 x^{6} + 54 x^{5} + 81 x^{4} + 126 x^{3} + 378 x^{2} + 441$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(9 t + 12\right) x^{3} + 9 x^{2} + 21$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.93 |
$12$ |
$x^{12} - 18 x^{9} + 18 x^{8} - 18 x^{7} + 663 x^{6} - 162 x^{5} + 675 x^{4} + 216 x^{3} + 216 x^{2} + 108 x + 90$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(24 t + 15\right) x^{3} + 9 x^{2} + 9 t x + 9 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.95 |
$12$ |
$x^{12} + 6 x^{9} + 18 x^{8} + 258 x^{6} + 324 x^{5} + 432 x^{4} + 234 x^{3} + 297 x^{2} + 144$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(15 t + 18\right) x^{3} + \left(9 t + 18\right) x^{2} + \left(9 t + 9\right) x + 12$ |
$[6, 0]$ |
$[1, 1]$ |
