| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.18.33 |
$12$ |
$x^{12} - 4 x^{11} + 4 x^{10} + 8 x^{9} + 18 x^{8} - 48 x^{7} + 24 x^{6} + 108 x^{4} - 144 x^{3} + 216$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^3:A_4$ (as 12T59) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + 6$ |
$[3, 3, 0]$ |
$[2]$ |
| 2.12.18.54 |
$12$ |
$x^{12} + 2 x^{11} + 18 x^{10} + 36 x^{9} + 82 x^{8} + 64 x^{7} + 128 x^{6} + 72 x^{5} + 108 x^{4} + 72 x^{3} + 72 x^{2} + 216$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^3:A_4$ (as 12T59) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + \left(2 t^{2} + 2\right) x^{2} + 6$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.24.118 |
$12$ |
$x^{12} + 18 x^{10} - 8 x^{9} + 146 x^{8} + 24 x^{7} + 464 x^{6} + 64 x^{5} + 1228 x^{4} + 656 x^{3} + 968 x^{2} + 1184 x + 536$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 8 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.2 |
$12$ |
$x^{12} - 6 x^{10} + 14 x^{8} + 72 x^{7} + 320 x^{6} + 160 x^{5} + 1324 x^{4} + 592 x^{3} + 1960 x^{2} + 576 x + 2088$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 2\right) x^{2} + 4 t x + 8 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.253 |
$12$ |
$x^{12} + 30 x^{10} - 32 x^{9} + 142 x^{8} + 280 x^{7} + 448 x^{6} + 752 x^{5} + 1772 x^{4} + 1168 x^{3} + 3032 x^{2} + 1056 x + 2088$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 2 t + 6\right) x^{2} + 4 t^{2} x + 8 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.90 |
$12$ |
$x^{12} + 12 x^{11} + 70 x^{10} + 192 x^{9} + 470 x^{8} + 600 x^{7} + 608 x^{6} + 1152 x^{5} + 1468 x^{4} + 960 x^{3} + 760 x^{2} + 192 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t^{2} + 2 t + 6\right) x^{2} + 4 t^{2} x + 4 t^{2} + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.107 |
$12$ |
$x^{12} - 8 x^{11} + 22 x^{10} + 200 x^{9} + 22 x^{8} + 368 x^{7} - 2192 x^{6} + 464 x^{5} - 3764 x^{4} + 160 x^{3} - 2088 x^{2} - 376$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(14 t + 2\right) x^{2} + 8 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.214 |
$12$ |
$x^{12} + 12 x^{11} + 74 x^{10} + 256 x^{9} + 1042 x^{8} + 2848 x^{7} + 5760 x^{6} + 5344 x^{5} + 5996 x^{4} + 1936 x^{3} + 1864 x^{2} + 248$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(8 t^{2} + 14 t + 14\right) x^{2} + 8 t^{2} x + 4 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.216 |
$12$ |
$x^{12} + 34 x^{10} + 24 x^{9} + 494 x^{8} + 544 x^{7} + 3184 x^{6} + 4000 x^{5} + 4924 x^{4} + 3136 x^{3} + 648 x^{2} + 608 x - 376$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 6 t + 14\right) x^{2} + 8 x + 8 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.221 |
$12$ |
$x^{12} - 6 x^{10} - 16 x^{9} + 654 x^{8} + 848 x^{7} + 2528 x^{6} + 1152 x^{5} + 1276 x^{4} - 608 x^{3} - 120 x^{2} - 320 x + 72$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(12 t^{2} + 14 t + 6\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{2} + 8 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.28 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 216 x^{9} + 682 x^{8} + 2208 x^{7} + 2928 x^{6} + 6240 x^{5} + 6796 x^{4} + 12048 x^{3} + 12680 x^{2} + 9184 x + 4568$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(14 t + 6\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{2} + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.58 |
$12$ |
$x^{12} + 12 x^{11} + 38 x^{10} - 8 x^{9} + 10 x^{8} + 672 x^{7} + 1088 x^{6} + 2816 x^{5} + 5228 x^{4} + 4496 x^{3} + 3704 x^{2} + 6752 x + 3032$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(8 t^{2} + 2 t + 2\right) x^{2} + \left(8 t^{2} + 8\right) x + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.8 |
$12$ |
$x^{12} + 4 x^{11} + 18 x^{10} + 152 x^{9} + 1082 x^{8} + 3312 x^{7} + 5680 x^{6} + 6064 x^{5} + 11196 x^{4} + 2608 x^{3} + 7400 x^{2} + 632$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(12 t^{2} + 6 t + 14\right) x^{2} + 8 t^{2} + 12 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.99 |
$12$ |
$x^{12} + 10 x^{10} + 406 x^{8} + 320 x^{7} - 224 x^{6} - 2720 x^{5} + 2972 x^{4} + 3328 x^{3} + 3976 x^{2} + 1408 x + 552$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 14 t + 6\right) x^{2} + 8 t x + 8 t^{2} + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
