| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.10 |
$12$ |
$x^{12} + 8 x^{11} + 32 x^{10} + 120 x^{9} + 356 x^{8} + 16 x^{7} - 1312 x^{6} - 3936 x^{5} - 17296 x^{4} - 14272 x^{3} + 103296 x^{2} + 36352 x + 38848$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^3:A_4$ (as 12T58) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.9 |
$12$ |
$x^{12} + 2 x^{11} + 52 x^{10} + 116 x^{9} + 964 x^{8} + 2928 x^{7} + 10272 x^{6} + 24800 x^{5} + 47088 x^{4} + 67104 x^{3} + 107584 x^{2} + 64320 x + 107968$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^3:A_4$ (as 12T58) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.24.170 |
$12$ |
$x^{12} + 26 x^{10} + 28 x^{9} + 18 x^{8} + 384 x^{7} + 464 x^{6} + 864 x^{5} + 1620 x^{4} + 512 x^{3} + 1448 x^{2} + 304 x + 488$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 4 t + 6\right) x^{2} + \left(4 t + 4\right) x + 8 t^{2} + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.232 |
$12$ |
$x^{12} - 8 x^{11} + 26 x^{10} + 52 x^{9} + 354 x^{8} + 608 x^{7} + 1536 x^{6} + 2208 x^{5} + 3732 x^{4} + 3808 x^{3} + 4168 x^{2} + 2192 x + 1384$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(4 t^{2} + 4 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 4 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.233 |
$12$ |
$x^{12} + 34 x^{10} - 28 x^{9} + 110 x^{8} + 304 x^{7} + 864 x^{6} + 1008 x^{5} + 3652 x^{4} + 2752 x^{3} + 4808 x^{2} + 3376 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 4 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.82 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 14 x^{8} + 16 x^{7} + 16 x^{6} + 96 x^{5} + 244 x^{4} + 224 x^{3} + 1112 x^{2} + 1872 x + 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.30.122 |
$12$ |
$x^{12} + 4 x^{11} + 76 x^{10} + 328 x^{9} + 598 x^{8} + 1200 x^{7} + 2000 x^{6} + 1920 x^{5} + 1996 x^{4} + 2384 x^{3} + 1008 x^{2} - 32 x + 584$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t + 4\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.134 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 208 x^{9} + 1182 x^{8} + 2944 x^{7} + 3280 x^{6} + 5856 x^{5} + 3612 x^{4} + 3568 x^{3} + 1664 x^{2} - 376$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(8 t^{2} + 12 t + 8\right) x^{2} + 12 t^{2} + 12 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.152 |
$12$ |
$x^{12} + 4 x^{11} + 52 x^{10} + 360 x^{9} + 1366 x^{8} + 3696 x^{7} + 7280 x^{6} + 10176 x^{5} + 10620 x^{4} + 8400 x^{3} + 6032 x^{2} + 5088 x + 1384$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 4 t + 4\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.172 |
$12$ |
$x^{12} + 4 x^{11} + 76 x^{10} + 304 x^{9} + 374 x^{8} + 464 x^{7} + 912 x^{6} + 608 x^{5} + 396 x^{4} + 912 x^{3} + 368 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t + 4\right) x^{2} + 8 t^{2} + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.228 |
$12$ |
$x^{12} + 4 x^{11} + 52 x^{10} + 496 x^{9} + 1846 x^{8} + 3568 x^{7} + 5456 x^{6} + 7456 x^{5} + 6844 x^{4} + 6864 x^{3} + 3664 x^{2} + 1536 x + 1384$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 12 t + 4\right) x^{2} + 8 t^{2} x + 4 t^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.241 |
$12$ |
$x^{12} + 4 x^{11} + 92 x^{10} + 368 x^{9} + 1610 x^{8} + 2576 x^{7} + 5616 x^{6} + 4352 x^{5} + 7324 x^{4} + 3024 x^{3} + 2736 x^{2} + 960 x + 344$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 4 t + 12\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 4 t^{2} + 4 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.247 |
$12$ |
$x^{12} + 4 x^{11} + 88 x^{10} + 256 x^{9} + 710 x^{8} + 384 x^{7} + 2016 x^{6} + 1024 x^{5} + 348 x^{4} + 2608 x^{3} - 288 x^{2} + 1768$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 8 x^{2} + 12 t^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.6 |
$12$ |
$x^{12} + 4 x^{11} + 100 x^{10} + 512 x^{9} + 1594 x^{8} + 2864 x^{7} + 4880 x^{6} + 7072 x^{5} + 11404 x^{4} + 1168 x^{3} + 8144 x^{2} + 192 x + 1016$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^3:A_4$ (as 12T58) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t + 12\right) x^{2} + 8 t^{2} x + 8 t^{2} + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
