| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.28.1 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.10 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.100 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 12 x^{2} + 8 x + 14$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T221) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 12 x^{2} + 8 x + 14$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.101 |
$12$ |
$x^{12} + 6 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.102 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$[17, 12, 0]$ |
$[1, 2]$ |
| 2.12.28.103 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 4 x^{5} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2 \times S_4$ (as 12T24) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 4 x^{5} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.104 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{5} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^2\wr S_3$ (as 12T139) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{5} + 4 x^{2} + 10$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.105 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 14$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 14$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.106 |
$12$ |
$x^{12} + 4 x^{10} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T221) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 12 x^{2} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.107 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T221) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.108 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.109 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$ |
$[17, 12, 0]$ |
$[1, 2]$ |
| 2.12.28.11 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2$ |
$[17, 12, 0]$ |
$[1, 2]$ |
| 2.12.28.110 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{6} + 4 x^{5} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^3:S_4$ (as 12T103) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{6} + 4 x^{5} + 6$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.111 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 14$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 14$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.112 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 14$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^3:S_4$ (as 12T101) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 14$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.113 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 14$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T225) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 14$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.114 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T221) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 6$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.115 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{3} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{3} + 12 x^{2} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.116 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T225) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 6$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.117 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 8 x + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T225) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 8 x + 6$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.118 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.119 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T221) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.12 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^3:S_4$ (as 12T100) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.120 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T221) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 2$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.121 |
$12$ |
$x^{12} + 4 x^{9} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T225) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 4 x^{2} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.122 |
$12$ |
$x^{12} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 2$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.123 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.124 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T225) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.125 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$[17, 12, 0]$ |
$[1, 2]$ |
| 2.12.28.126 |
$12$ |
$x^{12} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.127 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^3.S_4$ (as 12T102) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 6$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.128 |
$12$ |
$x^{12} + 4 x^{9} + 6 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{2} + 14$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 6 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{2} + 14$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.129 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ |
$[17, 12, 0]$ |
$[1, 2]$ |
| 2.12.28.13 |
$12$ |
$x^{12} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T221) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.130 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2\wr S_3$ (as 12T148) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.131 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.132 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{2} + 8 x + 2$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.133 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 10$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.134 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.135 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2\wr S_3$ (as 12T148) |
$2$ |
$3$ |
$[8/3, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{5} + 4 x^{2} + 2$ |
$[17, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.136 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 6$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.137 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 2$ |
$[17, 12, 0]$ |
$[1, 2]$ |
| 2.12.28.138 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 12 x^{2} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.139 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{5} + 4 x^{2} + 2$ |
$[17, 12, 0]$ |
$[1, 2]$ |
| 2.12.28.14 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T221) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{3} + 8 x^{2} + 10$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.140 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_4^3:S_4$ (as 12T225) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.141 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$[17, 12, 0]$ |
$[1, 2]$ |
| 2.12.28.142 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 14$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 10/3]$ |
$[2, 2, 8/3, 8/3, 10/3, 10/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 14$ |
$[17, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.28.143 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$28$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[26/9, 26/9]$ |
$[26/9, 26/9, 26/9, 26/9, 26/9, 26/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$[17, 12, 0]$ |
$[1, 2]$ |
