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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.25.10 $x^{12} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 10 x^{2} + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 10 x^{2} + 6$
2.12.25.103 $x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 6 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 6 x^{2} + 8 x + 2$
2.12.25.105 $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{5} + 2 x^{2} + 8 x + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{5} + 2 x^{2} + 8 x + 14$
2.12.25.109 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 2 x^{6} + 4 x^{3} + 14 x^{2} + 8 x + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 2 x^{6} + 4 x^{3} + 14 x^{2} + 8 x + 14$
2.12.25.111 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{5} + 10 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{5} + 10 x^{2} + 14$
2.12.25.114 $x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 8 x + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 8 x + 6$
2.12.25.115 $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 2 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 2 x^{2} + 2$
2.12.25.117 $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{5} + 10 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{5} + 10 x^{2} + 14$
2.12.25.118 $x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{6} + 4 x^{4} + 10 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{6} + 4 x^{4} + 10 x^{2} + 2$
2.12.25.120 $x^{12} + 4 x^{10} + 6 x^{6} + 4 x^{3} + 14 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 6 x^{6} + 4 x^{3} + 14 x^{2} + 14$
2.12.25.121 $x^{12} + 4 x^{11} + 4 x^{10} + 6 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 6 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 14$
2.12.25.123 $x^{12} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 6 x^{2} + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 6 x^{2} + 6$
2.12.25.126 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 2 x^{6} + 4 x^{3} + 6 x^{2} + 8 x + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 2 x^{6} + 4 x^{3} + 6 x^{2} + 8 x + 14$
2.12.25.14 $x^{12} + 2 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{2} + 2$
2.12.25.15 $x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 14$
2.12.25.16 $x^{12} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{4} + 2 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{4} + 2 x^{2} + 2$
2.12.25.17 $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{4} + 6 x^{2} + 10$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{7} + 4 x^{4} + 6 x^{2} + 10$
2.12.25.18 $x^{12} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 14 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 14 x^{2} + 8 x + 2$
2.12.25.20 $x^{12} + 4 x^{11} + 6 x^{6} + 4 x^{3} + 14 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{6} + 4 x^{3} + 14 x^{2} + 14$
2.12.25.21 $x^{12} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{4} + 2 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{4} + 2 x^{2} + 8 x + 2$
2.12.25.22 $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 6 x^{2} + 8 x + 10$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 6 x^{2} + 8 x + 10$
2.12.25.24 $x^{12} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 14 x^{2} + 8 x + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 14 x^{2} + 8 x + 6$
2.12.25.26 $x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 14 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 14 x^{2} + 8 x + 2$
2.12.25.27 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 2 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 2 x^{2} + 8 x + 2$
2.12.25.28 $x^{12} + 4 x^{10} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 6 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 6 x^{2} + 8 x + 2$
2.12.25.29 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 8 x + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 8 x + 14$
2.12.25.31 $x^{12} + 2 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{2} + 8 x + 2$
2.12.25.34 $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 6 x^{2} + 10$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{4} + 6 x^{2} + 10$
2.12.25.35 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 4 x^{5} + 6 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 4 x^{5} + 6 x^{2} + 14$
2.12.25.37 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{5} + 10 x^{2} + 8 x + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{5} + 10 x^{2} + 8 x + 14$
2.12.25.40 $x^{12} + 4 x^{11} + 6 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 6 x^{2} + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 6 x^{2} + 6$
2.12.25.41 $x^{12} + 10 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 10 x^{2} + 2$
2.12.25.44 $x^{12} + 4 x^{11} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 6 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 6 x^{2} + 8 x + 2$
2.12.25.45 $x^{12} + 4 x^{11} + 6 x^{6} + 4 x^{3} + 6 x^{2} + 8 x + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{6} + 4 x^{3} + 6 x^{2} + 8 x + 14$
2.12.25.47 $x^{12} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 10 x^{2} + 8 x + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 10 x^{2} + 8 x + 6$
2.12.25.49 $x^{12} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 14 x^{2} + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 14 x^{2} + 6$
2.12.25.50 $x^{12} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{4} + 10 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{4} + 10 x^{2} + 2$
2.12.25.51 $x^{12} + 2 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{4} + 6 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{4} + 6 x^{2} + 2$
2.12.25.56 $x^{12} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 8 x + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 8 x + 6$
2.12.25.57 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 10 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 10 x^{2} + 14$
2.12.25.58 $x^{12} + 4 x^{11} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 14 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 14 x^{2} + 2$
2.12.25.63 $x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 6 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 6 x^{2} + 2$
2.12.25.64 $x^{12} + 4 x^{9} + 6 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 6 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 14$
2.12.25.67 $x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{6} + 4 x^{4} + 2 x^{2} + 8 x + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{6} + 4 x^{4} + 2 x^{2} + 8 x + 2$
2.12.25.68 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 10 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 10 x^{2} + 2$
2.12.25.71 $x^{12} + 2 x^{10} + 4 x^{9} + 2 x^{8} + 4 x^{5} + 6 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 2 x^{8} + 4 x^{5} + 6 x^{2} + 14$
2.12.25.72 $x^{12} + 6 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{4} + 2 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{4} + 2 x^{2} + 2$
2.12.25.74 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 2 x^{2} + 2$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 2 x^{2} + 2$
2.12.25.75 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 4 x^{5} + 14 x^{2} + 14$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 4 x^{5} + 14 x^{2} + 14$
2.12.25.8 $x^{12} + 6 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 6$ $2$ $12$ $1$ $25$ $C_2\wr S_4$ (as 12T224) $[4/3, 19/6]$ $[4/3, 4/3, 8/3, 8/3, 3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 6$
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