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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.28.113 $x^{12} + 4 x^{11} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{8} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 14$
2.12.28.116 $x^{12} + 4 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 6$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 6$
2.12.28.117 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 8 x + 6$
2.12.28.121 $x^{12} + 4 x^{9} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 4 x^{2} + 10$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 4 x^{2} + 10$
2.12.28.124 $x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 10$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 10$
2.12.28.140 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 8 x^{2} + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 8 x^{2} + 2$
2.12.28.149 $x^{12} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$
2.12.28.150 $x^{12} + 4 x^{11} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 14$
2.12.28.151 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$
2.12.28.156 $x^{12} + 2 x^{10} + 2 x^{6} + 4 x^{5} + 8 x^{2} + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 2 x^{6} + 4 x^{5} + 8 x^{2} + 2$
2.12.28.160 $x^{12} + 4 x^{11} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 14$
2.12.28.169 $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{2} + 6$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{2} + 6$
2.12.28.175 $x^{12} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 2$
2.12.28.178 $x^{12} + 4 x^{11} + 4 x^{10} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 6$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 6$
2.12.28.183 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{2} + 8 x + 6$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{2} + 8 x + 6$
2.12.28.184 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 10$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 10$
2.12.28.188 $x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{3} + 4 x^{2} + 10$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 4 x^{4} + 8 x^{3} + 4 x^{2} + 10$
2.12.28.190 $x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{3} + 4 x^{2} + 8 x + 2$
2.12.28.222 $x^{12} + 2 x^{10} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 14$
2.12.28.228 $x^{12} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 14$
2.12.28.232 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{2} + 8 x + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{2} + 8 x + 2$
2.12.28.249 $x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{2} + 8 x + 6$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{2} + 8 x + 6$
2.12.28.32 $x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 4 x^{2} + 2$
2.12.28.33 $x^{12} + 4 x^{11} + 6 x^{10} + 2 x^{6} + 4 x^{5} + 8 x^{2} + 8 x + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 2 x^{6} + 4 x^{5} + 8 x^{2} + 8 x + 2$
2.12.28.34 $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 10$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} + 10$
2.12.28.40 $x^{12} + 4 x^{9} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x + 14$
2.12.28.45 $x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$
2.12.28.46 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{2} + 14$
2.12.28.64 $x^{12} + 4 x^{11} + 4 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 14$
2.12.28.74 $x^{12} + 4 x^{10} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 12 x^{2} + 10$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 12 x^{4} + 12 x^{2} + 10$
2.12.28.82 $x^{12} + 2 x^{10} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 2$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 2$
2.12.28.84 $x^{12} + 4 x^{11} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 14$ $2$ $12$ $1$ $28$ $C_4^3:S_4$ (as 12T225) $[2, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 14$
2.12.30.309 $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 8 x + 6$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 8 x^{4} + 8 x^{3} + 8 x + 6$
2.12.30.313 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{2} + 8 x + 10$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{2} + 8 x + 10$
2.12.30.323 $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 8 x + 10$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 8 x + 10$
2.12.30.324 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 12 x^{4} + 2$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 12 x^{4} + 2$
2.12.30.327 $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 12 x^{4} + 8 x^{2} + 8 x + 2$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 12 x^{4} + 8 x^{2} + 8 x + 2$
2.12.30.351 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 14$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 8 x^{2} + 14$
2.12.30.377 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 8 x^{2} + 2$
2.12.30.397 $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{4} + 8 x^{2} + 8 x + 2$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{4} + 8 x^{2} + 8 x + 2$
2.12.30.398 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 8 x^{3} + 8 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 8 x^{3} + 8 x^{2} + 2$
2.12.30.409 $x^{12} + 2 x^{10} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{2} + 8 x + 10$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{2} + 8 x + 10$
2.12.30.420 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 12 x^{4} + 8 x + 2$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 12 x^{4} + 8 x + 2$
2.12.30.421 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 8 x^{4} + 10$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 8 x^{4} + 10$
2.12.30.422 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 8 x + 10$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 8 x + 10$
2.12.30.426 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 8 x^{4} + 8 x + 6$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 8 x^{4} + 8 x + 6$
2.12.30.429 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{7} + 4 x^{6} + 8 x^{4} + 10$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{7} + 4 x^{6} + 8 x^{4} + 10$
2.12.30.440 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{7} + 4 x^{6} + 8 x + 10$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{7} + 4 x^{6} + 8 x + 10$
2.12.30.447 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 8 x^{4} + 8 x + 10$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 11/4, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{7} + 4 x^{6} + 8 x^{4} + 8 x + 10$
2.12.30.450 $x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 2$ $2$ $12$ $1$ $30$ $C_4^3:S_4$ (as 12T225) $[8/3, 10/3]$ $[4/3, 4/3, 2, 8/3, 8/3, 3, 10/3, 10/3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 2$
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