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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.22.109 $x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 2$ $2$ $12$ $1$ $22$ $C_4^2:D_6$ (as 12T112) $[2, 7/3]$ $[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 2$
2.12.22.136 $x^{12} + 2 x^{11} + 2 x^{6} + 4 x^{3} + 4 x + 6$ $2$ $12$ $1$ $22$ $C_4^2:D_6$ (as 12T112) $[2, 7/3]$ $[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{6} + 4 x^{3} + 4 x + 6$
2.12.24.324 $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{2} + 4 x + 6$ $2$ $12$ $1$ $24$ $C_4^2:D_6$ (as 12T112) $[2, 8/3]$ $[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{2} + 4 x + 6$
2.12.24.371 $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{4} + 4 x + 2$ $2$ $12$ $1$ $24$ $C_4^2:D_6$ (as 12T112) $[2, 8/3]$ $[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{4} + 4 x + 2$
2.12.30.345 $x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_4^2:D_6$ (as 12T112) $[3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{2} + 2$
2.12.30.412 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_4^2:D_6$ (as 12T112) $[3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{2} + 2$
2.12.30.414 $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_4^2:D_6$ (as 12T112) $[3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{2} + 10$
2.12.30.443 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_4^2:D_6$ (as 12T112) $[3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{2} + 2$
2.12.30.448 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_4^2:D_6$ (as 12T112) $[3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{2} + 10$
2.12.30.519 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_4^2:D_6$ (as 12T112) $[3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{2} + 10$
2.12.30.529 $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{2} + 10$ $2$ $12$ $1$ $30$ $C_4^2:D_6$ (as 12T112) $[3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{10} + 4 x^{7} + 4 x^{2} + 10$
2.12.30.535 $x^{12} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 12 x^{2} + 2$ $2$ $12$ $1$ $30$ $C_4^2:D_6$ (as 12T112) $[3, 19/6]$ $[4/3, 4/3, 3, 19/6, 19/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{9} + 4 x^{7} + 4 x^{4} + 12 x^{2} + 2$
2.12.32.147 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 2$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T112) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 2$
2.12.32.153 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 8 x + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T112) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 8 x + 10$
2.12.32.204 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 8 x^{6} + 8 x^{2} + 8 x + 2$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T112) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 8 x^{6} + 8 x^{2} + 8 x + 2$
2.12.32.235 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{4} + 8 x + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T112) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{4} + 8 x + 10$
2.12.32.31 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T112) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$
2.12.32.425 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{2} + 2$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T112) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{2} + 2$
2.12.32.436 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{4} + 8 x + 2$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T112) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{4} + 8 x + 2$
2.12.32.457 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$ $2$ $12$ $1$ $32$ $C_4^2:D_6$ (as 12T112) $[8/3, 11/3]$ $[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 10$
2.12.34.145 $x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{4} + 4 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{4} + 4 x^{2} + 10$
2.12.34.147 $x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 10$
2.12.34.18 $x^{12} + 4 x^{11} + 8 x^{9} + 8 x^{5} + 4 x^{4} + 4 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 8 x^{9} + 8 x^{5} + 4 x^{4} + 4 x^{2} + 10$
2.12.34.193 $x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{7} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{7} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 10$
2.12.34.198 $x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$
2.12.34.206 $x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$
2.12.34.280 $x^{12} + 4 x^{11} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 10$
2.12.34.302 $x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{8} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{8} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 10$
2.12.34.313 $x^{12} + 4 x^{11} + 8 x^{5} + 4 x^{4} + 4 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 8 x^{5} + 4 x^{4} + 4 x^{2} + 10$
2.12.34.34 $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 8 x^{5} + 4 x^{4} + 12 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 8 x^{5} + 4 x^{4} + 12 x^{2} + 10$
2.12.34.343 $x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 10$
2.12.34.347 $x^{12} + 4 x^{11} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$
2.12.34.39 $x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 10$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 10$
2.12.34.468 $x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{7} + 12 x^{6} + 8 x^{3} + 4 x^{2} + 2$
2.12.34.74 $x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 2$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{3} + 12 x^{2} + 2$
2.12.34.84 $x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $34$ $C_4^2:D_6$ (as 12T112) $[3, 23/6]$ $[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 2$
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