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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
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Residue field degree Top slope Wild Visible Wild inertia subgroup
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Results (24 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.20.55 $x^{12} + 2 x^{10} + 2 x^{9} + 2$ $2$ $12$ $1$ $20$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[2, 2]$ $[4/3, 4/3, 2, 2]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 2 x^{9} + 2$
2.12.20.71 $x^{12} + 2 x^{11} + 2 x^{9} + 2$ $2$ $12$ $1$ $20$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[2, 2]$ $[4/3, 4/3, 2, 2]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{9} + 2$
2.12.20.76 $x^{12} + 2 x^{10} + 2 x^{9} + 6$ $2$ $12$ $1$ $20$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[2, 2]$ $[4/3, 4/3, 2, 2]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 2 x^{9} + 6$
2.12.20.79 $x^{12} + 2 x^{11} + 2 x^{9} + 6$ $2$ $12$ $1$ $20$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[2, 2]$ $[4/3, 4/3, 2, 2]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{11} + 2 x^{9} + 6$
2.12.26.102 $x^{12} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$
2.12.26.107 $x^{12} + 4 x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 6$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 6$
2.12.26.11 $x^{12} + 4 x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$
2.12.26.114 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[2, 3]$ $[4/3, 4/3, 2, 3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$
2.12.26.126 $x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 14$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[2, 3]$ $[4/3, 4/3, 2, 3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 14$
2.12.26.14 $x^{12} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 2$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 2$
2.12.26.16 $x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[2, 3]$ $[4/3, 4/3, 2, 3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$
2.12.26.42 $x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 2$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 2$
2.12.26.6 $x^{12} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 6$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 6$
2.12.26.70 $x^{12} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 6$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 6$
2.12.26.93 $x^{12} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 2$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 2$
2.12.26.97 $x^{12} + 6 x^{10} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 10$ $2$ $12$ $1$ $26$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[2, 3]$ $[4/3, 4/3, 2, 3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 10$
2.12.28.1 $x^{12} + 6 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ $2$ $12$ $1$ $28$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$
2.12.28.118 $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$ $2$ $12$ $1$ $28$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 6$
2.12.28.123 $x^{12} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ $2$ $12$ $1$ $28$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$
2.12.28.145 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{5} + 4 x^{2} + 2$ $2$ $12$ $1$ $28$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{5} + 4 x^{2} + 2$
2.12.28.148 $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{2} + 2$ $2$ $12$ $1$ $28$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{2} + 2$
2.12.28.229 $x^{12} + 6 x^{10} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ $2$ $12$ $1$ $28$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{12} + 6 x^{10} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$
2.12.28.69 $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{5} + 4 x^{2} + 2$ $2$ $12$ $1$ $28$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{5} + 4 x^{2} + 2$
2.12.28.78 $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ $2$ $12$ $1$ $28$ $\GL(2,\mathbb{Z}/4)$ (as 12T49) $[8/3, 3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t + 1$ $x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$
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