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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.16.15 $x^{12} + 2 x^{10} - 2 x^{9} + 8 x^{8} + 4 x^{7} + 12 x^{6} - 4 x^{5} + 8 x^{4} - 4 x^{3} + 8 x^{2} + 4$ $2$ $6$ $2$ $16$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[2]$ $[4/3, 4/3, 2, 2]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + \left(2 t + 2\right) x^{4} + 2 t x^{3} + 2 x^{2} + 2$
2.12.16.5 $x^{12} + 2 x^{11} + 4 x^{10} - 2 x^{9} + 8 x^{8} + 4 x^{7} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 12 x^{3} + 12$ $2$ $6$ $2$ $16$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[2]$ $[4/3, 4/3, 2, 2]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + \left(2 t + 2\right) x^{5} + 2 t x^{3} + 2 x^{2} + 4 t + 2$
2.12.20.27 $x^{12} - 2 x^{11} - 2 x^{10} + 28 x^{9} + 56 x^{8} + 12 x^{7} - 12 x^{6} + 28 x^{5} + 48 x^{4} + 40 x^{3} + 48 x^{2} + 28$ $2$ $6$ $2$ $20$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 2 t x^{5} + 6 t x^{4} + \left(4 t + 4\right) x^{3} + 6 x^{2} + 4 t + 6$
2.12.20.29 $x^{12} - 2 x^{11} + 10 x^{10} + 8 x^{9} + 4 x^{8} + 36 x^{7} + 36 x^{6} + 4 x^{5} + 48 x^{4} + 32 x^{3} + 24 x^{2} + 28$ $2$ $6$ $2$ $20$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 2 t x^{5} + \left(2 t + 4\right) x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t + 6$
2.12.20.3 $x^{12} - 2 x^{11} + 2 x^{10} + 16 x^{9} - 4 x^{8} + 4 x^{7} + 36 x^{6} + 4 x^{5} + 16 x^{4} + 32 x^{3} + 24 x^{2} + 28$ $2$ $6$ $2$ $20$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 2 t x^{5} + 2 t x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t + 6$
2.12.20.41 $x^{12} - 2 x^{11} + 2 x^{10} + 12 x^{9} + 24 x^{8} - 4 x^{7} + 12 x^{6} + 28 x^{5} + 40 x^{4} + 40 x^{3} + 48 x^{2} + 28$ $2$ $6$ $2$ $20$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[8/3]$ $[2, 2, 8/3, 8/3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 2 t x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{3} + 6 x^{2} + 4 t + 6$
2.12.22.38 $x^{12} + 8 x^{11} + 28 x^{10} + 44 x^{9} + 18 x^{8} - 32 x^{7} + 16 x^{6} + 64 x^{5} + 76 x^{4} - 24 x^{3} - 12 x^{2} + 36$ $2$ $6$ $2$ $22$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 4 x^{5} + 6 x^{4} + 4 t x^{3} + 2 t x^{2} + 6$
2.12.22.40 $x^{12} + 4 x^{10} - 4 x^{9} + 6 x^{8} - 8 x^{7} + 40 x^{6} + 32 x^{5} + 68 x^{4} + 8 x^{3} + 92 x^{2} + 148$ $2$ $6$ $2$ $22$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 2 x^{4} + 4 t x^{3} + \left(6 t + 4\right) x^{2} + 8 t + 14$
2.12.22.45 $x^{12} + 8 x^{11} + 28 x^{10} + 44 x^{9} + 18 x^{8} - 32 x^{7} + 8 x^{6} + 32 x^{5} + 28 x^{4} + 40 x^{3} + 20 x^{2} + 52$ $2$ $6$ $2$ $22$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 4 x^{5} + 6 x^{4} + 4 t x^{3} + 2 t x^{2} + 8 t + 6$
2.12.22.6 $x^{12} + 12 x^{10} - 4 x^{9} + 40 x^{8} - 16 x^{7} + 52 x^{6} + 40 x^{5} + 60 x^{4} + 40 x^{3} + 40 x^{2} + 48 x + 84$ $2$ $6$ $2$ $22$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[3]$ $[4/3, 4/3, 2, 3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 6 x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 8 t + 10$
2.12.22.70 $x^{12} + 12 x^{10} - 4 x^{9} + 40 x^{8} - 16 x^{7} + 44 x^{6} + 40 x^{5} + 12 x^{4} + 8 x^{3} + 24 x^{2} + 16 x + 4$ $2$ $6$ $2$ $22$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[3]$ $[4/3, 4/3, 2, 3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + 6 x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 2$
2.12.22.73 $x^{12} - 4 x^{9} + 12 x^{8} + 24 x^{7} + 60 x^{6} + 24 x^{5} + 60 x^{4} + 8 x^{3} + 48 x^{2} + 148$ $2$ $6$ $2$ $22$ $\GL(2,\mathbb{Z}/4)$ (as 12T50) $[3]$ $[2, 8/3, 8/3, 3]_{3}^{2}$ $t^{2} + t + 1$ $x^{6} + \left(4 t + 2\right) x^{4} + 4 t x^{3} + \left(4 t + 2\right) x^{2} + 8 t + 14$
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