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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 (20 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.12.12.24 $x^{12} - 12 x^{7} - 6 x^{6} + 72 x^{2} + 72 x + 18$ $3$ $6$ $2$ $12$ $C_3^4:\OD_{16}$ (as 12T215) $[5/4]$ $[5/4, 5/4, 5/4, 5/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 6 t x + 3 t$
3.12.12.25 $x^{12} - 6 x^{7} - 6 x^{6} + 9 x^{4} + 36 x^{3} + 63 x^{2} + 54 x + 18$ $3$ $6$ $2$ $12$ $C_3^4:\OD_{16}$ (as 12T215) $[5/4]$ $[5/4, 5/4, 5/4, 5/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 3\right) x^{2} + \left(6 t + 3\right) x + 3 t$
3.12.20.25 $x^{12} - 6 x^{11} + 18 x^{10} + 6 x^{9} - 15 x^{6} + 252 x^{5} + 162 x^{4} - 72 x^{3} + 162 x^{2} + 585$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 3 t x^{5} + 3 x^{3} + \left(9 t + 18\right) x^{2} + 21 t + 9$
3.12.20.26 $x^{12} - 12 x^{11} + 72 x^{10} - 18 x^{8} + 234 x^{7} - 114 x^{6} + 180 x^{5} + 162 x^{4} - 162 x^{3} + 351 x^{2} - 54 x + 153$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 6 t x^{5} + 9 t x^{2} + 9 x + 12 t + 9$
3.12.20.27 $x^{12} + 6 x^{11} + 9 x^{10} - 36 x^{7} - 105 x^{6} + 90 x^{5} + 432 x^{4} + 774 x^{3} + 1404 x^{2} + 864 x + 450$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 3 x^{5} + \left(3 t + 3\right) x^{3} + \left(18 t + 18\right) x^{2} + 18 t x + 21 t + 18$
3.12.20.28 $x^{12} + 6 x^{11} + 18 x^{10} + 6 x^{9} + 54 x^{7} + 21 x^{6} + 405 x^{4} + 36 x^{3} + 45$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 6\right) x^{5} + 3 x^{3} + \left(18 t + 9\right) x^{2} + 3 t + 9$
3.12.20.29 $x^{12} + 36 x^{10} + 12 x^{9} - 36 x^{8} + 216 x^{7} + 264 x^{6} - 180 x^{5} + 648 x^{4} + 720 x^{3} + 216 x^{2} + 108 x + 45$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 6\right) x^{5} + 6 x^{3} + 18 t x^{2} + \left(18 t + 18\right) x + 3 t + 9$
3.12.20.35 $x^{12} + 6 x^{11} + 9 x^{10} + 12 x^{9} + 36 x^{8} + 66 x^{6} + 90 x^{5} + 81 x^{4} + 342 x^{3} + 135 x^{2} + 54 x + 234$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 3 x^{5} + 6 x^{3} + \left(9 t + 9\right) x^{2} + \left(9 t + 9\right) x + 3 t + 18$
3.12.20.36 $x^{12} - 12 x^{11} + 72 x^{10} + 414 x^{7} + 219 x^{6} + 396 x^{5} + 702 x^{4} + 774 x^{3} + 1026 x^{2} + 432 x + 450$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 6 t x^{5} + \left(3 t + 3\right) x^{3} + 18 t x^{2} + 9 t x + 21 t + 18$
3.12.20.37 $x^{12} - 12 x^{11} + 72 x^{10} - 6 x^{9} + 108 x^{8} + 216 x^{7} + 237 x^{6} + 612 x^{5} + 540 x^{4} + 972 x^{3} + 1080 x^{2} + 756 x + 585$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 6 t x^{5} + \left(6 t + 3\right) x^{3} + \left(18 t + 18\right) x^{2} + \left(18 t + 18\right) x + 21 t + 9$
3.12.20.40 $x^{12} + 36 x^{10} + 6 x^{9} + 18 x^{8} + 144 x^{7} + 48 x^{6} + 36 x^{5} + 270 x^{4} - 216 x^{3} + 108 x^{2} + 540 x + 234$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 6\right) x^{5} + \left(3 t + 6\right) x^{3} + 9 t x^{2} + 18 x + 3 t + 18$
3.12.20.41 $x^{12} + 9 x^{10} + 12 x^{9} + 108 x^{7} + 84 x^{6} + 126 x^{5} + 324 x^{4} + 288 x^{3} + 837 x^{2} + 378 x + 450$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(3 t + 3\right) x^{5} + 6 x^{3} + \left(18 t + 18\right) x^{2} + \left(9 t + 9\right) x + 21 t + 18$
3.12.20.43 $x^{12} - 6 x^{11} + 45 x^{10} + 6 x^{9} - 18 x^{8} + 90 x^{7} + 201 x^{6} - 54 x^{5} + 27 x^{4} + 252 x^{3} + 216 x^{2} - 216 x + 234$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 3\right) x^{5} + 3 x^{3} + \left(9 t + 9\right) x^{2} + 9 t x + 3 t + 18$
3.12.20.44 $x^{12} + 36 x^{10} - 6 x^{9} + 36 x^{8} + 198 x^{7} + 210 x^{6} + 252 x^{5} + 486 x^{4} + 792 x^{3} + 837 x^{2} + 648 x + 288$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 6\right) x^{5} + 3 t x^{3} + \left(18 t + 18\right) x^{2} + \left(18 t + 9\right) x + 12 t$
3.12.20.46 $x^{12} - 6 x^{11} + 45 x^{10} - 12 x^{9} + 108 x^{8} + 198 x^{7} + 336 x^{6} + 486 x^{5} + 648 x^{4} + 936 x^{3} + 1161 x^{2} + 810 x + 450$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 3\right) x^{5} + 6 t x^{3} + \left(18 t + 18\right) x^{2} + \left(18 t + 9\right) x + 21 t + 18$
3.12.20.49 $x^{12} - 6 x^{11} + 45 x^{10} + 18 x^{8} + 36 x^{7} + 264 x^{6} + 162 x^{5} + 162 x^{4} + 162 x^{3} + 567 x^{2} + 486 x + 153$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 3\right) x^{5} + \left(9 t + 18\right) x^{2} + \left(18 t + 9\right) x + 12 t + 9$
3.12.20.50 $x^{12} - 6 x^{11} + 18 x^{10} - 6 x^{9} + 90 x^{8} - 72 x^{7} - 33 x^{6} - 180 x^{5} + 216 x^{4} + 594 x^{3} + 864 x^{2} + 540 x + 234$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 3 t x^{5} + \left(6 t + 3\right) x^{3} + 18 x^{2} + 18 x + 3 t + 18$
3.12.20.53 $x^{12} + 12 x^{11} + 36 x^{10} + 12 x^{6} + 72 x^{5} + 324 x^{4} + 108 x^{2} + 45$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 6 x^{5} + \left(18 t + 18\right) x^{2} + 3 t + 9$
3.12.20.54 $x^{12} - 12 x^{11} + 72 x^{10} + 72 x^{8} + 126 x^{7} - 60 x^{6} + 72 x^{5} + 81 x^{4} + 36 x^{3} + 135 x^{2} + 108 x + 45$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + 6 t x^{5} + \left(6 t + 6\right) x^{3} + \left(9 t + 9\right) x^{2} + 9 x + 3 t + 9$
3.12.20.58 $x^{12} + 36 x^{10} - 36 x^{8} + 180 x^{7} + 246 x^{6} + 36 x^{5} + 648 x^{4} + 1296 x^{3} + 216 x^{2} - 432 x + 234$ $3$ $6$ $2$ $20$ $C_3^4:\OD_{16}$ (as 12T215) $[9/4]$ $[9/4, 9/4, 9/4, 9/4]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{6} + \left(6 t + 6\right) x^{5} + 18 t x^{2} + 18 t x + 3 t + 18$
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