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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 (16 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group $u$ $t$ Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
2.16.44.6 $x^{16} + 4 x^{15} + 20 x^{14} + 32 x^{13} + 36 x^{12} + 96 x^{11} + 164 x^{10} + 104 x^{9} + 256 x^{8} + 264 x^{7} + 288 x^{6} + 112 x^{5} + 392 x^{4} + 112 x^{3} + 232 x^{2} - 112 x + 196$ $2$ $8$ $2$ $44$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 7/2]$ $[2, 3, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 14\right) x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t + 8\right) x^{2} + 8 t x + 14$ $[15, 10, 4, 0]$ $[1, 1, 1]$
2.16.44.7 $x^{16} + 4 x^{15} + 12 x^{14} + 16 x^{13} + 10 x^{12} + 48 x^{11} + 60 x^{10} + 40 x^{9} + 224 x^{8} + 88 x^{7} + 192 x^{6} + 144 x^{5} + 108 x^{4} + 192 x^{3} - 8 x^{2} - 48 x + 36$ $2$ $8$ $2$ $44$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + \left(10 t + 2\right) x^{4} + 12 t x^{2} + 8 t x + 6$ $[15, 10, 4, 0]$ $[1, 1, 1]$
2.16.44.8 $x^{16} + 4 x^{15} + 24 x^{14} + 16 x^{13} + 28 x^{12} + 16 x^{11} + 84 x^{10} + 56 x^{9} + 112 x^{8} + 24 x^{7} + 72 x^{6} + 176 x^{5} + 152 x^{4} + 272 x^{3} + 200 x^{2} + 80 x + 52$ $2$ $8$ $2$ $44$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 7/2]$ $[2, 3, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{7} + 4 x^{6} + 6 x^{4} + 8 t x^{3} + \left(12 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t + 2$ $[15, 10, 4, 0]$ $[1, 1, 1]$
2.16.46.1 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{10} + 12 x^{6} + 4 x^{4} + 8 x + 14$ $2$ $16$ $1$ $46$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 2, 3, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t + 1$ $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{10} + 12 x^{6} + 4 x^{4} + 8 x + 14$ $[31, 22, 12, 12, 0]$ $[1, 1, 2]$
2.16.48.14 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x^{2} + 8 x + 14$ $2$ $16$ $1$ $48$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 3, 7/2]$ $[2, 3, 3, 7/2]^{2}$ $t + 1$ $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x^{2} + 8 x + 14$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$
2.16.48.15 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x + 10$ $2$ $16$ $1$ $48$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 3, 7/2]$ $[2, 3, 3, 7/2]^{2}$ $t + 1$ $x^{16} + 4 x^{10} + 2 x^{8} + 8 x + 10$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$
2.16.50.5 $x^{16} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 12 x^{6} + 8 x^{3} + 30$ $2$ $16$ $1$ $50$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 2, 3, 4]$ $[2, 2, 3, 4]^{2}$ $t + 1$ $x^{16} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 12 x^{6} + 8 x^{3} + 30$ $[35, 22, 12, 12, 0]$ $[1, 1, 2]$
2.16.50.6 $x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{12} + 8 x^{9} + 8 x^{8} + 4 x^{6} + 8 x^{3} + 22$ $2$ $16$ $1$ $50$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 2, 3, 4]$ $[2, 2, 3, 4]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{12} + 8 x^{9} + 8 x^{8} + 4 x^{6} + 8 x^{3} + 22$ $[35, 22, 12, 12, 0]$ $[1, 1, 2]$
2.16.52.19 $x^{16} + 16 x^{15} + 88 x^{14} + 184 x^{13} + 100 x^{12} + 80 x^{11} + 432 x^{10} + 160 x^{9} + 32 x^{8} + 32 x^{7} - 128 x^{6} + 400 x^{5} + 8 x^{4} - 128 x^{3} + 652$ $2$ $8$ $2$ $52$ $C_4:D_4$ (as 16T34) $2$ $1$ $[3, 7/2, 4]$ $[2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + 12 x^{6} + 8 t x^{5} + \left(4 t + 12\right) x^{4} + 8 x^{3} + 28 t + 6$ $[19, 14, 8, 0]$ $[1, 1, 1]$
2.16.52.20 $x^{16} + 16 x^{15} + 80 x^{14} + 128 x^{13} + 136 x^{12} + 208 x^{11} + 320 x^{10} + 128 x^{9} + 204 x^{8} + 672 x^{7} + 544 x^{6} + 720 x^{4} + 480 x^{3} + 900$ $2$ $8$ $2$ $52$ $C_4:D_4$ (as 16T34) $2$ $1$ $[3, 7/2, 4]$ $[2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(8 t + 12\right) x^{6} + 12 x^{4} + 8 x^{3} + 30$ $[19, 14, 8, 0]$ $[1, 1, 1]$
2.16.52.21 $x^{16} + 16 x^{15} + 80 x^{14} + 128 x^{13} + 108 x^{12} - 16 x^{11} + 136 x^{10} + 64 x^{9} + 96 x^{8} + 352 x^{7} + 560 x^{6} - 64 x^{5} - 8 x^{4} + 384 x^{3} - 144 x^{2} + 588$ $2$ $8$ $2$ $52$ $C_4:D_4$ (as 16T34) $2$ $1$ $[3, 7/2, 4]$ $[2, 3, 7/2, 4]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(8 t + 12\right) x^{6} + 4 t x^{4} + 8 x^{3} + 8 t x^{2} + 4 t + 26$ $[19, 14, 8, 0]$ $[1, 1, 1]$
2.16.54.27 $x^{16} + 12 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 14$ $2$ $16$ $1$ $54$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 7/2, 4]$ $[2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{16} + 12 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 14$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$
2.16.54.28 $x^{16} + 4 x^{14} + 8 x^{13} + 12 x^{12} + 8 x^{9} + 14 x^{8} + 8 x^{7} + 4 x^{4} + 14$ $2$ $16$ $1$ $54$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 7/2, 4]$ $[2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 12 x^{12} + 8 x^{9} + 14 x^{8} + 8 x^{7} + 4 x^{4} + 14$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$
2.16.54.29 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 6 x^{8} + 8 x^{7} + 12 x^{4} + 10$ $2$ $16$ $1$ $54$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 7/2, 4]$ $[2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 6 x^{8} + 8 x^{7} + 12 x^{4} + 10$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$
2.16.54.30 $x^{16} + 8 x^{15} + 12 x^{14} + 8 x^{12} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 14$ $2$ $16$ $1$ $54$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 7/2, 4]$ $[2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{16} + 8 x^{15} + 12 x^{14} + 8 x^{12} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 14$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$
2.16.54.31 $x^{16} + 12 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $2$ $16$ $1$ $54$ $C_4:D_4$ (as 16T34) $2$ $1$ $[2, 3, 7/2, 4]$ $[2, 3, 7/2, 4]^{2}$ $t + 1$ $x^{16} + 12 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$
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