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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 (32 matches)

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
2.14.22.1	$14$	$x^{14} + 2 x^{12} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$6$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.10	$14$	$x^{14} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 6$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[10/7, 10/7, 10/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 6$	$[9, 0]$	$[1, 3]$
2.14.22.11	$14$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$14$	$1$	$22$	$F_8:C_6$ (as 14T18)	$3$	$7$	$[16/7]$	$[2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 3]$
2.14.22.12	$14$	$x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$6$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.13	$14$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$14$	$1$	$22$	$C_2^3:F_8:C_3$ (as 14T35)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 3]$
2.14.22.14	$14$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 3]$
2.14.22.15	$14$	$x^{14} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 6$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[10/7, 10/7, 10/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 6$	$[9, 0]$	$[1, 3]$
2.14.22.16	$14$	$x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$6$	$7$	$[16/7]$	$[10/7, 10/7, 10/7, 16/7, 16/7, 16/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.17	$14$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{2} + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[10/7, 10/7, 10/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{2} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.18	$14$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$6$	$7$	$[16/7]$	$[10/7, 10/7, 10/7, 16/7, 16/7, 16/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.19	$14$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 6$	$2$	$14$	$1$	$22$	$C_2^3:F_8:C_3$ (as 14T35)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 6$	$[9, 0]$	$[1, 3]$
2.14.22.2	$14$	$x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 4 x^{4} + 6$	$2$	$14$	$1$	$22$	$C_2^3:F_8:C_3$ (as 14T35)	$3$	$7$	$[16/7]$	$[10/7, 10/7, 10/7, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 4 x^{4} + 6$	$[9, 0]$	$[1, 3]$
2.14.22.20	$14$	$x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$6$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 3]$
2.14.22.21	$14$	$x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 4 x + 6$	$2$	$14$	$1$	$22$	$F_8:C_6$ (as 14T18)	$6$	$7$	$[16/7]$	$[16/7, 16/7, 16/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 4 x + 6$	$[9, 0]$	$[1, 3]$
2.14.22.22	$14$	$x^{14} + 2 x^{9} + 4 x^{2} + 6$	$2$	$14$	$1$	$22$	$F_8:C_6$ (as 14T18)	$6$	$7$	$[16/7]$	$[16/7, 16/7, 16/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{9} + 4 x^{2} + 6$	$[9, 0]$	$[1, 3]$
2.14.22.23	$14$	$x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{2} + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$6$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{2} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.24	$14$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2$	$2$	$14$	$1$	$22$	$F_8:C_6$ (as 14T18)	$3$	$7$	$[16/7]$	$[2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.25	$14$	$x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 3]$
2.14.22.26	$14$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{2} + 6$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[10/7, 10/7, 10/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{2} + 6$	$[9, 0]$	$[1, 3]$
2.14.22.27	$14$	$x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 6$	$2$	$14$	$1$	$22$	$C_2^3:F_8:C_3$ (as 14T35)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 6$	$[9, 0]$	$[1, 3]$
2.14.22.28	$14$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 2$	$2$	$14$	$1$	$22$	$F_8:C_6$ (as 14T18)	$3$	$7$	$[16/7]$	$[2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.29	$14$	$x^{14} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 4 x^{3} + 4 x + 6$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 4 x^{3} + 4 x + 6$	$[9, 0]$	$[1, 3]$
2.14.22.3	$14$	$x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 6$	$2$	$14$	$1$	$22$	$C_2^3:F_8:C_3$ (as 14T35)	$3$	$7$	$[16/7]$	$[10/7, 10/7, 10/7, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 6$	$[9, 0]$	$[1, 3]$
2.14.22.30	$14$	$x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 6$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 6$	$[9, 0]$	$[1, 3]$
2.14.22.31	$14$	$x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 6$	$2$	$14$	$1$	$22$	$C_2^3:F_8:C_3$ (as 14T35)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 6$	$[9, 0]$	$[1, 3]$
2.14.22.32	$14$	$x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{2} + 6$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{2} + 6$	$[9, 0]$	$[1, 3]$
2.14.22.4	$14$	$x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 3]$
2.14.22.5	$14$	$x^{14} + 2 x^{9} + 4 x^{4} + 6$	$2$	$14$	$1$	$22$	$F_8:C_3$ (as 14T11)	$3$	$7$	$[16/7]$	$[16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{9} + 4 x^{4} + 6$	$[9, 0]$	$[1, 3]$
2.14.22.6	$14$	$x^{14} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 3]$
2.14.22.7	$14$	$x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 6$	$2$	$14$	$1$	$22$	$C_2\wr C_7:C_3$ (as 14T44)	$3$	$7$	$[16/7]$	$[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 6$	$[9, 0]$	$[1, 3]$
2.14.22.8	$14$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$	$2$	$14$	$1$	$22$	$F_8:C_3$ (as 14T11)	$3$	$7$	$[16/7]$	$[16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$	$[9, 0]$	$[1, 3]$
2.14.22.9	$14$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x + 6$	$2$	$14$	$1$	$22$	$F_8:C_6$ (as 14T18)	$3$	$7$	$[16/7]$	$[2, 16/7, 16/7, 16/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x + 6$	$[9, 0]$	$[1, 3]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.