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Degree	Residue characteristic	Galois group	Galois unramified degree	Assoc. Inertia

Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree	Indices

Residue field degree	Top slope	Wild	Visible	Wild inertia subgroup

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Results (1-50 of 128 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
7.14.14.28	$14$	$x^{14} + 28 x^{2} + 14 x + 21$	$7$	$14$	$1$	$14$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$t + 4$	$x^{14} + 28 x^{2} + 14 x + 21$	$[1, 0]$	$[1, 1]$
7.14.14.29	$14$	$x^{14} + 35 x^{2} + 7 x + 21$	$7$	$14$	$1$	$14$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$t + 4$	$x^{14} + 35 x^{2} + 7 x + 21$	$[1, 0]$	$[1, 1]$
7.14.14.30	$14$	$x^{14} + 42 x^{2} + 21 x + 7$	$7$	$14$	$1$	$14$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$t + 4$	$x^{14} + 42 x^{2} + 21 x + 7$	$[1, 0]$	$[1, 1]$
7.14.14.31	$14$	$x^{14} + 35 x^{2} + 14 x + 7$	$7$	$14$	$1$	$14$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$t + 4$	$x^{14} + 35 x^{2} + 14 x + 7$	$[1, 0]$	$[1, 1]$
7.14.14.32	$14$	$x^{14} + 7 x^{2} + 21 x + 21$	$7$	$14$	$1$	$14$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$t + 4$	$x^{14} + 7 x^{2} + 21 x + 21$	$[1, 0]$	$[1, 1]$
7.14.14.33	$14$	$x^{14} + 21 x^{2} + 7 x + 7$	$7$	$14$	$1$	$14$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$t + 4$	$x^{14} + 21 x^{2} + 7 x + 7$	$[1, 0]$	$[1, 1]$
7.14.16.28	$14$	$x^{14} + 14 x^{4} + 7 x^{3} + 7$	$7$	$14$	$1$	$16$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{4} + 7 x^{3} + 7$	$[3, 0]$	$[3, 1]$
7.14.16.30	$14$	$x^{14} + 21 x^{4} + 7 x^{3} + 21$	$7$	$14$	$1$	$16$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{6}$	$t + 4$	$x^{14} + 21 x^{4} + 7 x^{3} + 21$	$[3, 0]$	$[3, 1]$
7.14.16.31	$14$	$x^{14} + 14 x^{4} + 21 x^{3} + 21$	$7$	$14$	$1$	$16$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{4} + 21 x^{3} + 21$	$[3, 0]$	$[3, 1]$
7.14.16.32	$14$	$x^{14} + 14 x^{3} + 7$	$7$	$14$	$1$	$16$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{3} + 7$	$[3, 0]$	$[3, 1]$
7.14.18.28	$14$	$x^{14} + 21 x^{6} + 21 x^{5} + 7$	$7$	$14$	$1$	$18$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[17/12]$	$[17/12, 17/12]_{12}^{2}$	$t + 4$	$x^{14} + 21 x^{6} + 21 x^{5} + 7$	$[5, 0]$	$[1, 1]$
7.14.18.29	$14$	$x^{14} + 14 x^{5} + 7$	$7$	$14$	$1$	$18$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[17/12]$	$[17/12, 17/12]_{12}^{2}$	$t + 4$	$x^{14} + 14 x^{5} + 7$	$[5, 0]$	$[1, 1]$
7.14.18.30	$14$	$x^{14} + 7 x^{5} + 21$	$7$	$14$	$1$	$18$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[17/12]$	$[17/12, 17/12]_{12}^{2}$	$t + 4$	$x^{14} + 7 x^{5} + 21$	$[5, 0]$	$[1, 1]$
7.14.18.31	$14$	$x^{14} + 14 x^{5} + 21$	$7$	$14$	$1$	$18$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[17/12]$	$[17/12, 17/12]_{12}^{2}$	$t + 4$	$x^{14} + 14 x^{5} + 21$	$[5, 0]$	$[1, 1]$
7.14.18.32	$14$	$x^{14} + 28 x^{6} + 21 x^{5} + 21$	$7$	$14$	$1$	$18$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[17/12]$	$[17/12, 17/12]_{12}^{2}$	$t + 4$	$x^{14} + 28 x^{6} + 21 x^{5} + 21$	$[5, 0]$	$[1, 1]$
7.14.18.33	$14$	$x^{14} + 21 x^{6} + 7 x^{5} + 7$	$7$	$14$	$1$	$18$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[17/12]$	$[17/12, 17/12]_{12}^{2}$	$t + 4$	$x^{14} + 21 x^{6} + 7 x^{5} + 7$	$[5, 0]$	$[1, 1]$
7.14.22.30	$14$	$x^{14} + 28 x^{11} + 14 x^{10} + 14 x^{9} + 21 x^{7} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 28 x^{11} + 14 x^{10} + 14 x^{9} + 21 x^{7} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.31	$14$	$x^{14} + 21 x^{11} + 35 x^{10} + 21 x^{9} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 21 x^{11} + 35 x^{10} + 21 x^{9} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.32	$14$	$x^{14} + 14 x^{11} + 21 x^{9} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{11} + 21 x^{9} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.33	$14$	$x^{14} + 14 x^{11} + 42 x^{10} + 42 x^{9} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{11} + 42 x^{10} + 42 x^{9} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.35	$14$	$x^{14} + 14 x^{11} + 14 x^{10} + 14 x^{9} + 42 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{11} + 14 x^{10} + 14 x^{9} + 42 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.36	$14$	$x^{14} + 35 x^{11} + 21 x^{10} + 35 x^{9} + 14 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 35 x^{11} + 21 x^{10} + 35 x^{9} + 14 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.37	$14$	$x^{14} + 14 x^{11} + 21 x^{10} + 21 x^{9} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{11} + 21 x^{10} + 21 x^{9} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.38	$14$	$x^{14} + 14 x^{11} + 7 x^{10} + 21 x^{9} + 35 x^{7} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{11} + 7 x^{10} + 21 x^{9} + 35 x^{7} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.39	$14$	$x^{14} + 35 x^{11} + 28 x^{10} + 35 x^{9} + 42 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 35 x^{11} + 28 x^{10} + 35 x^{9} + 42 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.40	$14$	$x^{14} + 28 x^{11} + 21 x^{10} + 14 x^{9} + 35 x^{7} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 28 x^{11} + 21 x^{10} + 14 x^{9} + 35 x^{7} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.41	$14$	$x^{14} + 14 x^{10} + 35 x^{9} + 42 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{10} + 35 x^{9} + 42 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.42	$14$	$x^{14} + 7 x^{11} + 35 x^{10} + 42 x^{9} + 7 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 7 x^{11} + 35 x^{10} + 42 x^{9} + 7 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.43	$14$	$x^{14} + 28 x^{11} + 14 x^{10} + 14 x^{9} + 28 x^{7} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 28 x^{11} + 14 x^{10} + 14 x^{9} + 28 x^{7} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.47	$14$	$x^{14} + 35 x^{11} + 42 x^{10} + 28 x^{9} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 35 x^{11} + 42 x^{10} + 28 x^{9} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.48	$14$	$x^{14} + 7 x^{11} + 7 x^{10} + 42 x^{9} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 7 x^{11} + 7 x^{10} + 42 x^{9} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.49	$14$	$x^{14} + 35 x^{11} + 7 x^{9} + 14 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 35 x^{11} + 7 x^{9} + 14 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.51	$14$	$x^{14} + 14 x^{11} + 35 x^{10} + 14 x^{9} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{11} + 35 x^{10} + 14 x^{9} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.52	$14$	$x^{14} + 7 x^{11} + 7 x^{10} + 35 x^{9} + 14 x^{7} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 7 x^{11} + 7 x^{10} + 35 x^{9} + 14 x^{7} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.53	$14$	$x^{14} + 28 x^{11} + 14 x^{9} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 28 x^{11} + 14 x^{9} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.55	$14$	$x^{14} + 21 x^{11} + 14 x^{10} + 14 x^{9} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 21 x^{11} + 14 x^{10} + 14 x^{9} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.56	$14$	$x^{14} + 21 x^{11} + 28 x^{10} + 42 x^{9} + 28 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 21 x^{11} + 28 x^{10} + 42 x^{9} + 28 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.57	$14$	$x^{14} + 21 x^{11} + 35 x^{9} + 14 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 21 x^{11} + 35 x^{9} + 14 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.58	$14$	$x^{14} + 21 x^{11} + 21 x^{10} + 42 x^{9} + 21 x^{7} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 21 x^{11} + 21 x^{10} + 42 x^{9} + 21 x^{7} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.59	$14$	$x^{14} + 14 x^{10} + 35 x^{9} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{10} + 35 x^{9} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.60	$14$	$x^{14} + 7 x^{11} + 21 x^{10} + 35 x^{9} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 7 x^{11} + 21 x^{10} + 35 x^{9} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.63	$14$	$x^{14} + 21 x^{11} + 28 x^{10} + 7 x^{9} + 21$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 21 x^{11} + 28 x^{10} + 7 x^{9} + 21$	$[9, 0]$	$[3, 1]$
7.14.22.67	$14$	$x^{14} + 7 x^{11} + 28 x^{10} + 28 x^{9} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 7 x^{11} + 28 x^{10} + 28 x^{9} + 7$	$[9, 0]$	$[3, 1]$
7.14.22.69	$14$	$x^{14} + 14 x^{11} + 14 x^{10} + 21 x^{9} + 14 x^{7} + 7$	$7$	$14$	$1$	$22$	$D_7^2:C_6$ (as 14T32)	$6$	$4$	$[7/4]$	$[7/4, 7/4]_{4}^{6}$	$t + 4$	$x^{14} + 14 x^{11} + 14 x^{10} + 21 x^{9} + 14 x^{7} + 7$	$[9, 0]$	$[3, 1]$
7.14.24.55	$14$	$x^{14} + 21 x^{13} + 35 x^{11} + 21 x^{7} + 21$	$7$	$14$	$1$	$24$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[23/12]$	$[23/12, 23/12]_{12}^{2}$	$t + 4$	$x^{14} + 21 x^{13} + 35 x^{11} + 21 x^{7} + 21$	$[11, 0]$	$[1, 1]$
7.14.24.56	$14$	$x^{14} + 35 x^{13} + 7 x^{12} + 28 x^{11} + 21 x^{7} + 7$	$7$	$14$	$1$	$24$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[23/12]$	$[23/12, 23/12]_{12}^{2}$	$t + 4$	$x^{14} + 35 x^{13} + 7 x^{12} + 28 x^{11} + 21 x^{7} + 7$	$[11, 0]$	$[1, 1]$
7.14.24.57	$14$	$x^{14} + 7 x^{12} + 35 x^{11} + 7$	$7$	$14$	$1$	$24$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[23/12]$	$[23/12, 23/12]_{12}^{2}$	$t + 4$	$x^{14} + 7 x^{12} + 35 x^{11} + 7$	$[11, 0]$	$[1, 1]$
7.14.24.58	$14$	$x^{14} + 7 x^{13} + 14 x^{12} + 7 x^{11} + 7 x^{7} + 21$	$7$	$14$	$1$	$24$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[23/12]$	$[23/12, 23/12]_{12}^{2}$	$t + 4$	$x^{14} + 7 x^{13} + 14 x^{12} + 7 x^{11} + 7 x^{7} + 21$	$[11, 0]$	$[1, 1]$
7.14.24.59	$14$	$x^{14} + 21 x^{13} + 14 x^{12} + 35 x^{11} + 7$	$7$	$14$	$1$	$24$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[23/12]$	$[23/12, 23/12]_{12}^{2}$	$t + 4$	$x^{14} + 21 x^{13} + 14 x^{12} + 35 x^{11} + 7$	$[11, 0]$	$[1, 1]$
7.14.24.60	$14$	$x^{14} + 21 x^{13} + 14 x^{12} + 28 x^{11} + 28 x^{7} + 7$	$7$	$14$	$1$	$24$	$D_7^2:C_6$ (as 14T32)	$2$	$12$	$[23/12]$	$[23/12, 23/12]_{12}^{2}$	$t + 4$	$x^{14} + 21 x^{13} + 14 x^{12} + 28 x^{11} + 28 x^{7} + 7$	$[11, 0]$	$[1, 1]$

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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.