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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 (11 matches)

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
5.8.0.1	$8$	x⁸ + x⁴ + 3x² + 4x + 2	$5$	$1$	$8$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]^{8}$	$[0]$	$[]$
5.8.4.1	$8$	x⁸ + 80x⁷ + 2428x⁶ + 33688x⁵ + 195810x⁴ + 305952x³ + 870132x² + 1037416x + 503089	$5$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$[0]$	$[1]$
5.8.4.2	$8$	x⁸ + 100x⁴ - 500x² + 1250	$5$	$2$	$4$	$4$	$C_8$ (as 8T1)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$[0]$	$[1]$
5.8.6.1	$8$	x⁸ + 16x⁷ + 104x⁶ + 352x⁵ + 674x⁴ + 784x³ + 776x² + 928x + 721	$5$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
5.8.6.2	$8$	x⁸ + 10x⁴ - 25	$5$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
5.8.6.3	$8$	x⁸ - 50x⁴ - 175	$5$	$4$	$2$	$6$	$C_8$ (as 8T1)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
5.8.6.4	$8$	x⁸ - 20x⁴ + 50	$5$	$4$	$2$	$6$	$C_8$ (as 8T1)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
5.8.7.1	$8$	x⁸ + 20	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$
5.8.7.2	$8$	x⁸ + 5	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$
5.8.7.3	$8$	x⁸ + 10	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$
5.8.7.4	$8$	x⁸ + 15	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$

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