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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
13.8.0.1	$8$	x⁸ + 8x⁴ + 12x³ + 2x² + 3x + 2	$13$	$1$	$8$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]^{8}$	$[0]$	$[]$
13.8.4.1	$8$	x⁸ + 520x⁷ + 101458x⁶ + 8810644x⁵ + 288610205x⁴ + 142111548x³ + 982314112x² + 3617879976x + 920156436	$13$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$[0]$	$[1]$
13.8.4.2	$8$	x⁸ + 507x⁴ - 26364x² + 57122	$13$	$2$	$4$	$4$	$C_8$ (as 8T1)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$[0]$	$[1]$
13.8.6.1	$8$	x⁸ + 48x⁷ + 872x⁶ + 7200x⁵ + 24242x⁴ + 15024x³ + 14408x² + 86496x + 254881	$13$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
13.8.6.2	$8$	x⁸ + 130x⁴ - 1521	$13$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
13.8.6.3	$8$	x⁸ - 1586x⁴ - 198575	$13$	$4$	$2$	$6$	$C_8$ (as 8T1)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
13.8.6.4	$8$	x⁸ - 156x⁴ + 338	$13$	$4$	$2$	$6$	$C_8$ (as 8T1)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
13.8.7.1	$8$	x⁸ + 52	$13$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$
13.8.7.2	$8$	x⁸ + 13	$13$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$
13.8.7.3	$8$	x⁸ + 26	$13$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$
13.8.7.4	$8$	x⁸ + 91	$13$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$

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