$p$-adic field search results

Results (displaying both matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
2.8.14.5	$8$	$x^{8} + 2 x^{7} + 2 x^{6} + 2$	$2$	$8$	$1$	$14$	$C_2^3:C_7$ (as 8T25)	$7$	$1$	$[2, 2, 2]$	$[2, 2, 2]^{7}$	$t + 1$	$x^{8} + 2 x^{7} + 2 x^{6} + 2$	$[7, 6, 6, 0]$	$[7]$
2.8.14.6	$8$	$x^{8} + 2 x^{7} + 2 x^{4} + 6$	$2$	$8$	$1$	$14$	$C_2^3:C_7$ (as 8T25)	$7$	$1$	$[2, 2, 2]$	$[2, 2, 2]^{7}$	$t + 1$	$x^{8} + 2 x^{7} + 2 x^{4} + 6$	$[7, 7, 4, 0]$	$[7]$