$p$-adic field search results

Results (unique match)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
2.8.16.6	$8$	$x^{8} + 4 x^{7} + 24 x^{6} + 48 x^{5} + 56 x^{4} + 56 x^{3} + 64 x^{2} + 48 x + 36$	$2$	$4$	$2$	$16$	$C_2^3$ (as 8T3)	$2$	$1$	$[2, 3]$	$[2, 3]^{2}$	$t^{2} + t + 1$	$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 6\right) x^{2} + 4 x + 6$	$[5, 2, 0]$	$[1, 1]$