$p$-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
2.8.16.20	$8$	$x^{8} - 4 x^{6} + 8 x^{5} + 20 x^{4} - 16 x^{3} + 8 x^{2} + 16 x + 4$	$2$	$4$	$2$	$16$	$V_4^2:S_3$ (as 8T34)	$2$	$3$	$[8/3, 8/3]$	$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$	$t^{2} + t + 1$	$x^{4} + 4 t x^{2} + 4 x + 2$	$[5, 4, 0]$	$[1]$