$p$-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
2.12.20.53	$12$	$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2$	$2$	$12$	$1$	$20$	$S_3\times A_4$ (as 12T43)	$6$	$3$	$[2, 2]$	$[2, 2]_{3}^{6}$	$t + 1$	$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2$	$[9, 6, 0]$	$[3, 2]$