$p$-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
2.12.20.39	$12$	$x^{12} + 4 x^{11} + 12 x^{10} + 20 x^{9} + 40 x^{8} + 48 x^{7} + 44 x^{6} + 32 x^{5} + 52 x^{4} + 24 x^{3} + 24 x^{2} + 36$	$2$	$6$	$2$	$20$	$C_2^2:S_4$ (as 12T69)	$2$	$3$	$[8/3]$	$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$	$t^{2} + t + 1$	$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 6$	$[5, 0]$	$[1, 1]$