$p$-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
2.12.18.59	$12$	$x^{12} + 6 x^{11} + 22 x^{10} + 56 x^{9} + 126 x^{8} + 240 x^{7} + 332 x^{6} - 18 x^{5} - 459 x^{4} - 394 x^{3} - 344 x^{2} + 138 x + 423$	$2$	$4$	$3$	$18$	$A_4$ (as 12T4)	$3$	$1$	$[2, 2]$	$[2, 2]^{3}$	$t^{3} + t + 1$	$x^{4} + 2 x^{3} + 2 x^{2} + 6$	$[3, 2, 0]$	$[1]$