$p$-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
3.9.12.1	$9$	$x^{9} + 18 x^{8} + 108 x^{7} + 225 x^{6} + 108 x^{5} + 324 x^{4} + 675 x^{3} + 4050 x^{2} - 3861$	$3$	$3$	$3$	$12$	$C_3^2$ (as 9T2)	$3$	$1$	$[2]$	$[2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + 6 x^{2} + 18 t + 3$	$[2, 0]$	$[1]$