$p$-adic field search results

Results (displaying both matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
3.12.9.1	$12$	$x^{12} + 18 x^{4} - 27$	$3$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$t^{3} + 2 t + 1$	$x^{4} + 3 t$	$[0]$	$[2]$
3.12.9.2	$12$	$x^{12} + 8 x^{10} + 4 x^{9} + 33 x^{8} + 24 x^{7} - 10 x^{6} - 96 x^{5} + 163 x^{4} + 12 x^{3} - 6 x^{2} + 68 x + 172$	$3$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$t^{3} + 2 t + 1$	$x^{4} + 3$	$[0]$	$[2]$