$p$-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
3.12.6.1	$12$	$x^{12} + 18 x^{8} + 81 x^{4} - 486 x^{2} + 1458$	$3$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$	$x^{2} + 3 t$	$[0]$	$[1]$
3.12.6.2	$12$	$x^{12} + 22 x^{10} + 177 x^{8} + 4 x^{7} + 644 x^{6} - 100 x^{5} + 876 x^{4} - 224 x^{3} + 1076 x^{2} + 344 x + 112$	$3$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$	$x^{2} + 3$	$[0]$	$[1]$