$p$-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
2.12.24.254	$12$	$x^{12} - 8 x^{11} + 74 x^{10} + 108 x^{9} + 146 x^{8} + 448 x^{7} + 2256 x^{6} + 3536 x^{5} + 2460 x^{4} - 1280 x^{3} - 1176 x^{2} + 784 x + 2744$	$2$	$4$	$3$	$24$	$C_4^2:C_3$ (as 12T31)	$3$	$1$	$[2, 3]$	$[2, 2, 3, 3]^{3}$	$t^{3} + t + 1$	$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(6 t^{2} + 4 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 14$	$[5, 2, 0]$	$[1, 1]$
2.12.24.94	$12$	$x^{12} + 6 x^{10} + 4 x^{9} + 126 x^{8} + 192 x^{7} + 1168 x^{6} + 1600 x^{5} + 3948 x^{4} + 3456 x^{3} + 3704 x^{2} + 1744 x - 376$	$2$	$4$	$3$	$24$	$C_4^2:C_3$ (as 12T31)	$3$	$1$	$[2, 3]$	$[2, 2, 3, 3]^{3}$	$t^{3} + t + 1$	$x^{4} + \left(6 t^{2} + 6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{2} + 12 t + 2$	$[5, 2, 0]$	$[1, 1]$