$p$-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
3.14.12.1	$14$	$x^{14} + 14 x^{13} + 98 x^{12} + 448 x^{11} + 1484 x^{10} + 3752 x^{9} + 7448 x^{8} + 11782 x^{7} + 14938 x^{6} + 15008 x^{5} + 11452 x^{4} + 6328 x^{3} + 2632 x^{2} + 896 x + 185$	$3$	$7$	$2$	$12$	$F_7$ (as 14T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t^{2} + 2 t + 2$	$x^{7} + 3$	$[0]$	$[3]$