$p$-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
7.5.0.1	$5$	$x^{5} + x + 4$	$7$	$1$	$5$	$0$	$C_5$ (as 5T1)	$5$	$1$	$[\ ]$	$[\ ]^{5}$	$t^{5} + t + 4$	$x - 7$	$[0]$	$[]$
7.5.4.1	$5$	$x^{5} + 7$	$7$	$5$	$1$	$4$	$F_5$ (as 5T3)	$4$	$5$	$[\ ]$	$[\ ]_{5}^{4}$	$t + 4$	$x^{5} + 7$	$[0]$	$[4]$