$p$-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
5.7.0.1	$7$	$x^{7} + 3 x + 3$	$5$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$	$t^{7} + 3 t + 3$	$x - 5$	$[0]$	$[]$
5.7.6.1	$7$	$x^{7} + 5$	$5$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 3$	$x^{7} + 5$	$[0]$	$[6]$