$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (displaying both matches)

 

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
5.13.0.1	x^13 + x^2 - 2x + 2	$5$	$1$	$13$	$0$	$C_{13}$ (as 13T1)	$ [\ ]^{13}$
5.13.12.1	x^13 - 5	$5$	$13$	$1$	$12$	$C_{13}:C_4$ (as 13T4)	$ [\ ]_{13}^{4}$