$p$-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
19.13.0.1	x^13 - x + 4	$19$	$1$	$13$	$0$	$C_{13}$ (as 13T1)	$ [\ ]^{13}$
19.13.12.1	x^13 - 19	$19$	$13$	$1$	$12$	$F_{13}$ (as 13T6)	$ [\ ]_{13}^{12}$