$p$-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
2.14.12.1	$14$	$x^{14} + 7 x^{13} + 28 x^{12} + 77 x^{11} + 161 x^{10} + 266 x^{9} + 357 x^{8} + 397 x^{7} + 371 x^{6} + 224 x^{5} + 21 x^{4} + 7 x^{3} + 70 x^{2} + 35 x + 7$	$2$	$7$	$2$	$12$	$(C_7:C_3) \times C_2$ (as 14T5)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t^{2} + t + 1$	$x^{7} + 2$	$[0]$	$[3]$