$p$-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
2.14.14.23	$14$	$x^{14} - 12 x^{13} + 142 x^{12} - 640 x^{11} + 2548 x^{10} - 3904 x^{9} + 12280 x^{8} - 34048 x^{7} + 159536 x^{6} - 121792 x^{5} - 109152 x^{4} - 121344 x^{3} + 389056 x^{2} - 197120 x + 9856$	$2$	$2$	$7$	$14$	$F_8$ (as 14T6)	$7$	$1$	$[2]$	$[2, 2, 2]^{7}$	$t^{7} + t + 1$	$x^{2} + \left(2 t^{6} + 2 t^{4} + 2 t^{3} + 2 t\right) x + 4 t^{5} + 4 t^{2} + 4 t + 2$	$[1, 0]$	$[1]$
2.14.14.3	$14$	$x^{14} + 2 x^{13} + 30 x^{12} + 904 x^{11} + 7764 x^{10} + 37432 x^{9} + 112280 x^{8} + 199872 x^{7} + 219312 x^{6} + 231392 x^{5} + 682912 x^{4} + 1931904 x^{3} + 3165120 x^{2} + 2978944 x + 1331328$	$2$	$2$	$7$	$14$	$F_8$ (as 14T6)	$7$	$1$	$[2]$	$[2, 2, 2]^{7}$	$t^{7} + t + 1$	$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2} + 2$	$[1, 0]$	$[1]$