$p$-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
2.15.10.1	$15$	$x^{15} + 13 x^{12} + 3 x^{10} + 13 x^{9} - 174 x^{7} - 45 x^{6} + 3 x^{5} + 513 x^{4} + 63 x^{2} - 216 x + 109$	$2$	$3$	$5$	$10$	$S_3 \times C_5$ (as 15T4)	$10$	$3$	$[\ ]$	$[\ ]_{3}^{10}$	$t^{5} + t^{2} + 1$	$x^{3} + 2$	$[0]$	$[2]$