$p$-adic field search results

Results (3 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
2.8.8.11	$8$	$x^{8} + 4 x^{7} + 14 x^{6} + 32 x^{5} + 55 x^{4} + 60 x^{3} + 36 x^{2} + 18 x + 9$	$2$	$4$	$2$	$8$	$S_4$ (as 8T14)	$2$	$3$	$[4/3, 4/3]$	$[4/3, 4/3]_{3}^{2}$	$t^{2} + t + 1$	$x^{4} + 2 x^{2} + 2 x + 2$	$[1, 1, 0]$	$[1]$
2.8.16.8	$8$	$x^{8} + 4 x^{7} + 10 x^{6} + 24 x^{5} + 51 x^{4} + 48 x^{3} - 18 x^{2} + 63$	$2$	$4$	$2$	$16$	$S_4$ (as 8T14)	$2$	$3$	$[8/3, 8/3]$	$[8/3, 8/3]_{3}^{2}$	$t^{2} + t + 1$	$x^{4} + 4 x + 6$	$[5, 4, 0]$	$[1]$
2.8.16.9	$8$	$x^{8} + 4 x^{7} + 18 x^{6} + 48 x^{5} + 103 x^{4} + 144 x^{3} + 138 x^{2} + 128 x + 67$	$2$	$4$	$2$	$16$	$S_4$ (as 8T14)	$2$	$3$	$[8/3, 8/3]$	$[8/3, 8/3]_{3}^{2}$	$t^{2} + t + 1$	$x^{4} + 4 x^{2} + 4 x + 6$	$[5, 4, 0]$	$[1]$