$p$-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
3.8.6.1	$8$	$x^{8} + 9$	$3$	$4$	$2$	$6$	$Q_8$ (as 8T5)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 2 t + 2$	$x^{4} + 3 t + 3$	$[0]$	$[1]$
3.8.6.2	$8$	$x^{8} + 6 x^{5} + 6 x^{4} + 18 x^{2} + 18 x + 9$	$3$	$4$	$2$	$6$	$D_4$ (as 8T4)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 2 t + 2$	$x^{4} + \left(3 t + 6\right) x + 3$	$[0]$	$[1]$
3.8.6.3	$8$	$x^{8} - 6 x^{4} + 18$	$3$	$4$	$2$	$6$	$C_8:C_2$ (as 8T7)	$4$	$4$	$[\ ]$	$[\ ]_{4}^{4}$	$t^{2} + 2 t + 2$	$x^{4} + 3 t$	$[0]$	$[1]$