$p$-adic field search results

Results (8 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
3.8.0.1	$8$	$x^{8} + 2 x^{5} + x^{4} + 2 x^{2} + 2 x + 2$	$3$	$1$	$8$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]^{8}$	$t^{8} + 2 t^{5} + t^{4} + 2 t^{2} + 2 t + 2$	$x - 3$	$[0]$	$[]$
3.8.4.1	$8$	$x^{8} + 4 x^{7} + 16 x^{6} + 36 x^{5} + 94 x^{4} + 116 x^{3} + 144 x^{2} + 36 x + 229$	$3$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$t^{4} + 2 t^{3} + 2$	$x^{2} + 3$	$[0]$	$[1]$
3.8.4.2	$8$	$x^{8} - 6 x^{6} + 162$	$3$	$2$	$4$	$4$	$C_8$ (as 8T1)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$t^{4} + 2 t^{3} + 2$	$x^{2} + 3 t$	$[0]$	$[1]$
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)	$4$	$4$	$[\ ]$	$[\ ]_{4}^{4}$	$t^{2} + 2 t + 2$	$x^{4} + 3 t$	$[0]$	$[1]$
3.8.7.1	$8$	$x^{8} + 3$	$3$	$8$	$1$	$7$	$QD_{16}$ (as 8T8)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$t + 1$	$x^{8} + 3$	$[0]$	$[2]$
3.8.7.2	$8$	$x^{8} + 6$	$3$	$8$	$1$	$7$	$QD_{16}$ (as 8T8)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$t + 1$	$x^{8} + 6$	$[0]$	$[2]$