$p$-adic field search results

Results (11 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
5.8.0.1	$8$	$x^{8} + x^{4} + 3 x^{2} + 4 x + 2$	$5$	$1$	$8$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]^{8}$	$t^{8} + t^{4} + 3 t^{2} + 4 t + 2$	$x - 5$	$[0]$	$[]$
5.8.4.1	$8$	$x^{8} + 80 x^{7} + 2428 x^{6} + 33688 x^{5} + 195810 x^{4} + 305952 x^{3} + 870132 x^{2} + 1037416 x + 503089$	$5$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$t^{4} + 4 t^{2} + 4 t + 2$	$x^{2} + 20 x + 5$	$[0]$	$[1]$
5.8.4.2	$8$	$x^{8} + 100 x^{4} - 500 x^{2} + 1250$	$5$	$2$	$4$	$4$	$C_8$ (as 8T1)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$t^{4} + 4 t^{2} + 4 t + 2$	$x^{2} + 5 t$	$[0]$	$[1]$
5.8.6.1	$8$	$x^{8} + 16 x^{7} + 104 x^{6} + 352 x^{5} + 674 x^{4} + 784 x^{3} + 776 x^{2} + 928 x + 721$	$5$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{4} + 5$	$[0]$	$[1]$
5.8.6.2	$8$	$x^{8} + 10 x^{4} - 25$	$5$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{4} + 5 t + 15$	$[0]$	$[1]$
5.8.6.3	$8$	$x^{8} - 50 x^{4} - 175$	$5$	$4$	$2$	$6$	$C_8$ (as 8T1)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{4} + 20 t + 15$	$[0]$	$[1]$
5.8.6.4	$8$	$x^{8} - 20 x^{4} + 50$	$5$	$4$	$2$	$6$	$C_8$ (as 8T1)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{4} + 5 t$	$[0]$	$[1]$
5.8.7.1	$8$	$x^{8} + 20$	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$t + 3$	$x^{8} + 20$	$[0]$	$[2]$
5.8.7.2	$8$	$x^{8} + 5$	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$t + 3$	$x^{8} + 5$	$[0]$	$[2]$
5.8.7.3	$8$	$x^{8} + 10$	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$t + 3$	$x^{8} + 10$	$[0]$	$[2]$
5.8.7.4	$8$	$x^{8} + 15$	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$t + 3$	$x^{8} + 15$	$[0]$	$[2]$