$p$-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
2.10.10.1	$10$	$x^{10} + 4 x^{9} + 6 x^{8} + 80 x^{7} + 616 x^{6} + 2352 x^{5} + 6000 x^{4} + 11136 x^{3} + 13776 x^{2} + 9472 x + 2784$	$2$	$2$	$5$	$10$	$C_2^4 : C_5$ (as 10T8)	$5$	$1$	$[2]$	$[2, 2, 2, 2]^{5}$	$t^{5} + t^{2} + 1$	$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 2$	$[1, 0]$	$[1]$
2.10.10.2	$10$	$x^{10} + 4 x^{9} + 46 x^{8} + 328 x^{7} + 1232 x^{6} + 4048 x^{5} + 5824 x^{4} + 6496 x^{3} - 8272 x^{2} - 14336 x - 17632$	$2$	$2$	$5$	$10$	$C_2^4 : C_5$ (as 10T8)	$5$	$1$	$[2]$	$[2, 2, 2, 2]^{5}$	$t^{5} + t^{2} + 1$	$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 4 t^{3} + 4 t + 6$	$[1, 0]$	$[1]$
2.10.10.3	$10$	$x^{10} + 10 x^{9} + 74 x^{8} + 320 x^{7} + 1104 x^{6} + 2752 x^{5} + 6176 x^{4} + 12096 x^{3} + 17712 x^{2} + 15968 x + 8416$	$2$	$2$	$5$	$10$	$C_2^4 : C_5$ (as 10T8)	$5$	$1$	$[2]$	$[2, 2, 2, 2]^{5}$	$t^{5} + t^{2} + 1$	$x^{2} + \left(2 t^{4} + 2 t + 2\right) x + 4 t^{4} + 4 t^{2} + 6$	$[1, 0]$	$[1]$