$p$-adic field search results

Results (4 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
3.6.6.1	$6$	$x^{6} - 6 x^{5} + 24 x^{4} + 6 x^{3} + 18 x + 9$	$3$	$3$	$2$	$6$	$C_3^2:C_4$ (as 6T10)	$2$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{2}$	$t^{2} + 2 t + 2$	$x^{3} + 3 t x^{2} + \left(3 t + 6\right) x + 3$	$[1, 0]$	$[1]$
3.6.6.2	$6$	$x^{6} - 6 x^{5} + 39 x^{4} + 60 x^{3} - 18 x + 9$	$3$	$3$	$2$	$6$	$C_3^2:C_4$ (as 6T10)	$2$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{2}$	$t^{2} + 2 t + 2$	$x^{3} + \left(6 t + 3\right) x^{2} + 3 t x + 3$	$[1, 0]$	$[1]$
3.6.8.1	$6$	$x^{6} - 6 x^{5} + 45 x^{4} + 6 x^{3} - 18 x^{2} + 9$	$3$	$3$	$2$	$8$	$C_3^2:C_4$ (as 6T10)	$4$	$1$	$[2]$	$[2, 2]^{4}$	$t^{2} + 2 t + 2$	$x^{3} + \left(6 t + 3\right) x^{2} + 3$	$[2, 0]$	$[2]$
3.6.8.2	$6$	$x^{6} - 12 x^{5} + 72 x^{4} + 6 x^{3} + 72 x^{2} + 90$	$3$	$3$	$2$	$8$	$C_3^2:C_4$ (as 6T10)	$4$	$1$	$[2]$	$[2, 2]^{4}$	$t^{2} + 2 t + 2$	$x^{3} + 6 t x^{2} + 9 t + 12$	$[2, 0]$	$[2]$