$p$-adic field search results

Results (5 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
2.4.4.1	$4$	$x^{4} + 6 x^{3} + 17 x^{2} + 24 x + 13$	$2$	$2$	$2$	$4$	$C_2^2$ (as 4T2)	$2$	$1$	$[2]$	$[2]^{2}$	$t^{2} + t + 1$	$x^{2} + 2 x + 2$	$[1, 0]$	$[1]$
2.4.4.2	$4$	$x^{4} + 4 x^{3} + 4 x^{2} + 12$	$2$	$2$	$2$	$4$	$C_4$ (as 4T1)	$2$	$1$	$[2]$	$[2]^{2}$	$t^{2} + t + 1$	$x^{2} + 2 x + 4 t + 2$	$[1, 0]$	$[1]$
2.4.4.3	$4$	$x^{4} + 2 x^{3} + 4 x^{2} + 12 x + 12$	$2$	$2$	$2$	$4$	$D_{4}$ (as 4T3)	$2$	$1$	$[2]$	$[2, 2]^{2}$	$t^{2} + t + 1$	$x^{2} + \left(2 t + 2\right) x + 4 t + 2$	$[1, 0]$	$[1]$
2.4.4.4	$4$	$x^{4} - 2 x^{3} + 4 x^{2} + 12 x + 12$	$2$	$2$	$2$	$4$	$D_{4}$ (as 4T3)	$2$	$1$	$[2]$	$[2, 2]^{2}$	$t^{2} + t + 1$	$x^{2} + 2 t x + 4 t + 2$	$[1, 0]$	$[1]$
2.4.4.5	$4$	$x^{4} + 2 x + 2$	$2$	$4$	$1$	$4$	$S_4$ (as 4T5)	$2$	$3$	$[4/3, 4/3]$	$[4/3, 4/3]_{3}^{2}$	$t + 1$	$x^{4} + 2 x + 2$	$[1, 1, 0]$	$[1]$