$p$-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
7.4.0.1	$4$	$x^{4} + 5 x^{2} + 4 x + 3$	$7$	$1$	$4$	$0$	$C_4$ (as 4T1)	$4$	$1$	$[\ ]$	$[\ ]^{4}$	$t^{4} + 5 t^{2} + 4 t + 3$	$x - 7$	$[0]$	$[]$
7.4.2.1	$4$	$x^{4} + 12 x^{3} + 56 x^{2} + 120 x + 268$	$7$	$2$	$2$	$2$	$C_2^2$ (as 4T2)	$2$	$2$	$[\ ]$	$[\ ]_{2}^{2}$	$t^{2} + 6 t + 3$	$x^{2} + 7$	$[0]$	$[1]$
7.4.2.2	$4$	$x^{4} - 42 x^{2} + 147$	$7$	$2$	$2$	$2$	$C_4$ (as 4T1)	$2$	$2$	$[\ ]$	$[\ ]_{2}^{2}$	$t^{2} + 6 t + 3$	$x^{2} + 7 t$	$[0]$	$[1]$
7.4.3.1	$4$	$x^{4} + 7$	$7$	$4$	$1$	$3$	$D_{4}$ (as 4T3)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t + 4$	$x^{4} + 7$	$[0]$	$[2]$
7.4.3.2	$4$	$x^{4} + 21$	$7$	$4$	$1$	$3$	$D_{4}$ (as 4T3)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t + 4$	$x^{4} + 21$	$[0]$	$[2]$