$p$-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
19.4.0.1	$4$	$x^{4} + 2 x^{2} + 11 x + 2$	$19$	$1$	$4$	$0$	$C_4$ (as 4T1)	$4$	$1$	$[\ ]$	$[\ ]^{4}$	$t^{4} + 2 t^{2} + 11 t + 2$	$x - 19$	$[0]$	$[]$
19.4.2.1	$4$	$x^{4} + 36 x^{3} + 366 x^{2} + 756 x + 6445$	$19$	$2$	$2$	$2$	$C_2^2$ (as 4T2)	$2$	$2$	$[\ ]$	$[\ ]_{2}^{2}$	$t^{2} + 18 t + 2$	$x^{2} + 19$	$[0]$	$[1]$
19.4.2.2	$4$	$x^{4} - 2888 x^{3} - 767106 x^{2} - 76532 x + 722$	$19$	$2$	$2$	$2$	$C_4$ (as 4T1)	$2$	$2$	$[\ ]$	$[\ ]_{2}^{2}$	$t^{2} + 18 t + 2$	$x^{2} + \left(190 t + 266\right) x + 19 t$	$[0]$	$[1]$
19.4.3.1	$4$	$x^{4} + 19$	$19$	$4$	$1$	$3$	$D_{4}$ (as 4T3)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t + 17$	$x^{4} + 19$	$[0]$	$[2]$
19.4.3.2	$4$	$x^{4} + 38$	$19$	$4$	$1$	$3$	$D_{4}$ (as 4T3)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t + 17$	$x^{4} + 38$	$[0]$	$[2]$