$p$-adic field search results

Degree	Residue characteristic	Galois group	Galois unramified degree
Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree
Residue field degree	Top slope	Wild inertia subgroup

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Results (7 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
5.4.0.1	$4$	x^4 + x^2 - 2x + 2	$5$	$1$	$4$	$0$	$C_4$ (as 4T1)	$4$	$1$	$[\ ]^{4}$
5.4.2.1	$4$	x^4 + 15x^2 + 100	$5$	$2$	$2$	$2$	$C_2^2$ (as 4T2)	$2$	$2$	$[\ ]_{2}^{2}$
5.4.2.2	$4$	x^4 - 5x^2 + 50	$5$	$2$	$2$	$2$	$C_4$ (as 4T1)	$2$	$2$	$[\ ]_{2}^{2}$
5.4.3.1	$4$	x^4 - 5	$5$	$4$	$1$	$3$	$C_4$ (as 4T1)	$1$	$4$	$[\ ]_{4}$
5.4.3.2	$4$	x^4 - 20	$5$	$4$	$1$	$3$	$C_4$ (as 4T1)	$1$	$4$	$[\ ]_{4}$
5.4.3.3	$4$	x^4 + 10	$5$	$4$	$1$	$3$	$C_4$ (as 4T1)	$1$	$4$	$[\ ]_{4}$
5.4.3.4	$4$	x^4 + 40	$5$	$4$	$1$	$3$	$C_4$ (as 4T1)	$1$	$4$	$[\ ]_{4}$