$p$-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 (10 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
3.3.0.1	$3$	x^3 - x + 1	$3$	$1$	$3$	$0$	$C_3$ (as 3T1)	$3$	$1$	$[\ ]^{3}$
3.3.3.1	$3$	x^3 + 6x + 3	$3$	$3$	$1$	$3$	$S_3$ (as 3T2)	$1$	$2$	$[3/2]_{2}$
3.3.3.2	$3$	x^3 + 3x + 3	$3$	$3$	$1$	$3$	$S_3$ (as 3T2)	$1$	$2$	$[3/2]_{2}$
3.3.4.1	$3$	x^3 - 3x^2 + 21	$3$	$3$	$1$	$4$	$C_3$ (as 3T1)	$1$	$1$	$[2]$
3.3.4.2	$3$	x^3 - 3x^2 + 3	$3$	$3$	$1$	$4$	$C_3$ (as 3T1)	$1$	$1$	$[2]$
3.3.4.3	$3$	x^3 - 3x^2 + 12	$3$	$3$	$1$	$4$	$C_3$ (as 3T1)	$1$	$1$	$[2]$
3.3.4.4	$3$	x^3 + 3x^2 + 3	$3$	$3$	$1$	$4$	$S_3$ (as 3T2)	$2$	$1$	$[2]^{2}$
3.3.5.1	$3$	x^3 + 3	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$1$	$2$	$[5/2]_{2}$
3.3.5.2	$3$	x^3 + 21	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$1$	$2$	$[5/2]_{2}$
3.3.5.3	$3$	x^3 + 12	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$1$	$2$	$[5/2]_{2}$