$p$-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
7.9.0.1	$9$	x^9 + x^2 - 6x + 2	$7$	$1$	$9$	$0$	$C_9$ (as 9T1)	$9$	$1$	$[\ ]^{9}$
7.9.6.1	$9$	x^9 + 42x^6 + 539x^3 + 2744	$7$	$3$	$3$	$6$	$C_3^2$ (as 9T2)	$3$	$3$	$[\ ]_{3}^{3}$
7.9.6.2	$9$	x^9 - 49x^3 + 686	$7$	$3$	$3$	$6$	$C_9$ (as 9T1)	$3$	$3$	$[\ ]_{3}^{3}$
7.9.6.3	$9$	x^9 - 14x^6 + 49x^3 - 1372	$7$	$3$	$3$	$6$	$C_9$ (as 9T1)	$3$	$3$	$[\ ]_{3}^{3}$
7.9.8.1	$9$	x^9 + 14	$7$	$9$	$1$	$8$	$C_9:C_3$ (as 9T6)	$3$	$9$	$[\ ]_{9}^{3}$
7.9.8.2	$9$	x^9 - 7	$7$	$9$	$1$	$8$	$C_9:C_3$ (as 9T6)	$3$	$9$	$[\ ]_{9}^{3}$
7.9.8.3	$9$	x^9 - 28	$7$	$9$	$1$	$8$	$C_9:C_3$ (as 9T6)	$3$	$9$	$[\ ]_{9}^{3}$