$p$-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 (30 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content
2.3.2.1	$3$	x^3 - 2	$2$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
3.3.3.1	$3$	x^3 + 6x + 3	$3$	$3$	$1$	$3$	$S_3$ (as 3T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$
3.3.3.2	$3$	x^3 + 3x + 3	$3$	$3$	$1$	$3$	$S_3$ (as 3T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$
3.3.4.4	$3$	x^3 + 3x^2 + 3	$3$	$3$	$1$	$4$	$S_3$ (as 3T2)	$2$	$1$	$[2]$	$[2]^{2}$
3.3.5.1	$3$	x^3 + 3	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$
3.3.5.2	$3$	x^3 + 21	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$
3.3.5.3	$3$	x^3 + 12	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$
5.3.2.1	$3$	x^3 - 5	$5$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
11.3.2.1	$3$	x^3 - 11	$11$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
17.3.2.1	$3$	x^3 - 17	$17$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
23.3.2.1	$3$	x^3 - 23	$23$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
29.3.2.1	$3$	x^3 - 29	$29$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
41.3.2.1	$3$	x^3 - 41	$41$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
47.3.2.1	$3$	x^3 - 47	$47$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
53.3.2.1	$3$	x^3 - 53	$53$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
59.3.2.1	$3$	x^3 - 59	$59$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
71.3.2.1	$3$	x^3 - 71	$71$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
83.3.2.1	$3$	x^3 - 83	$83$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
89.3.2.1	$3$	x^3 - 89	$89$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
101.3.2.1	$3$	x^3 - 101	$101$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
107.3.2.1	$3$	x^3 - 107	$107$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
113.3.2.1	$3$	x^3 - 113	$113$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
131.3.2.1	$3$	x^3 - 131	$131$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
137.3.2.1	$3$	x^3 - 137	$137$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
149.3.2.1	$3$	x^3 - 149	$149$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
167.3.2.1	$3$	x^3 - 167	$167$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
173.3.2.1	$3$	x^3 - 173	$173$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
179.3.2.1	$3$	x^3 - 179	$179$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
191.3.2.1	$3$	x^3 - 191	$191$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
197.3.2.1	$3$	x^3 - 197	$197$	$3$	$1$	$2$	$S_3$ (as 3T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$