$p$-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
2.6.4.1	$6$	x^6 + 3x^5 + 6x^4 + 3x^3 + 9x + 9	$2$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
3.6.7.1	$6$	x^6 + 6x^2 + 6	$3$	$6$	$1$	$7$	$S_3$ (as 6T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$
3.6.7.4	$6$	x^6 + 3x^2 + 3	$3$	$6$	$1$	$7$	$S_3$ (as 6T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$
3.6.8.5	$6$	x^6 + 9x^2 + 9	$3$	$3$	$2$	$8$	$S_3$ (as 6T2)	$2$	$1$	$[2]$	$[2]^{2}$
3.6.11.7	$6$	x^6 + 21	$3$	$6$	$1$	$11$	$S_3$ (as 6T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$
3.6.11.8	$6$	x^6 + 12	$3$	$6$	$1$	$11$	$S_3$ (as 6T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$
3.6.11.9	$6$	x^6 + 3	$3$	$6$	$1$	$11$	$S_3$ (as 6T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$
5.6.4.1	$6$	x^6 + 25x^3 + 200	$5$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
11.6.4.1	$6$	x^6 + 220x^3 + 41503	$11$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
17.6.4.1	$6$	x^6 + 136x^3 + 7803	$17$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
23.6.4.1	$6$	x^6 + 460x^3 + 181447	$23$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
29.6.4.1	$6$	x^6 + 232x^3 + 22707	$29$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
41.6.4.1	$6$	x^6 + 1435x^3 + 2904768	$41$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
47.6.4.1	$6$	x^6 + 1786x^3 + 4853173	$47$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
53.6.4.1	$6$	x^6 + 742x^3 + 351125	$53$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
59.6.4.1	$6$	x^6 + 295x^3 + 27848	$59$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
71.6.4.1	$6$	x^6 + 2272x^3 + 6709571	$71$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
83.6.4.1	$6$	x^6 + 415x^3 + 55112	$83$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
89.6.4.1	$6$	x^6 + 1513x^3 + 1710936	$89$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
101.6.4.1	$6$	x^6 + 808x^3 + 275427	$101$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
107.6.4.1	$6$	x^6 + 1498x^3 + 1431125	$107$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
113.6.4.1	$6$	x^6 + 3277x^3 + 12769000	$113$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
131.6.4.1	$6$	x^6 + 5371x^3 + 47089784	$131$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
137.6.4.1	$6$	x^6 + 2329x^3 + 4054104	$137$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
149.6.4.1	$6$	x^6 + 1192x^3 + 599427	$149$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
167.6.4.1	$6$	x^6 + 2338x^3 + 3486125	$167$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
173.6.4.1	$6$	x^6 + 2422x^3 + 3741125	$173$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
179.6.4.1	$6$	x^6 + 3580x^3 + 10990063	$179$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
191.6.4.1	$6$	x^6 + 10696x^3 + 250223179	$191$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$
197.6.4.1	$6$	x^6 + 1576x^3 + 1047843	$197$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$