$p$-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

Sort order

Select

Results (1-50 of 95 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content
2.7.0.1	$7$	x^7 - x + 1	$2$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
3.7.0.1	$7$	x^7 + x^2 - x + 1	$3$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
5.7.0.1	$7$	x^7 - x + 2	$5$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
7.7.0.1	$7$	x^7 - x + 2	$7$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
7.7.12.1	$7$	x^7 - 7x^6 + 7	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$
7.7.12.2	$7$	x^7 - 7x^6 + 56	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$
7.7.12.3	$7$	x^7 - 7x^6 + 105	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$
7.7.12.4	$7$	x^7 - 7x^6 + 154	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$
7.7.12.5	$7$	x^7 - 7x^6 + 203	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$
7.7.12.6	$7$	x^7 - 7x^6 + 252	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$
7.7.12.7	$7$	x^7 - 7x^6 + 301	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$
11.7.0.1	$7$	x^7 - x + 4	$11$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
13.7.0.1	$7$	x^7 - 10x + 2	$13$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
17.7.0.1	$7$	x^7 - x + 3	$17$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
19.7.0.1	$7$	x^7 - 8x + 4	$19$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
23.7.0.1	$7$	x^7 - x + 8	$23$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
29.7.0.1	$7$	x^7 - x + 3	$29$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
29.7.6.1	$7$	x^7 + 232	$29$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
29.7.6.2	$7$	x^7 - 29	$29$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
29.7.6.3	$7$	x^7 + 928	$29$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
29.7.6.4	$7$	x^7 - 1856	$29$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
29.7.6.5	$7$	x^7 + 58	$29$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
29.7.6.6	$7$	x^7 - 464	$29$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
29.7.6.7	$7$	x^7 - 116	$29$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
31.7.0.1	$7$	x^7 - x + 18	$31$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
37.7.0.1	$7$	x^7 - 4x + 5	$37$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
41.7.0.1	$7$	x^7 - 3x + 7	$41$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
43.7.0.1	$7$	x^7 - 2x + 9	$43$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
43.7.6.1	$7$	x^7 - 43	$43$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
43.7.6.2	$7$	x^7 + 387	$43$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
43.7.6.3	$7$	x^7 - 3483	$43$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
43.7.6.4	$7$	x^7 + 31347	$43$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
43.7.6.5	$7$	x^7 - 282123	$43$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
43.7.6.6	$7$	x^7 + 2539107	$43$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
43.7.6.7	$7$	x^7 - 22851963	$43$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
47.7.0.1	$7$	x^7 - x + 7	$47$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
53.7.0.1	$7$	x^7 - x + 18	$53$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
59.7.0.1	$7$	x^7 - x + 16	$59$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
61.7.0.1	$7$	x^7 - x + 2	$61$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
67.7.0.1	$7$	x^7 - x + 19	$67$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
71.7.0.1	$7$	x^7 - x + 6	$71$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
71.7.6.1	$7$	x^7 - 71	$71$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
71.7.6.2	$7$	x^7 + 142	$71$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
71.7.6.3	$7$	x^7 - 284	$71$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
71.7.6.4	$7$	x^7 + 568	$71$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
71.7.6.5	$7$	x^7 - 1136	$71$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
71.7.6.6	$7$	x^7 + 2272	$71$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
71.7.6.7	$7$	x^7 - 4544	$71$	$7$	$1$	$6$	$C_7$ (as 7T1)	$1$	$7$	$[\ ]$	$[\ ]_{7}$
73.7.0.1	$7$	x^7 - 3x + 13	$73$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$
79.7.0.1	$7$	x^7 - x + 9	$79$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$