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Degree	Residue characteristic	Galois group	Galois unramified degree	Assoc. Inertia

Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree	Indices

Residue field degree	Top slope	Wild	Visible	Wild inertia subgroup

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Results (47 matches)

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
3.7.6.1	$7$	$x^{7} + 3$	$3$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 1$	$x^{7} + 3$	$[0]$	$[6]$
5.7.6.1	$7$	$x^{7} + 5$	$5$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 3$	$x^{7} + 5$	$[0]$	$[6]$
7.7.7.1	$7$	$x^{7} + 42 x + 7$	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 4$	$x^{7} + 42 x + 7$	$[1, 0]$	$[1]$
7.7.7.2	$7$	$x^{7} + 21 x + 7$	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 4$	$x^{7} + 21 x + 7$	$[1, 0]$	$[1]$
7.7.7.3	$7$	$x^{7} + 35 x + 7$	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 4$	$x^{7} + 35 x + 7$	$[1, 0]$	$[1]$
7.7.7.4	$7$	$x^{7} + 14 x + 7$	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 4$	$x^{7} + 14 x + 7$	$[1, 0]$	$[1]$
7.7.7.5	$7$	$x^{7} + 7 x + 7$	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 4$	$x^{7} + 7 x + 7$	$[1, 0]$	$[1]$
7.7.7.6	$7$	$x^{7} + 28 x + 7$	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 4$	$x^{7} + 28 x + 7$	$[1, 0]$	$[1]$
7.7.8.4	$7$	$x^{7} + 21 x^{2} + 7$	$7$	$7$	$1$	$8$	$F_7$ (as 7T4)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$t + 4$	$x^{7} + 21 x^{2} + 7$	$[2, 0]$	$[2]$
7.7.8.5	$7$	$x^{7} + 42 x^{2} + 7$	$7$	$7$	$1$	$8$	$F_7$ (as 7T4)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$t + 4$	$x^{7} + 42 x^{2} + 7$	$[2, 0]$	$[2]$
7.7.8.6	$7$	$x^{7} + 35 x^{2} + 7$	$7$	$7$	$1$	$8$	$F_7$ (as 7T4)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$t + 4$	$x^{7} + 35 x^{2} + 7$	$[2, 0]$	$[2]$
7.7.9.2	$7$	$x^{7} + 7 x^{3} + 7$	$7$	$7$	$1$	$9$	$F_7$ (as 7T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$t + 4$	$x^{7} + 7 x^{3} + 7$	$[3, 0]$	$[3]$
7.7.9.3	$7$	$x^{7} + 28 x^{3} + 7$	$7$	$7$	$1$	$9$	$F_7$ (as 7T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$t + 4$	$x^{7} + 28 x^{3} + 7$	$[3, 0]$	$[3]$
7.7.9.5	$7$	$x^{7} + 42 x^{3} + 7$	$7$	$7$	$1$	$9$	$F_7$ (as 7T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$t + 4$	$x^{7} + 42 x^{3} + 7$	$[3, 0]$	$[3]$
7.7.9.6	$7$	$x^{7} + 21 x^{3} + 7$	$7$	$7$	$1$	$9$	$F_7$ (as 7T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$t + 4$	$x^{7} + 21 x^{3} + 7$	$[3, 0]$	$[3]$
7.7.10.4	$7$	$x^{7} + 21 x^{4} + 7$	$7$	$7$	$1$	$10$	$F_7$ (as 7T4)	$2$	$3$	$[5/3]$	$[5/3]_{3}^{2}$	$t + 4$	$x^{7} + 21 x^{4} + 7$	$[4, 0]$	$[2]$
7.7.10.5	$7$	$x^{7} + 35 x^{4} + 7$	$7$	$7$	$1$	$10$	$F_7$ (as 7T4)	$2$	$3$	$[5/3]$	$[5/3]_{3}^{2}$	$t + 4$	$x^{7} + 35 x^{4} + 7$	$[4, 0]$	$[2]$
7.7.10.6	$7$	$x^{7} + 42 x^{4} + 7$	$7$	$7$	$1$	$10$	$F_7$ (as 7T4)	$2$	$3$	$[5/3]$	$[5/3]_{3}^{2}$	$t + 4$	$x^{7} + 42 x^{4} + 7$	$[4, 0]$	$[2]$
7.7.11.1	$7$	$x^{7} + 7 x^{5} + 7$	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$t + 4$	$x^{7} + 7 x^{5} + 7$	$[5, 0]$	$[1]$
7.7.11.2	$7$	$x^{7} + 28 x^{5} + 7$	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$t + 4$	$x^{7} + 28 x^{5} + 7$	$[5, 0]$	$[1]$
7.7.11.3	$7$	$x^{7} + 14 x^{5} + 7$	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$t + 4$	$x^{7} + 14 x^{5} + 7$	$[5, 0]$	$[1]$
7.7.11.4	$7$	$x^{7} + 21 x^{5} + 7$	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$t + 4$	$x^{7} + 21 x^{5} + 7$	$[5, 0]$	$[1]$
7.7.11.5	$7$	$x^{7} + 35 x^{5} + 7$	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$t + 4$	$x^{7} + 35 x^{5} + 7$	$[5, 0]$	$[1]$
7.7.11.6	$7$	$x^{7} + 42 x^{5} + 7$	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$t + 4$	$x^{7} + 42 x^{5} + 7$	$[5, 0]$	$[1]$
7.7.12.11	$7$	$x^{7} + 14 x^{6} + 7$	$7$	$7$	$1$	$12$	$F_7$ (as 7T4)	$6$	$1$	$[2]$	$[2]^{6}$	$t + 4$	$x^{7} + 14 x^{6} + 7$	$[6, 0]$	$[6]$
7.7.12.12	$7$	$x^{7} + 28 x^{6} + 7$	$7$	$7$	$1$	$12$	$F_7$ (as 7T4)	$6$	$1$	$[2]$	$[2]^{6}$	$t + 4$	$x^{7} + 28 x^{6} + 7$	$[6, 0]$	$[6]$
7.7.13.1	$7$	$x^{7} + 7$	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$t + 4$	$x^{7} + 7$	$[7, 0]$	$[1]$
7.7.13.2	$7$	$x^{7} + 49 x^{2} + 98 x + 7$	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$t + 4$	$x^{7} + 49 x^{2} + 98 x + 7$	$[7, 0]$	$[1]$
7.7.13.3	$7$	$x^{7} + 98 x^{2} + 294 x + 7$	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$t + 4$	$x^{7} + 98 x^{2} + 294 x + 7$	$[7, 0]$	$[1]$
7.7.13.4	$7$	$x^{7} + 196 x^{2} + 147 x + 7$	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$t + 4$	$x^{7} + 196 x^{2} + 147 x + 7$	$[7, 0]$	$[1]$
7.7.13.5	$7$	$x^{7} + 98 x^{2} + 49 x + 7$	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$t + 4$	$x^{7} + 98 x^{2} + 49 x + 7$	$[7, 0]$	$[1]$
7.7.13.6	$7$	$x^{7} + 196 x^{2} + 196 x + 7$	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$t + 4$	$x^{7} + 196 x^{2} + 196 x + 7$	$[7, 0]$	$[1]$
7.7.13.7	$7$	$x^{7} + 49 x^{2} + 245 x + 7$	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$t + 4$	$x^{7} + 49 x^{2} + 245 x + 7$	$[7, 0]$	$[1]$
17.7.6.1	$7$	$x^{7} + 17$	$17$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 14$	$x^{7} + 17$	$[0]$	$[6]$
19.7.6.1	$7$	$x^{7} + 19$	$19$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 17$	$x^{7} + 19$	$[0]$	$[6]$
31.7.6.1	$7$	$x^{7} + 31$	$31$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 28$	$x^{7} + 31$	$[0]$	$[6]$
47.7.6.1	$7$	$x^{7} + 47$	$47$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 42$	$x^{7} + 47$	$[0]$	$[6]$
59.7.6.1	$7$	$x^{7} + 59$	$59$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 57$	$x^{7} + 59$	$[0]$	$[6]$
61.7.6.1	$7$	$x^{7} + 61$	$61$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 59$	$x^{7} + 61$	$[0]$	$[6]$
73.7.6.1	$7$	$x^{7} + 73$	$73$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 68$	$x^{7} + 73$	$[0]$	$[6]$
89.7.6.1	$7$	$x^{7} + 89$	$89$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 86$	$x^{7} + 89$	$[0]$	$[6]$
101.7.6.1	$7$	$x^{7} + 101$	$101$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 99$	$x^{7} + 101$	$[0]$	$[6]$
103.7.6.1	$7$	$x^{7} + 103$	$103$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 98$	$x^{7} + 103$	$[0]$	$[6]$
131.7.6.1	$7$	$x^{7} + 131$	$131$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 129$	$x^{7} + 131$	$[0]$	$[6]$
157.7.6.1	$7$	$x^{7} + 157$	$157$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 152$	$x^{7} + 157$	$[0]$	$[6]$
173.7.6.1	$7$	$x^{7} + 173$	$173$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 171$	$x^{7} + 173$	$[0]$	$[6]$
199.7.6.1	$7$	$x^{7} + 199$	$199$	$7$	$1$	$6$	$F_7$ (as 7T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$t + 196$	$x^{7} + 199$	$[0]$	$[6]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.