LMFDB - p-adic field search results

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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 (50 matches)

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
7.7.0.1	$7$	x⁷ + 6x + 4	$7$	$1$	$7$	$0$	$C_7$ (as 7T1)	$7$	$1$	$[\ ]$	$[\ ]^{7}$	$[0]$	$[]$
7.7.7.1	$7$	x⁷ + 42x + 7	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[1, 0]$	$[1]$
7.7.7.2	$7$	x⁷ + 21x + 7	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[1, 0]$	$[1]$
7.7.7.3	$7$	x⁷ + 35x + 7	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[1, 0]$	$[1]$
7.7.7.4	$7$	x⁷ + 14x + 7	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[1, 0]$	$[1]$
7.7.7.5	$7$	x⁷ + 7x + 7	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[1, 0]$	$[1]$
7.7.7.6	$7$	x⁷ + 28x + 7	$7$	$7$	$1$	$7$	$F_7$ (as 7T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[1, 0]$	$[1]$
7.7.8.1	$7$	x⁷ + 14x² + 7	$7$	$7$	$1$	$8$	$C_7:C_3$ (as 7T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$[2, 0]$	$[1]$
7.7.8.2	$7$	x⁷ + 7x² + 7	$7$	$7$	$1$	$8$	$C_7:C_3$ (as 7T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$[2, 0]$	$[1]$
7.7.8.3	$7$	x⁷ + 28x² + 7	$7$	$7$	$1$	$8$	$C_7:C_3$ (as 7T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$[2, 0]$	$[1]$
7.7.8.4	$7$	x⁷ + 21x² + 7	$7$	$7$	$1$	$8$	$F_7$ (as 7T4)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$[2, 0]$	$[2]$
7.7.8.5	$7$	x⁷ + 42x² + 7	$7$	$7$	$1$	$8$	$F_7$ (as 7T4)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$[2, 0]$	$[2]$
7.7.8.6	$7$	x⁷ + 35x² + 7	$7$	$7$	$1$	$8$	$F_7$ (as 7T4)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$[2, 0]$	$[2]$
7.7.9.1	$7$	x⁷ + 14x³ + 7	$7$	$7$	$1$	$9$	$D_{7}$ (as 7T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$	$[3, 0]$	$[1]$
7.7.9.2	$7$	x⁷ + 7x³ + 7	$7$	$7$	$1$	$9$	$F_7$ (as 7T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$[3, 0]$	$[3]$
7.7.9.3	$7$	x⁷ + 28x³ + 7	$7$	$7$	$1$	$9$	$F_7$ (as 7T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$[3, 0]$	$[3]$
7.7.9.4	$7$	x⁷ + 35x³ + 7	$7$	$7$	$1$	$9$	$D_{7}$ (as 7T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$	$[3, 0]$	$[1]$
7.7.9.5	$7$	x⁷ + 42x³ + 7	$7$	$7$	$1$	$9$	$F_7$ (as 7T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$[3, 0]$	$[3]$
7.7.9.6	$7$	x⁷ + 21x³ + 7	$7$	$7$	$1$	$9$	$F_7$ (as 7T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$[3, 0]$	$[3]$
7.7.10.1	$7$	x⁷ + 28x⁴ + 7	$7$	$7$	$1$	$10$	$C_7:C_3$ (as 7T3)	$1$	$3$	$[5/3]$	$[5/3]_{3}$	$[4, 0]$	$[1]$
7.7.10.2	$7$	x⁷ + 7x⁴ + 7	$7$	$7$	$1$	$10$	$C_7:C_3$ (as 7T3)	$1$	$3$	$[5/3]$	$[5/3]_{3}$	$[4, 0]$	$[1]$
7.7.10.3	$7$	x⁷ + 14x⁴ + 7	$7$	$7$	$1$	$10$	$C_7:C_3$ (as 7T3)	$1$	$3$	$[5/3]$	$[5/3]_{3}$	$[4, 0]$	$[1]$
7.7.10.4	$7$	x⁷ + 21x⁴ + 7	$7$	$7$	$1$	$10$	$F_7$ (as 7T4)	$2$	$3$	$[5/3]$	$[5/3]_{3}^{2}$	$[4, 0]$	$[2]$
7.7.10.5	$7$	x⁷ + 35x⁴ + 7	$7$	$7$	$1$	$10$	$F_7$ (as 7T4)	$2$	$3$	$[5/3]$	$[5/3]_{3}^{2}$	$[4, 0]$	$[2]$
7.7.10.6	$7$	x⁷ + 42x⁴ + 7	$7$	$7$	$1$	$10$	$F_7$ (as 7T4)	$2$	$3$	$[5/3]$	$[5/3]_{3}^{2}$	$[4, 0]$	$[2]$
7.7.11.1	$7$	x⁷ + 7x⁵ + 7	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$[5, 0]$	$[1]$
7.7.11.2	$7$	x⁷ + 28x⁵ + 7	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$[5, 0]$	$[1]$
7.7.11.3	$7$	x⁷ + 14x⁵ + 7	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$[5, 0]$	$[1]$
7.7.11.4	$7$	x⁷ + 21x⁵ + 7	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$[5, 0]$	$[1]$
7.7.11.5	$7$	x⁷ + 35x⁵ + 7	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$[5, 0]$	$[1]$
7.7.11.6	$7$	x⁷ + 42x⁵ + 7	$7$	$7$	$1$	$11$	$F_7$ (as 7T4)	$1$	$6$	$[11/6]$	$[11/6]_{6}$	$[5, 0]$	$[1]$
7.7.12.1	$7$	x⁷ + 42x⁶ + 7	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$	$[6, 0]$	$[1]$
7.7.12.10	$7$	x⁷ + 7x⁶ + 7	$7$	$7$	$1$	$12$	$D_{7}$ (as 7T2)	$2$	$1$	$[2]$	$[2]^{2}$	$[6, 0]$	$[2]$
7.7.12.11	$7$	x⁷ + 14x⁶ + 7	$7$	$7$	$1$	$12$	$F_7$ (as 7T4)	$6$	$1$	$[2]$	$[2]^{6}$	$[6, 0]$	$[6]$
7.7.12.12	$7$	x⁷ + 28x⁶ + 7	$7$	$7$	$1$	$12$	$F_7$ (as 7T4)	$6$	$1$	$[2]$	$[2]^{6}$	$[6, 0]$	$[6]$
7.7.12.2	$7$	x⁷ + 42x⁶ + 56	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$	$[6, 0]$	$[1]$
7.7.12.3	$7$	x⁷ + 42x⁶ + 105	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$	$[6, 0]$	$[1]$
7.7.12.4	$7$	x⁷ + 42x⁶ + 154	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$	$[6, 0]$	$[1]$
7.7.12.5	$7$	x⁷ + 42x⁶ + 203	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$	$[6, 0]$	$[1]$
7.7.12.6	$7$	x⁷ + 42x⁶ + 252	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$	$[6, 0]$	$[1]$
7.7.12.7	$7$	x⁷ + 42x⁶ + 301	$7$	$7$	$1$	$12$	$C_7$ (as 7T1)	$1$	$1$	$[2]$	$[2]$	$[6, 0]$	$[1]$
7.7.12.8	$7$	x⁷ + 21x⁶ + 7	$7$	$7$	$1$	$12$	$C_7:C_3$ (as 7T3)	$3$	$1$	$[2]$	$[2]^{3}$	$[6, 0]$	$[3]$
7.7.12.9	$7$	x⁷ + 35x⁶ + 7	$7$	$7$	$1$	$12$	$C_7:C_3$ (as 7T3)	$3$	$1$	$[2]$	$[2]^{3}$	$[6, 0]$	$[3]$
7.7.13.1	$7$	x⁷ + 7	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$[7, 0]$	$[1]$
7.7.13.2	$7$	x⁷ + 49x² + 98x + 7	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$[7, 0]$	$[1]$
7.7.13.3	$7$	x⁷ + 98x² + 294x + 7	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$[7, 0]$	$[1]$
7.7.13.4	$7$	x⁷ + 196x² + 147x + 7	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$[7, 0]$	$[1]$
7.7.13.5	$7$	x⁷ + 98x² + 49x + 7	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$[7, 0]$	$[1]$
7.7.13.6	$7$	x⁷ + 196x² + 196x + 7	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$[7, 0]$	$[1]$
7.7.13.7	$7$	x⁷ + 49x² + 245x + 7	$7$	$7$	$1$	$13$	$F_7$ (as 7T4)	$1$	$6$	$[13/6]$	$[13/6]_{6}$	$[7, 0]$	$[1]$

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Elliptic curves over $\Q$
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