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 (1-50 of 122 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
11.11.0.1	$11$	x¹¹ + 10x + 9	$11$	$1$	$11$	$0$	$C_{11}$ (as 11T1)	$11$	$1$	$[\ ]$	$[\ ]^{11}$	$[0]$	$[]$
11.11.11.1	$11$	x¹¹ + 110x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.10	$11$	x¹¹ + 33x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.2	$11$	x¹¹ + 88x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.3	$11$	x¹¹ + 66x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.4	$11$	x¹¹ + 77x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.5	$11$	x¹¹ + 22x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.6	$11$	x¹¹ + 11x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.7	$11$	x¹¹ + 44x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.8	$11$	x¹¹ + 55x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.11.9	$11$	x¹¹ + 99x + 11	$11$	$11$	$1$	$11$	$F_{11}$ (as 11T4)	$1$	$10$	$[11/10]$	$[11/10]_{10}$	$[1, 0]$	$[1]$
11.11.12.1	$11$	x¹¹ + 88x² + 11	$11$	$11$	$1$	$12$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[6/5]$	$[6/5]_{5}$	$[2, 0]$	$[1]$
11.11.12.10	$11$	x¹¹ + 55x² + 11	$11$	$11$	$1$	$12$	$F_{11}$ (as 11T4)	$2$	$5$	$[6/5]$	$[6/5]_{5}^{2}$	$[2, 0]$	$[2]$
11.11.12.2	$11$	x¹¹ + 22x² + 11	$11$	$11$	$1$	$12$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[6/5]$	$[6/5]_{5}$	$[2, 0]$	$[1]$
11.11.12.3	$11$	x¹¹ + 77x² + 11	$11$	$11$	$1$	$12$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[6/5]$	$[6/5]_{5}$	$[2, 0]$	$[1]$
11.11.12.4	$11$	x¹¹ + 110x² + 11	$11$	$11$	$1$	$12$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[6/5]$	$[6/5]_{5}$	$[2, 0]$	$[1]$
11.11.12.5	$11$	x¹¹ + 66x² + 11	$11$	$11$	$1$	$12$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[6/5]$	$[6/5]_{5}$	$[2, 0]$	$[1]$
11.11.12.6	$11$	x¹¹ + 33x² + 11	$11$	$11$	$1$	$12$	$F_{11}$ (as 11T4)	$2$	$5$	$[6/5]$	$[6/5]_{5}^{2}$	$[2, 0]$	$[2]$
11.11.12.7	$11$	x¹¹ + 11x² + 11	$11$	$11$	$1$	$12$	$F_{11}$ (as 11T4)	$2$	$5$	$[6/5]$	$[6/5]_{5}^{2}$	$[2, 0]$	$[2]$
11.11.12.8	$11$	x¹¹ + 44x² + 11	$11$	$11$	$1$	$12$	$F_{11}$ (as 11T4)	$2$	$5$	$[6/5]$	$[6/5]_{5}^{2}$	$[2, 0]$	$[2]$
11.11.12.9	$11$	x¹¹ + 99x² + 11	$11$	$11$	$1$	$12$	$F_{11}$ (as 11T4)	$2$	$5$	$[6/5]$	$[6/5]_{5}^{2}$	$[2, 0]$	$[2]$
11.11.13.1	$11$	x¹¹ + 22x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.10	$11$	x¹¹ + 99x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.2	$11$	x¹¹ + 88x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.3	$11$	x¹¹ + 66x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.4	$11$	x¹¹ + 77x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.5	$11$	x¹¹ + 110x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.6	$11$	x¹¹ + 44x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.7	$11$	x¹¹ + 33x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.8	$11$	x¹¹ + 55x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.13.9	$11$	x¹¹ + 11x³ + 11	$11$	$11$	$1$	$13$	$F_{11}$ (as 11T4)	$1$	$10$	$[13/10]$	$[13/10]_{10}$	$[3, 0]$	$[1]$
11.11.14.1	$11$	x¹¹ + 33x⁴ + 11	$11$	$11$	$1$	$14$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[7/5]$	$[7/5]_{5}$	$[4, 0]$	$[1]$
11.11.14.10	$11$	x¹¹ + 22x⁴ + 11	$11$	$11$	$1$	$14$	$F_{11}$ (as 11T4)	$2$	$5$	$[7/5]$	$[7/5]_{5}^{2}$	$[4, 0]$	$[2]$
11.11.14.2	$11$	x¹¹ + 55x⁴ + 11	$11$	$11$	$1$	$14$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[7/5]$	$[7/5]_{5}$	$[4, 0]$	$[1]$
11.11.14.3	$11$	x¹¹ + 11x⁴ + 11	$11$	$11$	$1$	$14$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[7/5]$	$[7/5]_{5}$	$[4, 0]$	$[1]$
11.11.14.4	$11$	x¹¹ + 44x⁴ + 11	$11$	$11$	$1$	$14$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[7/5]$	$[7/5]_{5}$	$[4, 0]$	$[1]$
11.11.14.5	$11$	x¹¹ + 99x⁴ + 11	$11$	$11$	$1$	$14$	$C_{11}:C_5$ (as 11T3)	$1$	$5$	$[7/5]$	$[7/5]_{5}$	$[4, 0]$	$[1]$
11.11.14.6	$11$	x¹¹ + 66x⁴ + 11	$11$	$11$	$1$	$14$	$F_{11}$ (as 11T4)	$2$	$5$	$[7/5]$	$[7/5]_{5}^{2}$	$[4, 0]$	$[2]$
11.11.14.7	$11$	x¹¹ + 110x⁴ + 11	$11$	$11$	$1$	$14$	$F_{11}$ (as 11T4)	$2$	$5$	$[7/5]$	$[7/5]_{5}^{2}$	$[4, 0]$	$[2]$
11.11.14.8	$11$	x¹¹ + 77x⁴ + 11	$11$	$11$	$1$	$14$	$F_{11}$ (as 11T4)	$2$	$5$	$[7/5]$	$[7/5]_{5}^{2}$	$[4, 0]$	$[2]$
11.11.14.9	$11$	x¹¹ + 88x⁴ + 11	$11$	$11$	$1$	$14$	$F_{11}$ (as 11T4)	$2$	$5$	$[7/5]$	$[7/5]_{5}^{2}$	$[4, 0]$	$[2]$
11.11.15.1	$11$	x¹¹ + 22x⁵ + 11	$11$	$11$	$1$	$15$	$D_{11}$ (as 11T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$	$[5, 0]$	$[1]$
11.11.15.10	$11$	x¹¹ + 55x⁵ + 11	$11$	$11$	$1$	$15$	$F_{11}$ (as 11T4)	$5$	$2$	$[3/2]$	$[3/2]_{2}^{5}$	$[5, 0]$	$[5]$
11.11.15.2	$11$	x¹¹ + 88x⁵ + 11	$11$	$11$	$1$	$15$	$F_{11}$ (as 11T4)	$5$	$2$	$[3/2]$	$[3/2]_{2}^{5}$	$[5, 0]$	$[5]$
11.11.15.3	$11$	x¹¹ + 110x⁵ + 11	$11$	$11$	$1$	$15$	$F_{11}$ (as 11T4)	$5$	$2$	$[3/2]$	$[3/2]_{2}^{5}$	$[5, 0]$	$[5]$
11.11.15.4	$11$	x¹¹ + 77x⁵ + 11	$11$	$11$	$1$	$15$	$F_{11}$ (as 11T4)	$5$	$2$	$[3/2]$	$[3/2]_{2}^{5}$	$[5, 0]$	$[5]$
11.11.15.5	$11$	x¹¹ + 66x⁵ + 11	$11$	$11$	$1$	$15$	$F_{11}$ (as 11T4)	$5$	$2$	$[3/2]$	$[3/2]_{2}^{5}$	$[5, 0]$	$[5]$
11.11.15.6	$11$	x¹¹ + 99x⁵ + 11	$11$	$11$	$1$	$15$	$D_{11}$ (as 11T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$	$[5, 0]$	$[1]$
11.11.15.7	$11$	x¹¹ + 11x⁵ + 11	$11$	$11$	$1$	$15$	$F_{11}$ (as 11T4)	$5$	$2$	$[3/2]$	$[3/2]_{2}^{5}$	$[5, 0]$	$[5]$
11.11.15.8	$11$	x¹¹ + 33x⁵ + 11	$11$	$11$	$1$	$15$	$F_{11}$ (as 11T4)	$5$	$2$	$[3/2]$	$[3/2]_{2}^{5}$	$[5, 0]$	$[5]$

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