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 170 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
13.13.0.1	$13$	x¹³ + 12x + 11	$13$	$1$	$13$	$0$	$C_{13}$ (as 13T1)	$13$	$1$	$[\ ]$	$[\ ]^{13}$	$[0]$	$[]$
13.13.13.1	$13$	x¹³ + 13x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.10	$13$	x¹³ + 91x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.11	$13$	x¹³ + 104x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.12	$13$	x¹³ + 143x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.2	$13$	x¹³ + 39x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.3	$13$	x¹³ + 52x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.4	$13$	x¹³ + 117x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.5	$13$	x¹³ + 130x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.6	$13$	x¹³ + 156x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.7	$13$	x¹³ + 26x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.8	$13$	x¹³ + 65x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.13.9	$13$	x¹³ + 78x + 13	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$[1, 0]$	$[1]$
13.13.14.1	$13$	x¹³ + 26x² + 13	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1]$
13.13.14.10	$13$	x¹³ + 117x² + 13	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2]$
13.13.14.11	$13$	x¹³ + 130x² + 13	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2]$
13.13.14.12	$13$	x¹³ + 156x² + 13	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2]$
13.13.14.2	$13$	x¹³ + 65x² + 13	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1]$
13.13.14.3	$13$	x¹³ + 78x² + 13	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1]$
13.13.14.4	$13$	x¹³ + 91x² + 13	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1]$
13.13.14.5	$13$	x¹³ + 104x² + 13	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1]$
13.13.14.6	$13$	x¹³ + 143x² + 13	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1]$
13.13.14.7	$13$	x¹³ + 13x² + 13	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2]$
13.13.14.8	$13$	x¹³ + 39x² + 13	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2]$
13.13.14.9	$13$	x¹³ + 52x² + 13	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2]$
13.13.15.1	$13$	x¹³ + 52x³ + 13	$13$	$13$	$1$	$15$	$C_{13}:C_4$ (as 13T4)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$[3, 0]$	$[1]$
13.13.15.10	$13$	x¹³ + 65x³ + 13	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$[3, 0]$	$[3]$
13.13.15.11	$13$	x¹³ + 104x³ + 13	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$[3, 0]$	$[3]$
13.13.15.12	$13$	x¹³ + 143x³ + 13	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$[3, 0]$	$[3]$
13.13.15.2	$13$	x¹³ + 117x³ + 13	$13$	$13$	$1$	$15$	$C_{13}:C_4$ (as 13T4)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$[3, 0]$	$[1]$
13.13.15.3	$13$	x¹³ + 13x³ + 13	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$[3, 0]$	$[3]$
13.13.15.4	$13$	x¹³ + 39x³ + 13	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$[3, 0]$	$[3]$
13.13.15.5	$13$	x¹³ + 130x³ + 13	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$[3, 0]$	$[3]$
13.13.15.6	$13$	x¹³ + 156x³ + 13	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$[3, 0]$	$[3]$
13.13.15.7	$13$	x¹³ + 78x³ + 13	$13$	$13$	$1$	$15$	$C_{13}:C_4$ (as 13T4)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$[3, 0]$	$[1]$
13.13.15.8	$13$	x¹³ + 91x³ + 13	$13$	$13$	$1$	$15$	$C_{13}:C_4$ (as 13T4)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$[3, 0]$	$[1]$
13.13.15.9	$13$	x¹³ + 26x³ + 13	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$[3, 0]$	$[3]$
13.13.16.1	$13$	x¹³ + 52x⁴ + 13	$13$	$13$	$1$	$16$	$C_{13}:C_3$ (as 13T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$[4, 0]$	$[1]$
13.13.16.10	$13$	x¹³ + 91x⁴ + 13	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$[4, 0]$	$[4]$
13.13.16.11	$13$	x¹³ + 104x⁴ + 13	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$[4, 0]$	$[4]$
13.13.16.12	$13$	x¹³ + 143x⁴ + 13	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$[4, 0]$	$[4]$
13.13.16.2	$13$	x¹³ + 130x⁴ + 13	$13$	$13$	$1$	$16$	$C_{13}:C_3$ (as 13T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$[4, 0]$	$[1]$
13.13.16.3	$13$	x¹³ + 156x⁴ + 13	$13$	$13$	$1$	$16$	$C_{13}:C_3$ (as 13T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$[4, 0]$	$[1]$
13.13.16.4	$13$	x¹³ + 13x⁴ + 13	$13$	$13$	$1$	$16$	$C_{13}:C_6$ (as 13T5)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$[4, 0]$	$[2]$
13.13.16.5	$13$	x¹³ + 39x⁴ + 13	$13$	$13$	$1$	$16$	$C_{13}:C_6$ (as 13T5)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$[4, 0]$	$[2]$
13.13.16.6	$13$	x¹³ + 117x⁴ + 13	$13$	$13$	$1$	$16$	$C_{13}:C_6$ (as 13T5)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$[4, 0]$	$[2]$
13.13.16.7	$13$	x¹³ + 26x⁴ + 13	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$[4, 0]$	$[4]$
13.13.16.8	$13$	x¹³ + 65x⁴ + 13	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$[4, 0]$	$[4]$
13.13.16.9	$13$	x¹³ + 78x⁴ + 13	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$[4, 0]$	$[4]$
13.13.17.1	$13$	x¹³ + 26x⁵ + 13	$13$	$13$	$1$	$17$	$F_{13}$ (as 13T6)	$1$	$12$	$[17/12]$	$[17/12]_{12}$	$[5, 0]$	$[1]$

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