LMFDB - p-adic field search results

Refine search

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

		Sort order	Select

Results (1-50 of 170 matches)

Next Download displayed columns for results to

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
13.13.0.1	$13$	$x^{13} + 12 x + 11$	$13$	$1$	$13$	$0$	$C_{13}$ (as 13T1)	$13$	$1$	$[\ ]$	$[\ ]^{13}$	$t^{13} + 12 t + 11$	$x - 13$	$[0]$	$[]$
13.13.13.1	$13$	$x^{13} + 13 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 13 x + 13$	$[1, 0]$	$[1]$
13.13.13.2	$13$	$x^{13} + 39 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 39 x + 13$	$[1, 0]$	$[1]$
13.13.13.3	$13$	$x^{13} + 52 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 52 x + 13$	$[1, 0]$	$[1]$
13.13.13.4	$13$	$x^{13} + 117 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 117 x + 13$	$[1, 0]$	$[1]$
13.13.13.5	$13$	$x^{13} + 130 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 130 x + 13$	$[1, 0]$	$[1]$
13.13.13.6	$13$	$x^{13} + 156 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 156 x + 13$	$[1, 0]$	$[1]$
13.13.13.7	$13$	$x^{13} + 26 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 26 x + 13$	$[1, 0]$	$[1]$
13.13.13.8	$13$	$x^{13} + 65 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 65 x + 13$	$[1, 0]$	$[1]$
13.13.13.9	$13$	$x^{13} + 78 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 78 x + 13$	$[1, 0]$	$[1]$
13.13.13.10	$13$	$x^{13} + 91 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 91 x + 13$	$[1, 0]$	$[1]$
13.13.13.11	$13$	$x^{13} + 104 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 104 x + 13$	$[1, 0]$	$[1]$
13.13.13.12	$13$	$x^{13} + 143 x + 13$	$13$	$13$	$1$	$13$	$F_{13}$ (as 13T6)	$1$	$12$	$[13/12]$	$[13/12]_{12}$	$t + 11$	$x^{13} + 143 x + 13$	$[1, 0]$	$[1]$
13.13.14.1	$13$	$x^{13} + 26 x^{2} + 13$	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 11$	$x^{13} + 26 x^{2} + 13$	$[2, 0]$	$[1]$
13.13.14.2	$13$	$x^{13} + 65 x^{2} + 13$	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 11$	$x^{13} + 65 x^{2} + 13$	$[2, 0]$	$[1]$
13.13.14.3	$13$	$x^{13} + 78 x^{2} + 13$	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 11$	$x^{13} + 78 x^{2} + 13$	$[2, 0]$	$[1]$
13.13.14.4	$13$	$x^{13} + 91 x^{2} + 13$	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 11$	$x^{13} + 91 x^{2} + 13$	$[2, 0]$	$[1]$
13.13.14.5	$13$	$x^{13} + 104 x^{2} + 13$	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 11$	$x^{13} + 104 x^{2} + 13$	$[2, 0]$	$[1]$
13.13.14.6	$13$	$x^{13} + 143 x^{2} + 13$	$13$	$13$	$1$	$14$	$C_{13}:C_6$ (as 13T5)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$t + 11$	$x^{13} + 143 x^{2} + 13$	$[2, 0]$	$[1]$
13.13.14.7	$13$	$x^{13} + 13 x^{2} + 13$	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$t + 11$	$x^{13} + 13 x^{2} + 13$	$[2, 0]$	$[2]$
13.13.14.8	$13$	$x^{13} + 39 x^{2} + 13$	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$t + 11$	$x^{13} + 39 x^{2} + 13$	$[2, 0]$	$[2]$
13.13.14.9	$13$	$x^{13} + 52 x^{2} + 13$	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$t + 11$	$x^{13} + 52 x^{2} + 13$	$[2, 0]$	$[2]$
13.13.14.10	$13$	$x^{13} + 117 x^{2} + 13$	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$t + 11$	$x^{13} + 117 x^{2} + 13$	$[2, 0]$	$[2]$
13.13.14.11	$13$	$x^{13} + 130 x^{2} + 13$	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$t + 11$	$x^{13} + 130 x^{2} + 13$	$[2, 0]$	$[2]$
13.13.14.12	$13$	$x^{13} + 156 x^{2} + 13$	$13$	$13$	$1$	$14$	$F_{13}$ (as 13T6)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$t + 11$	$x^{13} + 156 x^{2} + 13$	$[2, 0]$	$[2]$
13.13.15.1	$13$	$x^{13} + 52 x^{3} + 13$	$13$	$13$	$1$	$15$	$C_{13}:C_4$ (as 13T4)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$t + 11$	$x^{13} + 52 x^{3} + 13$	$[3, 0]$	$[1]$
13.13.15.2	$13$	$x^{13} + 117 x^{3} + 13$	$13$	$13$	$1$	$15$	$C_{13}:C_4$ (as 13T4)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$t + 11$	$x^{13} + 117 x^{3} + 13$	$[3, 0]$	$[1]$
13.13.15.3	$13$	$x^{13} + 13 x^{3} + 13$	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$t + 11$	$x^{13} + 13 x^{3} + 13$	$[3, 0]$	$[3]$
13.13.15.4	$13$	$x^{13} + 39 x^{3} + 13$	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$t + 11$	$x^{13} + 39 x^{3} + 13$	$[3, 0]$	$[3]$
13.13.15.5	$13$	$x^{13} + 130 x^{3} + 13$	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$t + 11$	$x^{13} + 130 x^{3} + 13$	$[3, 0]$	$[3]$
13.13.15.6	$13$	$x^{13} + 156 x^{3} + 13$	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$t + 11$	$x^{13} + 156 x^{3} + 13$	$[3, 0]$	$[3]$
13.13.15.7	$13$	$x^{13} + 78 x^{3} + 13$	$13$	$13$	$1$	$15$	$C_{13}:C_4$ (as 13T4)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$t + 11$	$x^{13} + 78 x^{3} + 13$	$[3, 0]$	$[1]$
13.13.15.8	$13$	$x^{13} + 91 x^{3} + 13$	$13$	$13$	$1$	$15$	$C_{13}:C_4$ (as 13T4)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$t + 11$	$x^{13} + 91 x^{3} + 13$	$[3, 0]$	$[1]$
13.13.15.9	$13$	$x^{13} + 26 x^{3} + 13$	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$t + 11$	$x^{13} + 26 x^{3} + 13$	$[3, 0]$	$[3]$
13.13.15.10	$13$	$x^{13} + 65 x^{3} + 13$	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$t + 11$	$x^{13} + 65 x^{3} + 13$	$[3, 0]$	$[3]$
13.13.15.11	$13$	$x^{13} + 104 x^{3} + 13$	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$t + 11$	$x^{13} + 104 x^{3} + 13$	$[3, 0]$	$[3]$
13.13.15.12	$13$	$x^{13} + 143 x^{3} + 13$	$13$	$13$	$1$	$15$	$F_{13}$ (as 13T6)	$3$	$4$	$[5/4]$	$[5/4]_{4}^{3}$	$t + 11$	$x^{13} + 143 x^{3} + 13$	$[3, 0]$	$[3]$
13.13.16.1	$13$	$x^{13} + 52 x^{4} + 13$	$13$	$13$	$1$	$16$	$C_{13}:C_3$ (as 13T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$t + 11$	$x^{13} + 52 x^{4} + 13$	$[4, 0]$	$[1]$
13.13.16.2	$13$	$x^{13} + 130 x^{4} + 13$	$13$	$13$	$1$	$16$	$C_{13}:C_3$ (as 13T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$t + 11$	$x^{13} + 130 x^{4} + 13$	$[4, 0]$	$[1]$
13.13.16.3	$13$	$x^{13} + 156 x^{4} + 13$	$13$	$13$	$1$	$16$	$C_{13}:C_3$ (as 13T3)	$1$	$3$	$[4/3]$	$[4/3]_{3}$	$t + 11$	$x^{13} + 156 x^{4} + 13$	$[4, 0]$	$[1]$
13.13.16.4	$13$	$x^{13} + 13 x^{4} + 13$	$13$	$13$	$1$	$16$	$C_{13}:C_6$ (as 13T5)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$t + 11$	$x^{13} + 13 x^{4} + 13$	$[4, 0]$	$[2]$
13.13.16.5	$13$	$x^{13} + 39 x^{4} + 13$	$13$	$13$	$1$	$16$	$C_{13}:C_6$ (as 13T5)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$t + 11$	$x^{13} + 39 x^{4} + 13$	$[4, 0]$	$[2]$
13.13.16.6	$13$	$x^{13} + 117 x^{4} + 13$	$13$	$13$	$1$	$16$	$C_{13}:C_6$ (as 13T5)	$2$	$3$	$[4/3]$	$[4/3]_{3}^{2}$	$t + 11$	$x^{13} + 117 x^{4} + 13$	$[4, 0]$	$[2]$
13.13.16.7	$13$	$x^{13} + 26 x^{4} + 13$	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$t + 11$	$x^{13} + 26 x^{4} + 13$	$[4, 0]$	$[4]$
13.13.16.8	$13$	$x^{13} + 65 x^{4} + 13$	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$t + 11$	$x^{13} + 65 x^{4} + 13$	$[4, 0]$	$[4]$
13.13.16.9	$13$	$x^{13} + 78 x^{4} + 13$	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$t + 11$	$x^{13} + 78 x^{4} + 13$	$[4, 0]$	$[4]$
13.13.16.10	$13$	$x^{13} + 91 x^{4} + 13$	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$t + 11$	$x^{13} + 91 x^{4} + 13$	$[4, 0]$	$[4]$
13.13.16.11	$13$	$x^{13} + 104 x^{4} + 13$	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$t + 11$	$x^{13} + 104 x^{4} + 13$	$[4, 0]$	$[4]$
13.13.16.12	$13$	$x^{13} + 143 x^{4} + 13$	$13$	$13$	$1$	$16$	$F_{13}$ (as 13T6)	$4$	$3$	$[4/3]$	$[4/3]_{3}^{4}$	$t + 11$	$x^{13} + 143 x^{4} + 13$	$[4, 0]$	$[4]$
13.13.17.1	$13$	$x^{13} + 26 x^{5} + 13$	$13$	$13$	$1$	$17$	$F_{13}$ (as 13T6)	$1$	$12$	$[17/12]$	$[17/12]_{12}$	$t + 11$	$x^{13} + 26 x^{5} + 13$	$[5, 0]$	$[1]$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 170 matches)

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