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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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
2.10.14.2	$10$	x¹⁰ + 2x⁹ + 2x⁵ + 2	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.3	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 2x⁷ + 2x⁵ + 2	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.4	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁵ + 2	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.6	$10$	x¹⁰ + 2x⁹ + 2x⁷ + 2x⁵ + 2x⁴ + 6	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.7	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 2x⁶ + 2x⁵ + 2x⁴ + 2	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.8	$10$	x¹⁰ + 2x⁵ + 2x⁴ + 6	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.16.10	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁶ + 2x⁴ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.11	$10$	x¹⁰ + 2x⁹ + 2x⁷ + 4x³ + 6	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.12	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁴ + 4x³ + 4x² + 2	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.13	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁶ + 6x⁴ + 4x³ + 4x + 6	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.14	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 2x⁷ + 4x⁴ + 4x³ + 4x + 2	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.15	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁶ + 2x⁴ + 4x² + 2	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.16	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 2x⁷ + 4x⁴ + 4x² + 2	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.9	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁶ + 6x⁴ + 6	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.18.17	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 4x⁷ + 4x⁶ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.18	$10$	x¹⁰ + 2x⁹ + 4x⁸ + 4x⁴ + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.19	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 4x⁷ + 4x⁶ + 4x⁵ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.20	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 4x⁶ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.21	$10$	x¹⁰ + 2x⁹ + 4x⁸ + 4x⁵ + 4x⁴ + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.22	$10$	x¹⁰ + 2x⁹ + 4x⁸ + 4x⁷ + 4x⁴ + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.23	$10$	x¹⁰ + 2x⁹ + 4x⁸ + 4x⁷ + 4x⁵ + 4x⁴ + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.24	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 4x⁶ + 4x⁵ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.25	$10$	x¹⁰ + 2x⁹ + 6x⁸ + 4x⁷ + 4x⁶ + 4x⁵ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.26	$10$	x¹⁰ + 2x⁹ + 4x⁷ + 4x⁵ + 4x⁴ + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.27	$10$	x¹⁰ + 2x⁹ + 6x⁸ + 4x⁶ + 4x⁵ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.28	$10$	x¹⁰ + 2x⁹ + 4x⁵ + 4x⁴ + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.29	$10$	x¹⁰ + 2x⁹ + 4x⁷ + 4x⁴ + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.30	$10$	x¹⁰ + 2x⁹ + 6x⁸ + 4x⁷ + 4x⁶ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.31	$10$	x¹⁰ + 2x⁹ + 6x⁸ + 4x⁶ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.18.32	$10$	x¹⁰ + 2x⁹ + 4x⁴ + 2	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$[9, 0]$	$[1, 4]$
2.10.19.10	$10$	x¹⁰ + 2x⁸ + 4x⁵ + 4x⁴ + 2	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[6/5, 6/5, 6/5, 6/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.11	$10$	x¹⁰ + 4x⁸ + 4x⁶ + 4x⁵ + 4x³ + 4x² + 2	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[12/5, 12/5, 12/5, 12/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.12	$10$	x¹⁰ + 4x⁶ + 4x⁵ + 4x³ + 4x² + 2	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[12/5, 12/5, 12/5, 12/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.13	$10$	x¹⁰ + 4x⁷ + 4x⁵ + 6x⁴ + 4x³ + 4x + 6	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.14	$10$	x¹⁰ + 4x⁹ + 4x⁸ + 4x⁷ + 4x⁶ + 4x⁵ + 2	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[8/5, 8/5, 8/5, 8/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.15	$10$	x¹⁰ + 6x⁸ + 4x⁷ + 4x⁵ + 4x³ + 4x² + 10	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[12/5, 12/5, 12/5, 12/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.16	$10$	x¹⁰ + 4x⁶ + 4x⁵ + 6x⁴ + 4x³ + 4x + 14	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.18	$10$	x¹⁰ + 6x⁸ + 4x⁵ + 4x³ + 2	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[12/5, 12/5, 12/5, 12/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.19	$10$	x¹⁰ + 4x⁹ + 6x⁸ + 4x⁷ + 4x⁵ + 4x³ + 4x² + 2	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[12/5, 12/5, 12/5, 12/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.2	$10$	x¹⁰ + 4x⁹ + 4x⁸ + 4x⁶ + 6x⁴ + 4x² + 4x + 10	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.20	$10$	x¹⁰ + 4x⁹ + 6x⁶ + 2x⁴ + 4x² + 4x + 6	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.21	$10$	x¹⁰ + 4x⁸ + 6x⁴ + 4x³ + 4x + 10	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.22	$10$	x¹⁰ + 4x⁹ + 6x⁸ + 4x⁵ + 4x² + 10	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[8/5, 8/5, 8/5, 8/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.23	$10$	x¹⁰ + 4x⁸ + 4x⁷ + 2x⁶ + 2x⁴ + 4x² + 4x + 14	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.24	$10$	x¹⁰ + 4x⁸ + 6x⁶ + 4x⁵ + 2x⁴ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.25	$10$	x¹⁰ + 4x⁷ + 4x⁶ + 4x⁵ + 4x⁴ + 10	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[6/5, 6/5, 6/5, 6/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.26	$10$	x¹⁰ + 4x⁹ + 4x⁸ + 6x⁶ + 2x⁴ + 4x² + 4x + 14	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.27	$10$	x¹⁰ + 4x⁹ + 4x⁸ + 4x⁷ + 2x⁶ + 4x⁵ + 2x⁴ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.28	$10$	x¹⁰ + 4x⁹ + 4x⁸ + 4x⁶ + 4x⁵ + 2x⁴ + 4x² + 4x + 14	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[14/5, 14/5, 14/5, 14/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$
2.10.19.29	$10$	x¹⁰ + 4x⁹ + 4x⁷ + 4x⁵ + 10	$2$	$10$	$1$	$19$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[3]$	$[8/5, 8/5, 8/5, 8/5, 3]_{5}^{4}$	$[10, 0]$	$[1, 4]$

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Elliptic curves over $\Q$
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