LMFDB - p-adic field search results

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Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
3.9.0.1	x⁹ - x³ + x² + 1	$3$	$1$	$9$	$0$	$C_9$ (as 9T1)	$ [\ ]^{9}$
3.9.9.1	x⁹ + 54x⁵ + 27x³ + 189	$3$	$3$	$3$	$9$	$S_3\times C_3$ (as 9T4)	$ [3/2]_{2}^{3}$
3.9.9.10	x⁹ + 6x⁶ + 9x⁴ + 27	$3$	$3$	$3$	$9$	$C_3^3:C_3):C_2$ (as 9T22)	$ [3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.11	x⁹ + 3x + 3	$3$	$9$	$1$	$9$	$(C_3^2:C_8):C_2$ (as 9T19)	$ [9/8, 9/8]_{8}^{2}$
3.9.9.12	x⁹ + 6x + 6	$3$	$9$	$1$	$9$	$(C_3^2:C_8):C_2$ (as 9T19)	$ [9/8, 9/8]_{8}^{2}$
3.9.9.2	x⁹ + 18x³ + 27x + 27	$3$	$3$	$3$	$9$	$C_3^2 : S_3 $ (as 9T13)	$ [3/2, 3/2]_{2}^{3}$
3.9.9.3	x⁹ + 9x⁴ + 18x³ + 54	$3$	$3$	$3$	$9$	$C_3^3:C_3):C_2$ (as 9T22)	$ [3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.4	x⁹ + 3x⁶ + 9x⁴ + 54	$3$	$3$	$3$	$9$	$C_3^3:C_3):C_2$ (as 9T22)	$ [3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.5	x⁹ + 3x⁷ + 3x⁶ + 54	$3$	$3$	$3$	$9$	$C_3^3:C_3):C_2$ (as 9T22)	$ [3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.6	x⁹ + 3x⁷ + 3x⁶ + 18x⁴ + 54	$3$	$3$	$3$	$9$	$S_3\times C_3$ (as 9T4)	$ [3/2]_{2}^{3}$
3.9.9.7	x⁹ + 18x³ + 54x + 27	$3$	$3$	$3$	$9$	$C_3^2 : S_3 $ (as 9T13)	$ [3/2, 3/2]_{2}^{3}$
3.9.9.8	x⁹ + 6x⁷ + 18x³ + 27	$3$	$3$	$3$	$9$	$C_3^3:C_3):C_2$ (as 9T22)	$ [3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.9	x⁹ + 18x⁵ + 27x² + 54	$3$	$3$	$3$	$9$	$C_3^3:C_3):C_2$ (as 9T22)	$ [3/2, 3/2, 3/2]_{2}^{3}$
3.9.10.1	x⁹ + 3x² + 3	$3$	$9$	$1$	$10$	$C_3^2:Q_8$ (as 9T14)	$ [5/4, 5/4]_{4}^{2}$
3.9.10.2	x⁹ + 3x² + 6	$3$	$9$	$1$	$10$	$S_3^2:C_2$ (as 9T16)	$ [5/4, 5/4]_{4}^{2}$
3.9.12.1	x⁹ + 18x⁵ + 18x³ + 27x² + 216	$3$	$3$	$3$	$12$	$C_3^2$ (as 9T2)	$ [2]^{3}$
3.9.12.10	x⁹ + 24x⁶ + 18x⁵ + 27	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.12.11	x⁹ + 21x⁶ + 54x² + 54	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.12.12	x⁹ + 3x⁶ + 18x⁵ + 54	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.12.13	x⁹ + 3x⁸ + 72x³ + 27	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.12.14	x⁹ + 3x⁸ + 45x³ + 27	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.12.15	x⁹ + 72x³ + 54x² + 54	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.12.16	x⁹ + 9x⁵ + 18x³ + 27x² + 27	$3$	$3$	$3$	$12$	$S_3\times C_3$ (as 9T4)	$ [2]^{6}$
3.9.12.17	x⁹ + 6x⁸ + 6x⁶ + 27	$3$	$3$	$3$	$12$	$C_3^2 : S_3 $ (as 9T13)	$ [2, 2]^{6}$
3.9.12.18	x⁹ + 6x⁸ + 18x³ + 27	$3$	$3$	$3$	$12$	$C_3^3:C_3):C_2$ (as 9T22)	$ [2, 2, 2]^{6}$
3.9.12.19	x⁹ + 6x⁸ + 18x⁵ + 18x³ + 27	$3$	$3$	$3$	$12$	$C_3^3:C_3):C_2$ (as 9T22)	$ [2, 2, 2]^{6}$
3.9.12.2	x⁹ + 18x⁵ + 18x³ + 27x² + 54	$3$	$3$	$3$	$12$	$C_9$ (as 9T1)	$ [2]^{3}$
3.9.12.20	x⁹ + 6x⁶ + 54x² + 27	$3$	$3$	$3$	$12$	$C_3^3:C_3):C_2$ (as 9T22)	$ [2, 2, 2]^{6}$
3.9.12.21	x⁹ + 3x⁴ + 6	$3$	$9$	$1$	$12$	$C_3^2:C_4$ (as 9T9)	$ [3/2, 3/2]_{2}^{2}$
3.9.12.22	x⁹ + 6x⁴ + 6x³ + 3	$3$	$9$	$1$	$12$	$C_3^2 : C_6$ (as 9T11)	$ [3/2, 3/2]_{2}^{3}$
3.9.12.23	x⁹ + 6x⁴ + 3x³ + 3	$3$	$9$	$1$	$12$	$C_3^2 : C_6$ (as 9T11)	$ [3/2, 3/2]_{2}^{3}$
3.9.12.24	x⁹ + 3x⁴ + 3	$3$	$9$	$1$	$12$	$S_3^2$ (as 9T8)	$ [3/2, 3/2]_{2}^{2}$
3.9.12.25	x⁹ + 3x⁴ + 6x³ + 3	$3$	$9$	$1$	$12$	$C_3^2:C_8$ (as 9T15)	$ [3/2, 3/2]_{2}^{4}$
3.9.12.26	x⁹ + 3x⁴ + 3x³ + 3	$3$	$9$	$1$	$12$	$C_3^2:C_8$ (as 9T15)	$ [3/2, 3/2]_{2}^{4}$
3.9.12.3	x⁹ + 6x⁸ + 3x⁶ + 9x³ + 135	$3$	$3$	$3$	$12$	$C_9$ (as 9T1)	$ [2]^{3}$
3.9.12.4	x⁹ + 6x⁶ + 18x⁵ + 36x³ + 27	$3$	$3$	$3$	$12$	$C_3^2:C_3$ (as 9T7)	$ [2, 2]^{3}$
3.9.12.5	x⁹ + 18x⁵ + 18x³ + 27x² + 27	$3$	$3$	$3$	$12$	$C_9:C_3$ (as 9T6)	$ [2, 2]^{3}$
3.9.12.6	x⁹ + 3x⁸ + 6x⁶ + 27	$3$	$3$	$3$	$12$	$C_9:C_3$ (as 9T6)	$ [2, 2]^{3}$
3.9.12.7	x⁹ + 18x⁵ + 72x³ + 54	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.12.8	x⁹ + 12x⁶ + 54x² + 54	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.12.9	x⁹ + 15x⁶ + 18x⁵ + 27	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$ [2, 2, 2]^{3}$
3.9.13.1	x⁹ + 6x⁵ + 6	$3$	$9$	$1$	$13$	$(C_3^2:C_8):C_2$ (as 9T19)	$ [13/8, 13/8]_{8}^{2}$
3.9.13.10	x⁹ + 3x⁶ + 3x⁵ + 3x³ + 6	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$ [3/2, 3/2, 5/3]_{2}^{3}$
3.9.13.2	x⁹ + 6x⁵ + 3x³ + 3	$3$	$9$	$1$	$13$	$C_3^2 : D_{6} $ (as 9T18)	$ [3/2, 3/2, 5/3]_{2}^{2}$
3.9.13.3	x⁹ + 3x⁶ + 6x⁵ + 6x³ + 3	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$ [3/2, 3/2, 5/3]_{2}^{3}$
3.9.13.4	x⁹ + 6x⁵ + 6x³ + 3	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$ [3/2, 3/2, 5/3]_{2}^{3}$
3.9.13.5	x⁹ + 6x⁶ + 6x⁵ + 6x³ + 3	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$ [3/2, 3/2, 5/3]_{2}^{3}$
3.9.13.6	x⁹ + 3x⁵ + 3	$3$	$9$	$1$	$13$	$(C_3^2:C_8):C_2$ (as 9T19)	$ [13/8, 13/8]_{8}^{2}$
3.9.13.7	x⁹ + 3x⁵ + 6x³ + 3	$3$	$9$	$1$	$13$	$C_3^2 : D_{6} $ (as 9T18)	$ [3/2, 3/2, 5/3]_{2}^{2}$
3.9.13.8	x⁹ + 3x⁵ + 3x³ + 6	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$ [3/2, 3/2, 5/3]_{2}^{3}$

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