LMFDB - p-adic field search results

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Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
7.14.0.1	x¹⁴ + 2x² - 2x + 3	$7$	$1$	$14$	$0$	$C_{14}$ (as 14T1)	$ [\ ]^{14}$
7.14.7.1	x¹⁴ - 117649x² + 1647086	$7$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$ [\ ]_{2}^{7}$
7.14.7.2	x¹⁴ - 686x⁸ + 117649x² - 3294172	$7$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$ [\ ]_{2}^{7}$
7.14.14.1	x¹⁴ + 14x¹³ + 7x¹² + 21x¹¹ + 14x¹⁰ + 7x⁹ + 28x⁸ + 36x⁷ + 7x⁶ + 35x⁵ + 42x⁴ + 28x³ + 35x² + 28x + 31	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.14.10	x¹⁴ + 14x¹² + 7x¹¹ + 14x¹⁰ + 21x⁹ + 42x⁸ + 22x⁷ + 42x⁶ + 42x⁵ + 42x⁴ + 14x³ + 28x + 10	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.11	x¹⁴ + 7x¹³ + 35x¹² + 35x¹¹ + 21x⁸ + 15x⁷ + 42x⁶ + 42x⁵ + 21x³ + 3	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.14.12	x¹⁴ + 21x¹³ + 35x¹¹ + 42x¹⁰ + 14x⁹ + 14x⁸ + 22x⁷ + 42x⁶ + 14x⁵ + 42x⁴ + 7x³ + 35x² + 14x + 17	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.13	x¹⁴ + 28x¹³ + 21x¹² + 14x¹¹ + 7x¹⁰ + 7x⁹ + 43x⁷ + 21x⁵ + 21x⁴ + 14x³ + 35x² + 7x + 31	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.14	x¹⁴ + 28x¹³ + 28x¹² + 28x¹¹ + 28x¹⁰ + x⁷ + 21x⁶ + 21x⁵ + 42x⁴ + 21x² + 28x + 31	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.14.15	x¹⁴ + 14x¹³ + 42x¹¹ + 42x¹⁰ + 14x⁹ + 36x⁷ + 7x⁶ + 14x⁵ + 42x⁴ + 28x³ + 42x² + 10	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.14.16	x¹⁴ + 21x¹³ + 42x¹² + 7x¹¹ + 7x¹⁰ + 7x⁹ + 28x⁸ + 22x⁷ + 7x⁶ + 35x⁵ + 21x⁴ + 7x³ + 14x² + 35x + 45	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.17	x¹⁴ + 14x¹³ + 42x¹² + 14x¹¹ + 28x¹⁰ + 35x⁸ + 8x⁷ + 14x³ + 35x + 10	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.18	x¹⁴ + 42x¹³ + 21x¹² + 28x¹¹ + 35x¹⁰ + 14x⁸ + 22x⁷ + 21x⁶ + 21x⁵ + 21x⁴ + 21x³ + 21x² + 14x + 31	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.19	x¹⁴ + 35x¹³ + 21x¹² + 28x¹¹ + 7x¹⁰ + 7x⁹ + 43x⁷ + 28x⁶ + 28x⁵ + 21x⁴ + 7x² + 42x + 10	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.14.2	x¹⁴ + 14x¹³ + 21x¹¹ + 14x¹⁰ + 14x⁸ + 15x⁷ + 14x⁶ + 21x⁵ + 21x³ + 21x² + 35x + 45	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.20	x¹⁴ + 14x¹³ + 28x¹² + 28x¹¹ + 14x¹⁰ + 28x⁹ + 35x⁸ + 36x⁷ + 21x⁵ + 42x⁴ + 28x³ + 28x² + 42x + 3	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.14.21	x¹⁴ + 28x¹² + 42x¹¹ + 42x⁹ + 21x⁸ + 29x⁷ + 21x⁶ + 35x⁵ + 7x⁴ + 14x³ + 28x² + 42x + 45	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.14.22	x¹⁴ + 42x¹³ + 14x¹² + 14x¹¹ + 28x⁹ + 28x⁸ + 15x⁷ + 35x⁶ + 35x⁵ + 7x⁴ + 42x³ + 7x² + 28x + 31	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.14.23	x¹⁴ + 35x¹³ + 7x¹⁰ + 7x⁹ + 43x⁷ + 35x⁵ + 7x⁴ + 28x³ + 28x² + 28x + 24	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.24	x¹⁴ + 7x¹³ + 7x¹¹ + 7x¹⁰ + 42x⁹ + 14x⁸ + 22x⁷ + 35x⁶ + 21x⁴ + 7x³ + 7x² + 42x + 17	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.14.25	x¹⁴ + 14x¹³ + 14x¹² + 28x¹¹ + 7x⁹ + 28x⁸ + 22x⁷ + 35x⁶ + 21x⁵ + 14x⁴ + 21x + 38	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.14.26	x¹⁴ + 42x¹³ + 28x¹² + 21x¹¹ + 14x¹⁰ + 14x⁸ + 29x⁷ + 42x⁶ + 28x⁵ + 7x⁴ + 35x³ + 35x² + 35x + 31	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.27	x¹⁴ + 35x¹³ + 42x¹² + 42x¹¹ + 42x¹⁰ + 7x⁹ + 42x⁸ + 36x⁷ + 14x⁶ + 21x⁵ + 28x⁴ + 35x³ + 7x² + 17	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.14.28	x¹⁴ - 14x¹¹ - 21x⁸ - 14x⁶ + 21x⁵ - 7x⁴ - 7x³ - 21x² - 14x + 21	$7$	$14$	$1$	$14$	14T32	$ [13/12, 13/12]_{12}^{2}$
7.14.14.29	x¹⁴ + 7x¹³ - 21x¹¹ - 14x¹⁰ - 21x⁹ + 7x⁷ + 21x⁶ + 14x⁵ + 7x⁴ - 14x³ - 14x² - 14x - 14	$7$	$14$	$1$	$14$	14T32	$ [13/12, 13/12]_{12}^{2}$
7.14.14.3	x¹⁴ + 28x¹³ + 14x¹² + 21x¹¹ + 21x⁸ + 15x⁷ + 35x⁶ + 21x⁵ + 28x⁴ + 42x³ + 28x² + 3	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.30	x¹⁴ + 21x¹² + 21x¹¹ - 21x¹⁰ + 7x⁹ - 21x⁸ - 7x⁷ + 14x⁶ - 14x⁵ + 21x⁴ - 7x³ - 7x² - 7x - 21	$7$	$14$	$1$	$14$	14T32	$ [13/12, 13/12]_{12}^{2}$
7.14.14.31	x¹⁴ - 14x¹³ + 14x¹² + 21x¹⁰ - 21x⁹ + 14x⁸ - 7x⁶ - 14x⁵ - 14x⁴ - 14x³ - 14x² + 7x + 14	$7$	$14$	$1$	$14$	14T32	$ [13/12, 13/12]_{12}^{2}$
7.14.14.32	x¹⁴ + 21x¹³ - 14x¹² + 21x¹¹ + 7x¹⁰ + 14x⁸ - 21x⁷ - 14x⁶ + 14x⁵ - 14x⁴ + 21x³ + 7x² + 7x - 14	$7$	$14$	$1$	$14$	14T32	$ [13/12, 13/12]_{12}^{2}$
7.14.14.33	x¹⁴ - 14x¹² - 14x¹¹ - 7x¹⁰ - 21x⁹ - 21x⁸ + 14x⁷ - 14x⁶ - 14x⁴ + 21x² + 21x + 14	$7$	$14$	$1$	$14$	14T32	$ [13/12, 13/12]_{12}^{2}$
7.14.14.4	x¹⁴ + 35x¹³ + 21x¹² + 42x¹¹ + 35x¹⁰ + 42x⁹ + 15x⁷ + 7x⁶ + 14x⁵ + 7x² + 28x + 3	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.14.5	x¹⁴ + 35x¹² + 28x¹¹ + 14x¹⁰ + 42x⁹ + 21x⁸ + x⁷ + 21x⁶ + 42x⁵ + 7x³ + 21x² + 28x + 10	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.14.6	x¹⁴ + 35x¹³ + 14x¹¹ + 35x¹⁰ + 14x⁹ + 7x⁸ + 43x⁷ + 42x⁶ + 42x⁴ + 7x³ + 42x² + 28x + 24	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.7	x¹⁴ + 14x¹³ + 21x¹² + 35x¹¹ + 14x¹⁰ + 7x⁹ + 21x⁸ + 15x⁷ + 14x⁶ + 21x⁵ + 35x⁴ + 42x³ + 14x² + 14x + 38	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.14.8	x¹⁴ + 7x¹³ + 14x¹² + 14x¹¹ + 21x¹⁰ + 7x⁹ + 35x⁸ + 8x⁷ + 7x⁵ + 21x⁴ + 35x² + 28x + 45	$7$	$7$	$2$	$14$	14T23	$ [7/6, 7/6]_{6}^{2}$
7.14.14.9	x¹⁴ + 7x¹³ + 35x¹² + 7x¹¹ + 42x¹⁰ + 42x⁹ + 42x⁸ + 43x⁷ + 14x⁶ + 35x⁵ + 14x⁴ + 7x + 3	$7$	$7$	$2$	$14$	14T24	$ [7/6, 7/6]_{6}^{2}$
7.14.15.1	x¹⁴ + 21x¹³ + 14x¹² + 7x¹¹ - 14x¹⁰ - 7x⁹ - 7x⁸ - 7x⁷ - 7x⁶ - 21x⁵ - 7x⁴ - 14x³ + 7x² + 21	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.15.10	x¹⁴ + 14x¹² - 21x¹¹ + 7x¹⁰ - 21x⁹ + 21x⁸ - 7x⁷ - 7x⁶ + 21x⁵ - 21x⁴ - 7x³ - 14x² - 7	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$ [7/6]_{6}$
7.14.15.11	x¹⁴ - 14x¹¹ - 21x¹⁰ - 21x⁹ + 7x⁸ + 21x⁷ - 14x⁶ + 7x⁵ + 21x⁴ + 14x³ - 7x² + 14	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.15.12	x¹⁴ - 21x¹³ - 7x¹² + 14x¹¹ + 14x¹⁰ + 21x⁹ + 14x⁸ - 21x⁷ - 14x⁶ - 14x⁵ + 7x⁴ - 21x² - 14	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.15.2	x¹⁴ - 21x¹³ - 21x¹² - 21x¹¹ - 14x¹⁰ + 7x⁹ + 21x⁷ - 7x⁶ + 14x⁵ - 21x³ - 14x² - 21	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.15.3	x¹⁴ + 14x¹³ - 21x¹² - 21x¹⁰ + 21x⁸ + 14x⁷ + 21x⁶ + 21x⁵ + 14x⁴ - 14x³ + 21x² + 7	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.15.4	x¹⁴ + 14x¹² + 7x¹¹ + 7x¹⁰ - 21x⁹ - 21x⁸ + 14x⁷ - 7x⁶ + 21x⁵ - 21x³ + 14x² - 7	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$ [7/6]_{6}^{2}$
7.14.15.5	x¹⁴ - 21x¹³ + 7x¹² + 14x¹¹ - 21x⁹ + 7x⁷ + 14x⁶ - 21x⁴ + 14x³ + 7x² + 14	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$ [7/6]_{6}$
7.14.15.6	x¹⁴ + 14x¹³ + 7x¹² + 14x¹¹ - 7x¹⁰ - 14x⁸ + 21x⁷ + 7x⁶ - 7x⁵ + 14x⁴ - 14x³ + 21x² - 7	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$ [7/6]_{6}$
7.14.15.7	x¹⁴ + 21x¹³ - 14x¹² - 14x¹¹ + 14x¹⁰ - 14x⁹ - 14x⁸ - 21x⁷ - 14x⁶ - 21x⁵ - 7x⁴ + 14x³ - 21x² - 21	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$ [7/6]_{6}$
7.14.15.8	x¹⁴ - 21x¹² - 21x¹¹ + 21x¹⁰ + 21x⁹ - 14x⁷ + 7x⁶ + 7x⁵ + 7x³ - 7x² - 14	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$ [7/6]_{6}$
7.14.15.9	x¹⁴ - 7x¹³ - 21x¹² + 21x¹¹ + 21x¹⁰ + 14x⁹ - 7x⁷ - 14x⁵ - 14x⁴ + 7x³ + 14x² + 14	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$ [7/6]_{6}$
7.14.16.1	x¹⁴ + 28x¹³ + 21x¹² + 42x¹¹ + 14x¹⁰ + 28x⁸ + 37x⁷ + 28x⁵ + 7x⁴ + 7x³ + 35x² + 28x + 31	$7$	$7$	$2$	$16$	$C_7^2:C_6$ (as 14T14)	$ [4/3, 4/3]_{3}^{2}$
7.14.16.10	x¹⁴ + 7x¹³ + 42x¹² + 7x¹¹ + 21x⁹ + 14x⁸ + 44x⁷ + 35x⁶ + 35x⁵ + 21x⁴ + 21x³ + 21x² + 14x + 3	$7$	$7$	$2$	$16$	14T23	$ [4/3, 4/3]_{3}^{4}$

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