Local Number Field Search Results

Degree		Discriminant exponent $c$		Galois group
Prime $p$		Ramification index $e$		Top slope

Results (displaying matches 1-50 of 590)

Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
x^14 - x^5 - x^3 - x + 1	2	1	14	0	$C_{14}$ (as 14T1)	$ [\ ]^{14}$
x^14 - 2x^7 + 4	2	7	2	12	$(C_7:C_3) \times C_2$ (as 14T5)	$ [\ ]_{7}^{6}$
x^14 + 3x^12 - 2x^11 - 2x^10 + 4x^9 + 2x^7 + 2x^5 + 2x^4 - 2x^3 + 2x^2 + 4x - 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 2x^11 + 2x^9 + 2x^6 + 2x^5 + 2x^4 + 2x^3 + 2x^2 + 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 2x^10 + 2x^7 + 2x^5 + 2x^4 + 2x^3 - 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2]^{14}$
x^14 + x^12 + 2x^9 + 2x^7 + 2x^6 + 2x^5 + 2x^4 + 2x^3 - 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 - x^12 + 2x^11 + 2x^10 + 2x^4 + 2x^3 + 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 - x^12 + 2x^11 + 2x^10 + 2x^9 + 2x^7 + 2x^6 + 2x^5 + 2x^4 + 2x^2 - 1	2	2	7	14	$C_2\times F_8$ (as 14T9)	$ [2, 2, 2, 2]^{7}$
x^14 + 2x^13 + x^12 + 4x^11 - 2x^10 + 2x^9 + 4x^8 - 2x^6 + 4x^5 + 4x^4 + 2x^3 + 4x^2 + 1	2	2	7	14	$C_{14}$ (as 14T1)	$ [2]^{7}$
x^14 - 2x^13 - 3x^12 - 2x^10 + 4x^9 + 2x^8 - 2x^7 - 2x^6 + 4x^5 + 4x^4 + 4x^3 + 4x^2 + 2x + 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2]^{14}$
x^14 + x^12 + 2x^10 + 2x^8 + 2x^7 + 2x^5 + 2x^4 + 2x^3 + 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2]^{14}$
x^14 + 4x^13 + 3x^12 + 2x^11 - 2x^9 + 2x^7 - 2x^4 - 2x^3 - 2x^2 + 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + 4x^13 + x^12 + 4x^10 + 2x^9 - 2x^8 - 2x^7 + 4x^6 - 2x^5 + 4x^4 - 2x^3 + 2x^2 + 1	2	2	7	14	$C_2^3:F_8$ (as 14T21)	$ [2, 2, 2, 2, 2, 2]^{7}$
x^14 + 2x^13 - x^12 + 2x^10 + 2x^9 + 2x^7 + 2x + 1	2	2	7	14	$C_2\times F_8$ (as 14T9)	$ [2, 2, 2]^{14}$
x^14 + 4x^13 - x^12 - 2x^11 + 2x^10 + 2x^9 + 2x^8 + 2x^7 + 2x^6 + 4x^4 - 2x^3 + 2x^2 + 2x + 1	2	2	7	14	$C_2^3:F_8$ (as 14T21)	$ [2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 4x^11 - 2x^9 + 2x^8 + 2x^7 + 4x^4 + 4x^3 - 2x^2 - 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2]^{14}$
x^14 + 4x^13 + x^12 + 4x^11 - 2x^10 + 2x^9 - 2x^8 + 4x^7 + 2x^6 - 2x^5 - 2x^4 - 2x^3 - 2x^2 + 4x + 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 2x^11 + 2x^10 + 2x^9 + 2x^8 + 2x^4 + 2x^3 + 2x^2 + 2x + 1	2	2	7	14	$F_8$ (as 14T6)	$ [2, 2, 2]^{7}$
x^14 - 3x^12 + 2x^11 + 2x^10 + 4x^8 + 4x^7 + 2x^6 + 2x^4 + 2x^2 + 2x + 3	2	2	7	14	$C_2\times F_8$ (as 14T9)	$ [2, 2, 2, 2]^{7}$
x^14 + 4x^13 - 3x^12 - 2x^11 + 2x^9 - 2x^8 + 2x^7 + 2x^6 - 2x^3 + 4x^2 + 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2]^{14}$
x^14 + 2x^13 + x^12 + 2x^9 + 2x^8 + 2x^7 + 2x^6 + 2x^3 + 2x - 1	2	2	7	14	$C_2\times F_8$ (as 14T9)	$ [2, 2, 2]^{14}$
x^14 - x^12 + 2x^11 + 2x^9 + 2x^8 + 2x^7 + 2x^6 + 2x^5 + 2x^4 + 2x^3 + 2x - 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 2x^11 + 2x^9 + 2x^8 + 2x^5 + 2x^4 + 2x - 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2]^{14}$
x^14 + 2x^13 - x^12 + 2x^7 + 2x^5 + 2x^3 + 2x - 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2]^{14}$
x^14 + 2x^13 + x^12 + 2x^10 + 2x^5 - 1	2	2	7	14	$F_8$ (as 14T6)	$ [2, 2, 2]^{7}$
x^14 + 2x^13 + 3x^12 + 4x^8 + 4x^7 + 4x^6 - 2x^5 - 2x^3 + 2x^2 + 2x - 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 2x^11 + 2x^10 + 2x^9 + 2x^5 + 2x^3 + 2x^2 + 1	2	2	7	14	$C_2^3:F_8$ (as 14T21)	$ [2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 4x^11 - 2x^10 + 2x^9 - 2x^7 + 4x^6 - 2x^2 + 2x + 3	2	2	7	14	$C_2^3:F_8$ (as 14T21)	$ [2, 2, 2, 2, 2, 2]^{7}$
x^14 + 4x^13 + x^12 + 2x^11 + 4x^9 + 2x^7 + 2x^6 - 2x^5 + 2x^4 + 2x^3 + 2x^2 + 2x - 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 - x^12 + 2x^11 + 2x^10 + 2x^7 + 2x^4 + 2x^2 + 2x + 1	2	2	7	14	$C_2^3:F_8$ (as 14T21)	$ [2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 2x^11 + 2x^10 + 2x^9 + 2x^8 + 2x^4 + 2x^3 + 2x - 1	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 - x^12 + 2x^10 + 2x^9 + 2x^7 + 2x^6 + 2x^5 + 2x^2 + 2x + 1	2	2	7	14	$C_2^3:F_8$ (as 14T21)	$ [2, 2, 2, 2, 2, 2]^{7}$
x^14 + 4x^13 - 3x^12 - 2x^11 + 2x^10 - 2x^9 + 4x^7 + 2x^6 + 2x^5 + 4x^3 + 4x^2 - 2x - 3	2	2	7	14	$C_2^3:F_8$ (as 14T21)	$ [2, 2, 2, 2, 2, 2]^{7}$
x^14 + 4x^13 + 3x^12 - 2x^11 + 2x^10 - 2x^8 + 4x^6 - 2x^5 + 4x^3 - 2x^2 + 2x + 1	2	2	7	14	$C_{14}$ (as 14T1)	$ [2]^{7}$
x^14 + 2x^12 + 2x^10 + 2x^9 + 2x^8 + 2x^7 + 2x^6 + 2x^4 + 2x^3 + 2x + 2	2	14	1	14	$C_2\times F_8:C_3$ (as 14T18)	$ [8/7, 8/7, 8/7]_{7}^{6}$
x^14 + 3x^12 + 2x^10 + 4x^9 - 2x^8 + 4x^7 + 2x^5 + 2x^4 + 2x^3 + 2x - 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + 2x^9 + 2x^4 + 2x^2 + 2x + 2	2	14	1	14	$F_8:C_3$ (as 14T11)	$ [8/7, 8/7, 8/7]_{7}^{3}$
x^14 + 2x^13 + x^12 + 2x^11 - 2x^10 + 2x^8 + 4x^7 - 2x^6 + 4x^5 + 4x^4 + 2x^2 - 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 - 3x^12 + 4x^11 - 2x^10 + 4x^9 - 2x^8 + 4x^6 - 2x^5 - 2x^4 + 2x^2 - 2x + 3	2	2	7	14	$C_2\times F_8$ (as 14T9)	$ [2, 2, 2, 2]^{7}$
x^14 + 2x^13 + 3x^12 + 2x^11 - 2x^10 + 2x^8 + 2x^7 + 4x^6 - 2x^4 - 2x^3 - 2x^2 + 4x - 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + x^12 + 1	2	2	7	14	$C_2\times F_8$ (as 14T9)	$ [2, 2, 2, 2]^{7}$
x^14 - 2x^13 - x^12 - 2x^11 + 4x^10 - 2x^9 + 2x^8 + 4x^7 - 2x^6 + 2x^5 + 4x^4 - 2x^3 + 2x^2 - 2x + 3	2	2	7	14	$C_2 \wr C_7$ (as 14T29)	$ [2, 2, 2, 2, 2, 2, 2]^{7}$
x^14 + 2x^13 + 2x^11 + 2x^10 + 2x^7 + 2x^6 + 2x^3 + 2	2	14	1	16	$C_2\times F_8:C_3$ (as 14T18)	$ [10/7, 10/7, 10/7]_{7}^{6}$
x^14 + 2x^12 + 2x^8 + 2x^5 + 2x^4 + 2x^3 + 2x^2 + 2	2	14	1	16	14T44	$ [8/7, 8/7, 8/7, 10/7, 10/7, 10/7]_{7}^{6}$
x^14 + 2x^10 + 2x^8 + 2x^7 + 2x^6 + 2x^5 + 2x^4 + 2x^3 + 2x^2 + 2	2	14	1	16	14T35	$ [8/7, 8/7, 8/7, 10/7, 10/7, 10/7]_{7}^{3}$
x^14 + 2x^13 + 2x^12 + 2x^11 + 2x^10 + 2x^9 + 2x^5 + 2x^4 + 2x^3 + 2	2	14	1	16	$F_8:C_3$ (as 14T11)	$ [10/7, 10/7, 10/7]_{7}^{3}$
x^14 + 2x^13 + 2x^10 + 2x^8 + 2x^7 + 2x^5 + 2x^4 + 2	2	14	1	18	$F_8:C_3$ (as 14T11)	$ [12/7, 12/7, 12/7]_{7}^{3}$
x^14 + 2x^10 + 2x^8 + 2x^7 + 2x^5 + 2	2	14	1	18	$F_8:C_3$ (as 14T11)	$ [12/7, 12/7, 12/7]_{7}^{3}$
x^14 + 2x^10 + 2x^9 + 2x^8 + 2x^7 + 2x^5 + 2x^4 + 2	2	14	1	18	14T35	$ [8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{3}$
x^14 + 2x^12 + 2x^10 + 2x^9 + 2x^8 + 2x^5 + 2x^2 + 2	2	14	1	18	14T44	$ [8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{6}$

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