Local Number Field Search Results

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

Results (displaying matches 1-50 of 75)

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
3.6.0.1	x^6 - x + 2	3	1	6	0	$C_6$ (as 6T1)	$ [\ ]^{6}$
3.6.3.1	x^6 - 6x^4 + 9x^2 - 27	3	2	3	3	$C_6$ (as 6T1)	$ [\ ]_{2}^{3}$
3.6.3.2	x^6 - 9x^2 + 27	3	2	3	3	$C_6$ (as 6T1)	$ [\ ]_{2}^{3}$
3.6.6.1	x^6 + 3x^5 - 2	3	3	2	6	$C_3^2:C_4$ (as 6T10)	$ [3/2, 3/2]_{2}^{2}$
3.6.6.2	x^6 + 6x^4 + 6x^3 + 18	3	3	2	6	$C_3^2:C_4$ (as 6T10)	$ [3/2, 3/2]_{2}^{2}$
3.6.6.3	x^6 + 3x^4 + 9	3	3	2	6	$D_{6}$ (as 6T3)	$ [3/2]_{2}^{2}$
3.6.6.4	x^6 + 3x^4 + 6x^3 + 9x^2 + 63x + 9	3	3	2	6	$D_{6}$ (as 6T3)	$ [3/2]_{2}^{2}$
3.6.6.5	x^6 + 6x^3 + 9x^2 + 9	3	3	2	6	$S_3^2$ (as 6T9)	$ [3/2, 3/2]_{2}^{2}$
3.6.6.6	x^6 + 3x + 3	3	6	1	6	$C_3^2:D_4$ (as 6T13)	$ [5/4, 5/4]_{4}^{2}$
3.6.6.7	x^6 + 3x + 6	3	6	1	6	$C_3^2:D_4$ (as 6T13)	$ [5/4, 5/4]_{4}^{2}$
3.6.7.1	x^6 + 6x^2 + 6	3	6	1	7	$S_3$ (as 6T2)	$ [3/2]_{2}$
3.6.7.2	x^6 + 3x^2 + 6	3	6	1	7	$D_{6}$ (as 6T3)	$ [3/2]_{2}^{2}$
3.6.7.3	x^6 + 6x^3 + 6x^2 + 6	3	6	1	7	$S_3\times C_3$ (as 6T5)	$ [3/2]_{2}^{3}$
3.6.7.4	x^6 + 3x^2 + 3	3	6	1	7	$S_3$ (as 6T2)	$ [3/2]_{2}$
3.6.7.5	x^6 + 6x^2 + 3	3	6	1	7	$D_{6}$ (as 6T3)	$ [3/2]_{2}^{2}$
3.6.7.6	x^6 + 3x^3 + 3x^2 + 3	3	6	1	7	$S_3\times C_3$ (as 6T5)	$ [3/2]_{2}^{3}$
3.6.8.1	x^6 + 6x^5 + 18x^2 + 9	3	3	2	8	$C_3^2:C_4$ (as 6T10)	$ [2, 2]^{4}$
3.6.8.10	x^6 + 6x^5 + 36	3	3	2	8	$S_3\times C_3$ (as 6T5)	$ [2, 2]^{2}$
3.6.8.2	x^6 + 6x^5 + 9x^2 + 9	3	3	2	8	$C_3^2:C_4$ (as 6T10)	$ [2, 2]^{4}$
3.6.8.3	x^6 + 18x^2 + 9	3	3	2	8	$C_6$ (as 6T1)	$ [2]^{2}$
3.6.8.4	x^6 + 18x^2 + 63	3	3	2	8	$C_6$ (as 6T1)	$ [2]^{2}$
3.6.8.5	x^6 + 9x^2 + 9	3	3	2	8	$S_3$ (as 6T2)	$ [2]^{2}$
3.6.8.6	x^6 + 18x^2 + 36	3	3	2	8	$C_6$ (as 6T1)	$ [2]^{2}$
3.6.8.7	x^6 + 6x^5 + 6x^3 + 72	3	3	2	8	$S_3\times C_3$ (as 6T5)	$ [2]^{6}$
3.6.8.8	x^6 + 3x^5 + 63	3	3	2	8	$S_3\times C_3$ (as 6T5)	$ [2, 2]^{2}$
3.6.8.9	x^6 + 6x^5 + 9	3	3	2	8	$S_3\times C_3$ (as 6T5)	$ [2, 2]^{2}$
3.6.9.1	x^6 + 3x^4 + 15	3	6	1	9	$C_6$ (as 6T1)	$ [2]_{2}$
3.6.9.10	x^6 + 6x^4 + 3	3	6	1	9	$C_6$ (as 6T1)	$ [2]_{2}$
3.6.9.11	x^6 + 6x^4 + 12	3	6	1	9	$C_6$ (as 6T1)	$ [2]_{2}$
3.6.9.12	x^6 + 3x^4 + 3	3	6	1	9	$D_{6}$ (as 6T3)	$ [2]_{2}^{2}$
3.6.9.13	x^6 + 6x^5 + 6x^4 + 21	3	6	1	9	$S_3\times C_3$ (as 6T5)	$ [3/2, 2]_{2}$
3.6.9.14	x^6 + 6x^5 + 6x^4 + 12	3	6	1	9	$S_3\times C_3$ (as 6T5)	$ [3/2, 2]_{2}$
3.6.9.15	x^6 + 6x^4 + 6x^3 + 12	3	6	1	9	$S_3\times C_3$ (as 6T5)	$ [3/2, 2]_{2}$
3.6.9.16	x^6 + 3x^4 + 6x^3 + 3	3	6	1	9	$S_3^2$ (as 6T9)	$ [3/2, 2]_{2}^{2}$
3.6.9.2	x^6 + 3x^4 + 6	3	6	1	9	$C_6$ (as 6T1)	$ [2]_{2}$
3.6.9.3	x^6 + 3x^4 + 24	3	6	1	9	$C_6$ (as 6T1)	$ [2]_{2}$
3.6.9.4	x^6 + 6x^4 + 6	3	6	1	9	$D_{6}$ (as 6T3)	$ [2]_{2}^{2}$
3.6.9.5	x^6 + 3x^4 + 3x^3 + 15	3	6	1	9	$S_3\times C_3$ (as 6T5)	$ [3/2, 2]_{2}$
3.6.9.6	x^6 + 3x^4 + 6x^3 + 6	3	6	1	9	$S_3\times C_3$ (as 6T5)	$ [3/2, 2]_{2}$
3.6.9.7	x^6 + 6x^5 + 3x^4 + 15	3	6	1	9	$S_3\times C_3$ (as 6T5)	$ [3/2, 2]_{2}$
3.6.9.8	x^6 + 6x^4 + 3x^3 + 6	3	6	1	9	$S_3^2$ (as 6T9)	$ [3/2, 2]_{2}^{2}$
3.6.9.9	x^6 + 6x^4 + 21	3	6	1	9	$C_6$ (as 6T1)	$ [2]_{2}$
3.6.10.1	x^6 - 18	3	3	2	10	$D_{6}$ (as 6T3)	$ [5/2]_{2}^{2}$
3.6.10.10	x^6 + 3x^5 + 24	3	6	1	10	$C_3^2:D_4$ (as 6T13)	$ [9/4, 9/4]_{4}^{2}$
3.6.10.11	x^6 + 3x^5 + 15	3	6	1	10	$C_3^2:D_4$ (as 6T13)	$ [9/4, 9/4]_{4}^{2}$
3.6.10.12	x^6 + 3x^5 + 3	3	6	1	10	$C_3^2:D_4$ (as 6T13)	$ [9/4, 9/4]_{4}^{2}$
3.6.10.2	x^6 + 9	3	3	2	10	$D_{6}$ (as 6T3)	$ [5/2]_{2}^{2}$
3.6.10.3	x^6 + 36	3	3	2	10	$D_{6}$ (as 6T3)	$ [5/2]_{2}^{2}$
3.6.10.4	x^6 + 3x^3 + 72	3	3	2	10	$S_3^2$ (as 6T9)	$ [3/2, 5/2]_{2}^{2}$
3.6.10.5	x^6 + 6x^3 + 45	3	3	2	10	$S_3^2$ (as 6T9)	$ [3/2, 5/2]_{2}^{2}$