Local Number Field Search Results

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

Results (displaying all 17 matches)

Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
x^12 - x^3 - 2x + 3	5	1	12	0	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
x^12 + 500x^6 - 3125x^2 + 62500	5	2	6	6	$C_6\times C_2$ (as 12T2)	$ [\ ]_{2}^{6}$
x^12 - 3125x^2 + 31250	5	2	6	6	$C_{12}$ (as 12T1)	$ [\ ]_{2}^{6}$
x^12 - 30x^9 + 175x^6 + 500x^3 + 5000	5	3	4	8	$C_3 : C_4$ (as 12T5)	$ [\ ]_{3}^{4}$
x^12 + 25x^6 - 250x^3 + 1250	5	3	4	8	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{3}^{12}$
x^12 - 10x^8 - 375x^4 - 2000	5	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
x^12 - 10x^8 + 25x^4 - 500	5	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
x^12 - 25x^4 + 250	5	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
x^12 + 30x^8 + 275x^4 + 1000	5	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
x^12 + 6x^11 + 27x^10 + 80x^9 + 195x^8 + 366x^7 + 571x^6 + 702x^5 + 1005x^4 + 1140x^3 + 357x^2 - 138x + 44	5	6	2	10	$D_6$ (as 12T3)	$ [\ ]_{6}^{2}$
x^12 + 15x^6 + 100	5	6	2	10	$C_6\times S_3$ (as 12T18)	$ [\ ]_{6}^{6}$
x^12 + 25x^6 + 200	5	6	2	10	$C_3 : C_4$ (as 12T5)	$ [\ ]_{6}^{2}$
x^12 - 5x^6 + 50	5	6	2	10	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{6}^{6}$
x^12 - 5	5	12	1	11	$S_3 \times C_4$ (as 12T11)	$ [\ ]_{12}^{2}$
x^12 - 20	5	12	1	11	$S_3 \times C_4$ (as 12T11)	$ [\ ]_{12}^{2}$
x^12 + 10	5	12	1	11	$S_3 \times C_4$ (as 12T11)	$ [\ ]_{12}^{2}$
x^12 + 40	5	12	1	11	$S_3 \times C_4$ (as 12T11)	$ [\ ]_{12}^{2}$

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