Local Number Field Search Results

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

Results (displaying all 28 matches)

Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
x^12 + x^2 - x + 2	13	1	12	0	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
x^12 + 338x^8 + 8788x^6 + 28561x^4 + 19307236	13	2	6	6	$C_6\times C_2$ (as 12T2)	$ [\ ]_{2}^{6}$
x^12 + 28561x^4 - 742586x^2 + 9653618	13	2	6	6	$C_{12}$ (as 12T1)	$ [\ ]_{2}^{6}$
x^12 - 39x^9 - 338x^6 + 10985x^3 + 228488	13	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
x^12 + 169x^6 - 2197x^3 + 57122	13	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
x^12 + 26x^9 + 845x^6 + 6591x^3 + 114244	13	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
x^12 - 104x^8 - 45968x^4 - 2847312	13	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
x^12 - 52x^8 + 676x^4 - 79092	13	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
x^12 - 338x^4 + 13182	13	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
x^12 + 234x^8 + 16900x^4 + 474552	13	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
x^12 - 117x^6 + 10816	13	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
x^12 + 39x^6 + 676	13	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
x^12 - 13x^6 + 2704	13	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
x^12 - 13x^6 + 338	13	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
x^12 + 65x^6 + 1352	13	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
x^12 - 143x^6 + 5408	13	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
x^12 - 13	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 + 1664	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 + 6656	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 + 26624	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 - 52	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 - 208	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 - 832	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 - 3328	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 - 13312	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 + 26	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 + 104	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
x^12 + 416	13	12	1	11	$C_{12}$ (as 12T1)	$ [\ ]_{12}$

---