Local Number Field Search Results

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

Results (displaying matches 1-50 of )

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
2.12.0.1	x^12 - 26x^10 + 275x^8 - 1500x^6 + 4375x^4 - 6250x^2 + 7221	2	1	12	0	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
2.12.8.1	x^12 - 6x^9 + 12x^6 - 8x^3 + 16	2	3	4	8	$C_3 : C_4$ (as 12T5)	$ [\ ]_{3}^{4}$
2.12.8.2	x^12 - 8x^3 + 16	2	3	4	8	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{3}^{12}$
2.12.12.1	x^12 - 48x^10 + 49x^8 + 8x^6 + 19x^4 - 24x^2 + 59	2	2	6	12	$C_2^5.(C_2\times C_6)$ (as 12T134)	$ [2, 2, 2, 2, 2, 2]^{6}$
2.12.12.10	x^12 - 6x^10 + 23x^8 - 28x^6 - 9x^4 - 30x^2 - 15	2	2	6	12	$C_2^2\wr C_2:C_3$ (as 12T58)	$ [2, 2, 2, 2]^{6}$
2.12.12.11	x^12 - 6x^10 - 73x^8 + 140x^6 + 79x^4 - 6x^2 + 57	2	2	6	12	$A_4 \times C_2$ (as 12T7)	$ [2, 2]^{6}$
2.12.12.12	x^12 + 66x^10 - 93x^8 - 68x^6 - 41x^4 + 66x^2 - 123	2	2	6	12	$C_4\times A_4$ (as 12T29)	$ [2, 2, 2]^{6}$
2.12.12.13	x^12 - 18x^10 - 13x^8 - 44x^6 + 55x^4 + 62x^2 + 21	2	2	6	12	$C_2^5.C_6$ (as 12T105)	$ [2, 2, 2, 2, 2]^{6}$
2.12.12.14	x^12 + 4x^10 + 21x^8 - 16x^6 + 43x^4 + 12x^2 - 1	2	2	6	12	$C_2^5.(C_2\times C_6)$ (as 12T134)	$ [2, 2, 2, 2, 2, 2]^{6}$
2.12.12.15	x^12 - 28x^10 - 63x^8 - 32x^6 + 19x^4 + 60x^2 - 21	2	2	6	12	$C_2^5.(C_2\times C_6)$ (as 12T134)	$ [2, 2, 2, 2, 2, 2]^{6}$
2.12.12.16	x^12 - 16x^10 - 23x^8 + 24x^6 - 29x^4 - 8x^2 - 13	2	2	6	12	$C_2^5.(C_2\times C_6)$ (as 12T134)	$ [2, 2, 2, 2, 2, 2]^{6}$
2.12.12.17	x^12 + 22x^10 + 75x^8 - 12x^6 - 89x^4 + 54x^2 - 115	2	2	6	12	$C_4\times A_4$ (as 12T29)	$ [2, 2]^{12}$
2.12.12.18	x^12 + 80x^10 + 81x^8 - 160x^6 - 117x^4 + 80x^2 + 227	2	2	6	12	$D_4 \times C_3$ (as 12T14)	$ [2, 2]^{6}$
2.12.12.19	x^12 - 6x^10 + 27x^8 - 4x^6 + 7x^4 + 10x^2 + 29	2	2	6	12	$C_2^5.C_6$ (as 12T105)	$ [2, 2, 2, 2]^{12}$
2.12.12.2	x^12 - 6x^10 - 13x^8 - 28x^6 + 15x^4 - 30x^2 - 3	2	2	6	12	$C_2^5.C_6$ (as 12T105)	$ [2, 2, 2, 2, 2]^{6}$
2.12.12.20	x^12 - 18x^10 - 49x^8 - 52x^6 + 39x^4 + 6x^2 + 9	2	2	6	12	$C_2\times C_2^2\wr C_2:C_3$ (as 12T87)	$ [2, 2, 2, 2, 2]^{6}$
2.12.12.21	x^12 + 44x^10 + 45x^8 - 48x^6 + 59x^4 - 60x^2 + 23	2	2	6	12	$C_2^5.(C_2\times C_6)$ (as 12T134)	$ [2, 2, 2, 2, 2, 2]^{6}$
2.12.12.22	x^12 - 52x^10 - 7x^8 + 32x^6 + 35x^4 - 44x^2 - 29	2	2	6	12	$C_2^5.(C_2\times C_6)$ (as 12T134)	$ [2, 2, 2, 2, 2, 2]^{6}$
2.12.12.23	x^12 - 2x^10 - 65x^8 + 100x^6 - 97x^4 - 98x^2 + 97	2	2	6	12	$C_2^2 \times A_4$ (as 12T25)	$ [2, 2, 2]^{6}$
2.12.12.24	x^12 - 100x^10 - 59x^8 + 104x^6 + 387x^4 + 444x^2 + 439	2	2	6	12	$D_4 \times C_3$ (as 12T14)	$ [2, 2]^{6}$
2.12.12.25	x^12 - 78x^10 - 1621x^8 + 460x^6 - 1977x^4 + 866x^2 + 749	2	2	6	12	$C_{12}$ (as 12T1)	$ [2]^{6}$
2.12.12.26	x^12 - 162x^10 + 26423x^8 + 125508x^6 - 64481x^4 - 122498x^2 - 86071	2	2	6	12	$C_6\times C_2$ (as 12T2)	$ [2]^{6}$
2.12.12.27	x^12 - 18x^10 + 171x^8 + 116x^6 - 313x^4 + 190x^2 + 877	2	6	2	12	$A_4:C_4$ (as 12T30)	$ [4/3, 4/3]_{3}^{4}$
2.12.12.28	x^12 - x^10 + 2x^8 - x^6 - 2x^4 + 3x^2 + 1	2	6	2	12	$S_4$ (as 12T9)	$ [4/3, 4/3]_{3}^{2}$
2.12.12.29	x^12 + 6x^10 + 51x^8 - 252x^6 - 393x^4 - 234x^2 - 203	2	6	2	12	12T159	$ [4/3, 4/3, 4/3, 4/3]_{3}^{12}$
2.12.12.3	x^12 - 16x^10 - 51x^8 - 8x^6 + 43x^4 + 24x^2 - 57	2	2	6	12	$C_2^5.(C_2\times C_6)$ (as 12T134)	$ [2, 2, 2, 2, 2, 2]^{6}$
2.12.12.30	x^12 - 6x^10 + 15x^8 - 52x^6 + 111x^4 - 102x^2 - 991	2	6	2	12	$A_4\wr C_2$ (as 12T126)	$ [4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.12.12.31	x^12 + 4x^11 - 6x^10 + 8x^9 - 4x^8 + 8x^7 - 4x^6 + 4x^5 - 4x^4 + 8x + 8	2	4	3	12	12T205	$ [4/3, 4/3, 4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.12.12.32	x^12 + 6x^11 - 4x^10 - 2x^9 + 4x^8 - 8x^7 - 8x^6 - 8x^5 - 4x^4 - 8	2	4	3	12	$A_4\wr C_2$ (as 12T129)	$ [4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.12.12.33	x^12 + 6x^11 - 4x^9 - 2x^8 + 8x^7 + 8x^6 - 4x^5 + 8x^3 + 8x^2 + 8	2	4	3	12	$C_3\times S_4$ (as 12T45)	$ [4/3, 4/3]_{3}^{6}$
2.12.12.34	x^12 + 2x^11 + 2x^9 + 2x^7 + 2x^5 + 2x^3 + 2x + 2	2	12	1	12	12T254	$ [10/9, 10/9, 10/9, 10/9, 10/9, 10/9]_{9}^{6}$
2.12.12.4	x^12 - 6x^10 + 15x^8 - 20x^6 + 15x^4 - 38x^2 - 31	2	2	6	12	$C_2\times C_2^2\wr C_2:C_3$ (as 12T87)	$ [2, 2, 2, 2, 2]^{6}$
2.12.12.5	x^12 + 52x^10 - 11x^8 - 8x^6 - 45x^4 - 44x^2 - 9	2	2	6	12	$D_4\times A_4$ (as 12T51)	$ [2, 2, 2, 2]^{6}$
2.12.12.6	x^12 - 18x^10 + 11x^8 - 52x^6 - x^4 + 6x^2 - 11	2	2	6	12	$C_2^5.C_6$ (as 12T105)	$ [2, 2, 2, 2]^{12}$
2.12.12.7	x^12 - 48x^10 + 53x^8 + 40x^6 + 27x^4 - 56x^2 + 47	2	2	6	12	$C_2^5.(C_2\times C_6)$ (as 12T134)	$ [2, 2, 2, 2, 2, 2]^{6}$
2.12.12.8	x^12 + 8x^10 - 31x^8 + 64x^6 - 53x^4 - 8x^2 - 45	2	2	6	12	$D_4\times A_4$ (as 12T51)	$ [2, 2, 2, 2]^{6}$
2.12.12.9	x^12 - 18x^10 + 7x^8 - 28x^6 - x^4 - 18x^2 - 7	2	2	6	12	$C_2^2\wr C_2:C_3$ (as 12T58)	$ [2, 2, 2, 2]^{6}$
2.12.14.1	x^12 + 2x^3 + 2	2	12	1	14	$S_4$ (as 12T8)	$ [4/3, 4/3]_{3}^{2}$
2.12.14.2	x^12 + 2x^4 + 2x^3 + 2	2	12	1	14	$A_4:C_4$ (as 12T27)	$ [4/3, 4/3]_{3}^{4}$
2.12.14.3	x^12 + 2x^3 + 2x^2 + 2	2	12	1	14	$A_4\wr C_2$ (as 12T128)	$ [4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.12.16.1	x^12 + 48x^10 + 17x^8 - 128x^6 + 171x^4 - 176x^2 + 3	2	6	2	16	12T208	$ [4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$
2.12.16.10	x^12 + 54x^10 - 257x^8 - 492x^6 - 945x^4 + 342x^2 + 81	2	6	2	16	12T158	$ [4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$
2.12.16.11	x^12 + 20x^10 - 44x^8 - 4x^6 - 16x^4 - 48	2	6	2	16	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [2]_{3}^{6}$
2.12.16.12	x^12 + 18x^10 + 171x^8 - 404x^6 - 281x^4 - 286x^2 + 461	2	6	2	16	12T159	$ [4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$
2.12.16.13	x^12 + 12x^10 + 12x^8 + 8x^6 + 32x^4 - 16x^2 + 16	2	6	2	16	$D_6$ (as 12T3)	$ [2]_{3}^{2}$
2.12.16.14	x^12 + 36x^10 + 37x^8 + 88x^6 - 61x^4 + 68x^2 - 105	2	6	2	16	12T208	$ [4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$
2.12.16.15	x^12 - 71x^8 + 123x^4 - 245	2	6	2	16	$\GL(2,Z/4)$ (as 12T50)	$ [4/3, 4/3, 2, 2]_{3}^{2}$
2.12.16.16	x^12 - 54x^10 - 509x^8 - 964x^6 - 777x^4 - 934x^2 + 357	2	6	2	16	$A_4:C_4$ (as 12T30)	$ [4/3, 4/3, 2]_{3}^{2}$
2.12.16.17	x^12 + 9x^8 - 224x^6 + 187x^4 - 32x^2 - 133	2	6	2	16	12T208	$ [4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$
2.12.16.18	x^12 + x^10 + 6x^8 - 3x^6 + 6x^4 + x^2 - 3	2	6	2	16	$C_3 : C_4$ (as 12T5)	$ [2]_{3}^{2}$

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