Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 122)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.7695492605307.1	x^12 - x^10 - 8x^8 + 10x^6 - 4x^4 + 4x^2 - 3	\( -\,3^{13}\cdot 13^{6} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.7695492605307.3	x^12 - 4x^9 - 4x^6 + 3x^3 + 3	\( -\,3^{13}\cdot 13^{6} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.24321556876032.1	x^12 - 6x^11 + 14x^10 - 15x^9 + 7x^8 - 4x^7 + x^6 + 14x^5 - 17x^4 + 3x^3 + 7x^2 - 5x + 1	\( -\,2^{8}\cdot 3^{9}\cdot 13^{6} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.24321556876032.2	x^12 - x^10 - 4x^9 + 4x^8 + 9x^6 - 26x^5 + 12x^4 + 2x^3 - 5x^2 - 2x + 1	\( -\,2^{8}\cdot 3^{9}\cdot 13^{6} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.114516604000000.2	x^12 - 2x^11 + 3x^10 - 4x^9 + 14x^7 - 23x^6 + 14x^5 - 4x^3 + 3x^2 - 2x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 31^{5} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.114516604000000.3	x^12 - 3x^10 - 2x^9 - 3x^8 + 13x^6 + 16x^5 + 8x^4 - 10x^3 - 16x^2 - 4x + 4	\( -\,2^{8}\cdot 5^{6}\cdot 31^{5} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.130531955153488.1	x^12 - x^11 - 2x^10 + 2x^9 + 14x^8 - 4x^7 - 33x^6 - x^5 + 36x^4 + 12x^3 - 22x^2 - 8x + 8	\( 2^{4}\cdot 7^{6}\cdot 37^{5} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.130531955153488.2	x^12 - 3x^10 - 6x^9 + 3x^8 + 22x^7 - x^6 - 20x^5 - 11x^4 + 14x^3 + 13x^2 - 24x + 16	\( 2^{4}\cdot 7^{6}\cdot 37^{5} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.410797025187957.2	x^12 - 6x^11 + 27x^10 - 78x^9 + 162x^8 - 249x^7 + 282x^6 - 240x^5 + 168x^4 - 105x^3 + 54x^2 - 18x + 3	\( 3^{15}\cdot 31^{5} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.410797025187957.3	x^12 + 6x^10 - 7x^9 + 6x^8 - 24x^7 - 9x^6 + 51x^5 + 63x^4 - 43x^3 - 39x^2 + 9x + 7	\( 3^{15}\cdot 31^{5} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.1201907943079936.1	x^12 + 8x^10 + 22x^8 + 16x^6 - 31x^4 - 56x^2 - 16	\( -\,2^{32}\cdot 23^{4} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.1201907943079936.2	x^12 - 8x^10 + 22x^8 - 16x^6 - 31x^4 + 56x^2 - 16	\( -\,2^{32}\cdot 23^{4} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.1218719480020992.3	x^12 - 2x^9 - 8x^3 - 2	\( -\,2^{20}\cdot 3^{19} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.1218719480020992.4	x^12 - 2x^9 + 36x^6 + 28x^3 - 2	\( -\,2^{20}\cdot 3^{19} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.1518874382041088.21	x^12 - 4x^10 + 18x^8 - 52x^6 + 81x^4 - 72x^2 + 32	\( 2^{31}\cdot 29^{4} \)	$C_3^2:D_4$ (as 12T38)	Trivial (GRH)
12.0.1518874382041088.22	x^12 - 8x^10 + 22x^8 - 32x^6 + 49x^4 - 56x^2 + 32	\( 2^{31}\cdot 29^{4} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.9615263544639488.6	x^12 - 4x^10 + 6x^8 + 12x^6 + x^4 - 16x^2 - 2	\( -\,2^{35}\cdot 23^{4} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.9615263544639488.13	x^12 + 4x^10 + 6x^8 - 12x^6 + x^4 + 16x^2 - 2	\( -\,2^{35}\cdot 23^{4} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.24679069470425088.7	x^12 - 6x^6 - 3	\( -\,2^{18}\cdot 3^{23} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.24679069470425088.8	x^12 + 6x^6 - 3	\( -\,2^{18}\cdot 3^{23} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.54780521154084864.5	x^12 + 4x^10 + 10x^8 - 4x^6 + 8x^4 - 16x^2 + 6	\( 2^{35}\cdot 3^{13} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.54780521154084864.23	x^12 - 4x^10 + 10x^8 + 4x^6 + 8x^4 + 16x^2 + 6	\( 2^{35}\cdot 3^{13} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.54780521154084864.69	x^12 - 16x^6 + 96	\( 2^{35}\cdot 3^{13} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.54780521154084864.70	x^12 + 16x^6 + 96	\( 2^{35}\cdot 3^{13} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.77998046721343488.22	x^12 - 16x^9 + 90x^6 - 172x^3 - 2	\( -\,2^{26}\cdot 3^{19} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.77998046721343488.23	x^12 - 20x^9 + 54x^6 - 44x^3 - 2	\( -\,2^{26}\cdot 3^{19} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.98716277881700352.5	x^12 - 24x^6 - 48	\( -\,2^{20}\cdot 3^{23} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.98716277881700352.8	x^12 - 6x^9 + 12x^6 - 36x^3 - 18	\( -\,2^{20}\cdot 3^{23} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.98716277881700352.12	x^12 + 48x^6 - 12	\( -\,2^{20}\cdot 3^{23} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.98716277881700352.19	x^12 - 6x^9 - 12x^6 + 6	\( -\,2^{20}\cdot 3^{23} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.184884258895036416.2	x^12 + 12x^10 + 18x^8 - 40x^6 - 135x^4 - 36x^2 - 196	\( -\,2^{32}\cdot 3^{16} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.184884258895036416.3	x^12 - 12x^10 + 18x^8 + 40x^6 - 135x^4 + 36x^2 - 196	\( -\,2^{32}\cdot 3^{16} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.299170970322599936.2	x^12 - 44x^8 - 176x^6 - 264x^4 - 176x^2 - 44	\( -\,2^{20}\cdot 11^{11} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.299170970322599936.3	x^12 - 44x^8 + 176x^6 - 264x^4 + 176x^2 - 44	\( -\,2^{20}\cdot 11^{11} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.831979165027663872.26	x^12 + 12x^10 + 54x^8 + 96x^6 + 9x^4 - 108x^2 - 72	\( -\,2^{31}\cdot 3^{18} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.831979165027663872.32	x^12 - 12x^10 + 54x^8 - 96x^6 + 9x^4 + 108x^2 - 72	\( -\,2^{31}\cdot 3^{18} \)	$C_3^2:D_4$ (as 12T38)	$[3]$
12.2.831979165027663872.74	x^12 - 12x^10 + 54x^8 - 128x^6 + 201x^4 - 180x^2 - 8	\( -\,2^{31}\cdot 3^{18} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.831979165027663872.101	x^12 + 12x^10 + 54x^8 + 128x^6 + 201x^4 + 180x^2 - 8	\( -\,2^{31}\cdot 3^{18} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.12.905618826709203125.1	x^12 - 5x^11 - 17x^10 + 92x^9 + 121x^8 - 612x^7 - 515x^6 + 1685x^5 + 1331x^4 - 1411x^3 - 1330x^2 - 290x - 11	\( 5^{6}\cdot 29^{5}\cdot 41^{4} \)	$C_3^2:D_4$ (as 12T38)	Trivial (GRH)
12.12.905618826709203125.2	x^12 - 3x^11 - 16x^10 + 50x^9 + 76x^8 - 245x^7 - 162x^6 + 440x^5 + 229x^4 - 248x^3 - 172x^2 - 28x - 1	\( 5^{6}\cdot 29^{5}\cdot 41^{4} \)	$C_3^2:D_4$ (as 12T38)	Trivial (GRH)
12.0.1109305553370218496.10	x^12 - 8x^6 + 24	\( 2^{33}\cdot 3^{17} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.1109305553370218496.11	x^12 + 8x^6 + 24	\( 2^{33}\cdot 3^{17} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.1109305553370218496.45	x^12 - 72x^6 + 1944	\( 2^{33}\cdot 3^{17} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.0.1109305553370218496.46	x^12 + 72x^6 + 1944	\( 2^{33}\cdot 3^{17} \)	$C_3^2:D_4$ (as 12T38)	$[3]$
12.2.1479074071160291328.69	x^12 - 12x^10 + 54x^8 - 116x^6 + 129x^4 - 72x^2 - 2	\( -\,2^{35}\cdot 3^{16} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.1479074071160291328.93	x^12 + 12x^10 + 54x^8 + 116x^6 + 129x^4 + 72x^2 - 2	\( -\,2^{35}\cdot 3^{16} \)	$C_3^2:D_4$ (as 12T38)	$[3]$
12.2.1579460446107205632.36	x^12 - 24x^6 - 3	\( -\,2^{24}\cdot 3^{23} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.1579460446107205632.38	x^12 + 24x^6 - 3	\( -\,2^{24}\cdot 3^{23} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.1663958330055327744.29	x^12 - 12x^10 + 18x^8 + 120x^6 + 153x^4 - 108x^2 - 36	\( -\,2^{32}\cdot 3^{18} \)	$C_3^2:D_4$ (as 12T38)	Trivial
12.2.1663958330055327744.31	x^12 + 12x^10 + 18x^8 - 120x^6 + 153x^4 + 108x^2 - 36	\( -\,2^{32}\cdot 3^{18} \)	$C_3^2:D_4$ (as 12T38)	Trivial