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 334)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.4760622968832.1	x^12 - 6x^10 + 15x^8 - 21x^6 + 18x^4 - 9x^2 + 3	\( 2^{12}\cdot 3^{19} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.6889288847861.1	x^12 - 5x^11 + 20x^10 - 54x^9 + 121x^8 - 216x^7 + 321x^6 - 394x^5 + 400x^4 - 331x^3 + 215x^2 - 106x + 29	\( 7^{10}\cdot 29^{3} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.8099130339328.1	x^12 - 7x^10 + 21x^8 - 35x^6 + 35x^4 - 21x^2 + 7	\( 2^{12}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.9256148959232.1	x^12 - 8x^10 + 29x^8 - 57x^6 + 64x^4 - 36x^2 + 8	\( 2^{15}\cdot 7^{10} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.9256148959232.3	x^12 + 8x^10 + 29x^8 + 57x^6 + 64x^4 + 36x^2 + 8	\( 2^{15}\cdot 7^{10} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.64793042714624.2	x^12 - 7x^10 + 28x^8 - 77x^6 + 140x^4 - 140x^2 + 56	\( 2^{15}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.64793042714624.3	x^12 + 7x^10 + 28x^8 + 77x^6 + 140x^4 + 140x^2 + 56	\( 2^{15}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.93054481998075.1	x^12 - 2x^11 - 3x^10 + 8x^9 + 6x^8 - 12x^7 - 7x^6 + 5x^5 - 6x^4 - x^3 + 10x^2 + 3x - 1	\( -\,3^{3}\cdot 5^{2}\cdot 13^{10} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.304679870005248.1	x^12 - 6x^10 - 2x^9 + 21x^8 + 6x^7 - 42x^6 - 12x^5 + 48x^4 + 10x^3 - 24x^2 + 1	\( -\,2^{18}\cdot 3^{19} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.304679870005248.2	x^12 - 12x^10 + 60x^8 - 168x^6 + 288x^4 - 288x^2 + 192	\( 2^{18}\cdot 3^{19} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.518344341716992.2	x^12 - 2x^11 - 4x^10 + 10x^9 + 12x^8 - 34x^7 - 14x^6 + 64x^5 - 9x^4 - 46x^3 + 10x^2 + 12x + 1	\( -\,2^{18}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.518344341716992.2	x^12 - 14x^10 + 84x^8 - 280x^6 + 560x^4 - 672x^2 + 448	\( 2^{18}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.564668382613504.1	x^12 - 4x^10 - 2x^8 + 9x^6 + 2x^4 - 4x^2 - 1	\( -\,2^{12}\cdot 13^{10} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.677021181018112.1	x^12 - 4x^10 - 4x^9 - 9x^8 + 48x^7 - 6x^6 - 28x^5 - 38x^4 + 40x^3 + 8x^2 - 8x - 1	\( -\,2^{24}\cdot 7^{9} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.677021181018112.3	x^12 - 2x^10 - 4x^9 - 12x^8 - 32x^7 - 42x^6 + 12x^5 + 105x^4 + 144x^3 + 92x^2 + 24x + 1	\( -\,2^{24}\cdot 7^{9} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.773738492592128.2	x^12 - 2x^10 + 2x^8 + 4x^6 + 16x^4 - 16x^2 + 8	\( 2^{27}\cdot 7^{8} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.4.2196839556078125.1	x^12 - 6x^11 + 14x^10 - 12x^9 - 24x^8 + 95x^7 - 182x^6 + 254x^5 - 300x^4 + 233x^3 - 140x^2 - 5x + 1	\( 5^{6}\cdot 7^{8}\cdot 29^{3} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.2779905883635712.1	x^12 - 6x^11 + 20x^10 - 42x^9 + 53x^8 - 28x^7 - 14x^6 + 34x^5 - 10x^4 - 16x^3 + 24x^2 + 8x + 1	\( 2^{18}\cdot 13^{9} \)	$D_4\times A_4$ (as 12T51)	$[3]$
12.0.5777633090469888.8	x^12 - 4x^6 + 36x^4 - 24x^2 + 8	\( 2^{27}\cdot 3^{16} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.8.5904266017370112.1	x^12 - 7x^10 + 7x^8 + 28x^6 - 35x^4 + 7	\( 2^{12}\cdot 3^{6}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.4.5904266017370112.1	x^12 + 7x^10 + 7x^8 - 28x^6 - 35x^4 + 7	\( 2^{12}\cdot 3^{6}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.6189907940737024.3	x^12 - 2x^10 - 13x^8 + 10x^6 + 10x^4 - 4x^2 - 1	\( -\,2^{30}\cdot 7^{8} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.8.6208060151890625.1	x^12 - 3x^11 - 11x^10 + 21x^9 + 51x^8 - 42x^7 - 54x^6 + 147x^5 - 16x^4 - 599x^3 - 698x^2 - 279x - 29	\( 5^{6}\cdot 7^{8}\cdot 41^{3} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.7340688973975552.2	x^12 - 13x^8 + 26x^4 - 13	\( -\,2^{12}\cdot 13^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.9159316554578733.1	x^12 + 27x^10 - 16x^9 + 360x^8 - 306x^7 + 2919x^6 - 2718x^5 + 14679x^4 - 12427x^3 + 42426x^2 - 23661x + 50329	\( 3^{19}\cdot 199^{3} \)	$D_4\times A_4$ (as 12T51)	$[2, 2]$
12.6.19499511680335872.3	x^12 - 6x^8 + 9x^4 - 3	\( -\,2^{24}\cdot 3^{19} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.24919973321128389.1	x^12 + 2x^10 - 5x^9 - 15x^8 - 9x^7 + 19x^6 - 339x^5 + 1551x^4 - 3158x^3 + 5096x^2 - 5243x + 2149	\( 3^{6}\cdot 7^{8}\cdot 181^{3} \)	$D_4\times A_4$ (as 12T51)	$[2, 2]$
12.6.33174037869887488.1	x^12 - 14x^10 - 28x^9 + 42x^8 + 224x^7 + 280x^6 - 112x^5 - 784x^4 - 1120x^3 - 840x^2 - 336x - 56	\( -\,2^{24}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.33174037869887488.2	x^12 - 14x^10 + 42x^8 - 56x^7 - 28x^6 + 224x^5 - 56x^4 - 336x^3 + 168x^2 + 112x - 56	\( -\,2^{24}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.33174037869887488.5	x^12 - 7x^8 + 14x^4 - 7	\( -\,2^{24}\cdot 7^{11} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.36138776487264256.1	x^12 - 8x^10 - 8x^8 + 72x^6 + 32x^4 - 128x^2 - 64	\( -\,2^{18}\cdot 13^{10} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.4.37913186137014272.1	x^12 + 6x^10 - 6x^8 - 92x^6 - 160x^4 - 64x^2 + 8	\( 2^{27}\cdot 7^{10} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.8.37913186137014272.7	x^12 - 6x^10 - 6x^8 + 92x^6 - 160x^4 + 64x^2 + 8	\( 2^{27}\cdot 7^{10} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.37913186137014272.10	x^12 - 28x^6 + 196x^4 - 392x^2 + 392	\( 2^{27}\cdot 7^{10} \)	$D_4\times A_4$ (as 12T51)	$[2]$
12.8.43329355585159168.1	x^12 - 6x^10 - 9x^8 + 62x^6 + 42x^4 - 56x^2 + 7	\( 2^{30}\cdot 7^{9} \)	$D_4\times A_4$ (as 12T51)	Trivial (GRH)
12.4.43329355585159168.9	x^12 + 6x^10 - 9x^8 - 62x^6 + 42x^4 + 56x^2 + 7	\( 2^{30}\cdot 7^{9} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.46221064723759104.7	x^12 - 18x^8 - 14x^6 + 9x^4 + 6x^2 - 1	\( -\,2^{30}\cdot 3^{16} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.49519263525896192.4	x^12 - 10x^8 + 24x^4 - 8	\( -\,2^{33}\cdot 7^{8} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.49519263525896192.6	x^12 + 10x^8 + 24x^4 + 8	\( 2^{33}\cdot 7^{8} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.51998697814228992.9	x^12 - 24x^8 + 20x^6 + 36x^4 - 24x^2 - 8	\( -\,2^{27}\cdot 3^{18} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.51998697814228992.16	x^12 - 24x^8 - 20x^6 + 36x^4 + 24x^2 - 8	\( -\,2^{27}\cdot 3^{18} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.51998697814228992.14	x^12 - 6x^10 + 18x^8 - 12x^6 + 72	\( 2^{27}\cdot 3^{18} \)	$D_4\times A_4$ (as 12T51)	$[2]$
12.6.52206766144000000.1	x^12 - 5x^10 - 36x^8 + 4x^6 + 64x^4 - 2x^2 - 1	\( -\,2^{12}\cdot 5^{6}\cdot 13^{8} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.6.67969612962739111.1	x^12 - 4x^11 + 4x^10 - 11x^9 - 56x^8 + 35x^7 - 93x^6 - 108x^5 + 139x^4 - 24x^3 + 186x^2 + 35x - 25	\( -\,13^{10}\cdot 79^{3} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.109485524032421888.10	x^12 - 2x^10 + 2x^8 + 20x^6 + 64x^4 + 32x^2 + 8	\( 2^{27}\cdot 13^{8} \)	$D_4\times A_4$ (as 12T51)	$[3]$
12.0.138663194171277312.20	x^12 + 6x^8 - 10x^6 + 81x^4 - 54x^2 + 27	\( 2^{30}\cdot 3^{17} \)	$D_4\times A_4$ (as 12T51)	$[3]$
12.0.138663194171277312.28	x^12 + 6x^8 + 10x^6 + 81x^4 + 54x^2 + 27	\( 2^{30}\cdot 3^{17} \)	$D_4\times A_4$ (as 12T51)	$[3]$
12.8.155996093442686976.2	x^12 - 24x^8 + 36x^6 + 36x^4 - 72x^2 + 24	\( 2^{27}\cdot 3^{19} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.4.155996093442686976.14	x^12 - 24x^8 - 36x^6 + 36x^4 + 72x^2 + 24	\( 2^{27}\cdot 3^{19} \)	$D_4\times A_4$ (as 12T51)	Trivial
12.0.177913976552685568.12	x^12 - 12x^10 + 74x^8 - 272x^6 + 585x^4 - 676x^2 + 325	\( 2^{24}\cdot 13^{9} \)	$D_4\times A_4$ (as 12T51)	$[3]$