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 52151)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.41223887921.1	x^12 - 2x^11 + 2x^10 - x^9 + 2x^8 - 5x^7 + 8x^6 - 7x^5 + 4x^4 - 3x^3 + 4x^2 - 3x + 1	\( 37^{2}\cdot 41\cdot 857^{2} \)	12T293	Trivial
12.0.44223092609.1	x^12 - x^11 + x^9 - 2x^8 + x^7 + 3x^4 - x^3 - 2x^2 + 1	\( 89\cdot 22291^{2} \)	12T293	Trivial
12.0.45539379833.1	x^12 - x^11 - x^9 + 3x^8 - 2x^7 + x^6 - 2x^5 + 3x^4 - x^3 - x + 1	\( 17\cdot 73^{2}\cdot 709^{2} \)	12T293	Trivial
12.0.47724987301.1	x^12 - 3x^11 + 7x^10 - 11x^9 + 16x^8 - 19x^7 + 20x^6 - 18x^5 + 15x^4 - 11x^3 + 6x^2 - 3x + 1	\( 61\cdot 83^{2}\cdot 337^{2} \)	12T293	Trivial
12.2.167630295667.1	x^12 - 3x^11 + 4x^10 - x^9 - 6x^8 + 15x^7 - 19x^6 + 15x^5 - 6x^4 - x^3 + 4x^2 - 3x + 1	\( -\,29^{2}\cdot 43\cdot 2153^{2} \)	12T293	Trivial
12.2.168661105243.1	x^12 - 5x^11 + 12x^10 - 16x^9 + 12x^8 - 4x^7 + x^6 - 3x^5 + 4x^4 - 3x^3 + x^2 - 1	\( -\,67\cdot 131^{2}\cdot 383^{2} \)	12T293	Trivial
12.0.184052780197.1	x^12 + x^10 - x^9 + x^8 - 2x^7 + x^6 - 2x^5 + x^4 - x^3 + x^2 + 1	\( 11^{2}\cdot 13\cdot 29^{2}\cdot 373^{2} \)	12T293	Trivial
12.0.185583853913.1	x^12 - 2x^11 + 2x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + 2x^2 - 2x + 1	\( 17\cdot 163^{2}\cdot 641^{2} \)	12T293	Trivial
12.2.204800642687.1	x^12 - 3x^11 + 5x^10 - 3x^9 - 4x^8 + 12x^7 - 15x^6 + 12x^5 - 4x^4 - 3x^3 + 5x^2 - 3x + 1	\( -\,23\cdot 197^{2}\cdot 479^{2} \)	12T293	Trivial
12.2.266846228071.1	x^12 - x^11 + 2x^10 - 3x^9 + 3x^8 - 4x^7 + 3x^6 - 4x^5 + 3x^4 - 3x^3 + 2x^2 - x + 1	\( -\,31\cdot 92779^{2} \)	12T293	Trivial
12.4.734297685397.1	x^12 - x^11 - 2x^10 + x^9 + 2x^8 - x^7 - x^6 + x^5 + 2x^4 - x^3 - 2x^2 + x + 1	\( 157\cdot 68389^{2} \)	12T293	Trivial
12.4.750369026957.1	x^12 - 4x^11 + 3x^10 + 9x^9 - 17x^8 + 20x^6 - 10x^5 - 9x^4 + 6x^3 + 3x^2 - 2x - 1	\( 11^{2}\cdot 29^{2}\cdot 53\cdot 373^{2} \)	12T293	Trivial
12.4.777011613097.1	x^12 - 6x^11 + 19x^10 - 40x^9 + 62x^8 - 74x^7 + 67x^6 - 44x^5 + 16x^4 + 2x^3 - 8x^2 + 5x - 1	\( 97\cdot 89501^{2} \)	12T293	Trivial
12.4.796918902097.1	x^12 - 3x^11 + x^10 + 3x^9 - 2x^8 + 2x^7 + x^6 - 4x^5 - 2x^4 - x^3 + x^2 + 3x + 1	\( 73\cdot 163^{2}\cdot 641^{2} \)	12T293	Trivial
12.2.2458729426447.1	x^12 - x^11 + x^10 - x^9 - x^6 - x^3 + x^2 - x + 1	\( -\,7\cdot 592661^{2} \)	12T293	Trivial
12.6.3924967206547.1	x^12 - 2x^11 - 2x^10 + 10x^9 - 12x^8 + x^7 + 12x^6 - 20x^5 + 6x^4 + 12x^3 - 6x^2 - 2x + 1	\( -\,43\cdot 302123^{2} \)	12T293	Trivial
12.6.3959860197871.1	x^12 - x^11 - 5x^10 + 7x^9 + 7x^8 - 20x^7 + 3x^6 + 25x^5 - 15x^4 - 10x^3 + 11x^2 - x - 1	\( -\,67^{2}\cdot 151\cdot 2417^{2} \)	12T293	Trivial
12.4.4566211791973.1	x^12 - 4x^11 + 6x^10 - 4x^9 - 3x^8 + 11x^7 - 15x^6 + 11x^5 - 3x^4 - 4x^3 + 6x^2 - 4x + 1	\( 13\cdot 592661^{2} \)	12T293	Trivial
12.4.7235239012445.1	x^12 - x^11 - 3x^10 + x^9 + 3x^8 - x^7 - 5x^6 - x^5 + 3x^4 + x^3 - 3x^2 - x + 1	\( 5\cdot 79^{2}\cdot 15227^{2} \)	12T293	Trivial
12.2.10129334617423.1	x^12 - x^11 - x^7 + x^6 - x^5 - x + 1	\( -\,7\cdot 79^{2}\cdot 15227^{2} \)	12T293	Trivial
12.6.10888658888551.1	x^12 - 2x^11 - 2x^10 + 15x^9 - 21x^8 + x^7 + 36x^6 - 50x^5 + 29x^4 - 11x^2 + 6x - 1	\( -\,31\cdot 592661^{2} \)	12T293	Trivial
12.6.15691065834027.1	x^12 - 6x^10 - 4x^9 + 15x^8 + 18x^7 - 21x^6 - 21x^5 + 10x^4 + 7x^3 - x^2 + 2x + 1	\( -\,3\cdot 349^{2}\cdot 6553^{2} \)	12T293	Trivial
12.8.17497403356237.1	x^12 - x^11 - 9x^10 + 9x^9 + 30x^8 - 29x^7 - 46x^6 + 39x^5 + 33x^4 - 19x^3 - 10x^2 + 2x + 1	\( 7^{2}\cdot 373\cdot 30941^{2} \)	12T293	Trivial
12.8.18308160781573.1	x^12 - x^11 - 7x^10 + 7x^9 + 10x^8 - 14x^7 + 2x^6 + 19x^5 - 8x^4 - 17x^3 + x^2 + 5x + 1	\( 13^{2}\cdot 397\cdot 16519^{2} \)	12T293	Trivial
12.8.21426070716181.1	x^12 - 2x^11 - 2x^10 + 2x^9 - x^8 + 18x^7 + 3x^6 - 44x^5 + x^4 + 32x^3 - 3x^2 - 5x + 1	\( 61\cdot 592661^{2} \)	12T293	Trivial
12.8.25641035447233.1	x^12 - 5x^11 + 6x^10 + 6x^9 - 18x^8 + 17x^7 - 15x^6 + 17x^5 - 18x^4 + 6x^3 + 6x^2 - 5x + 1	\( 73\cdot 592661^{2} \)	12T293	Trivial
12.10.137691709155347.1	x^12 - 2x^11 - 8x^10 + 19x^9 + 21x^8 - 58x^7 - 27x^6 + 69x^5 + 26x^4 - 30x^3 - 13x^2 + 2x + 1	\( -\,107\cdot 1134389^{2} \)	12T293	Trivial
12.2.190210142896128.1	x^12 - 2x^10 - 5x^8 + 8x^6 + 3x^4 - 6x^2 - 3	\( -\,2^{30}\cdot 3^{11} \)	12T293	Trivial
12.2.190210142896128.2	x^12 + 2x^10 - 5x^8 - 8x^6 + 3x^4 + 6x^2 - 3	\( -\,2^{30}\cdot 3^{11} \)	12T293	Trivial
12.2.190210142896128.3	x^12 - 4x^11 + 10x^10 - 12x^9 + 7x^8 - 4x^7 - 4x^6 + 20x^5 + 7x^4 - 16x^3 - 6x^2 - 1	\( -\,2^{30}\cdot 3^{11} \)	12T293	Trivial
12.2.190210142896128.4	x^12 - 4x^11 + 6x^10 - 8x^9 + 11x^8 - 4x^7 + 4x^6 - 44x^5 + 85x^4 - 96x^3 + 70x^2 - 28x + 5	\( -\,2^{30}\cdot 3^{11} \)	12T293	Trivial
12.10.248331672071147.1	x^12 - 10x^10 - 2x^9 + 31x^8 + 6x^7 - 35x^6 - x^5 + 10x^4 - 5x^3 + 3x^2 + 2x - 1	\( -\,7\cdot 101\cdot 592661^{2} \)	12T293	Trivial
12.2.253613523861504.1	x^12 - 2x^10 + x^8 - 4x^6 - 9x^4 - 18x^2 - 9	\( -\,2^{32}\cdot 3^{10} \)	12T293	Trivial
12.2.253613523861504.2	x^12 + 2x^10 + x^8 + 4x^6 - 9x^4 + 18x^2 - 9	\( -\,2^{32}\cdot 3^{10} \)	12T293	Trivial
12.2.253613523861504.3	x^12 + 2x^10 + 5x^8 - x^4 - 10x^2 - 1	\( -\,2^{32}\cdot 3^{10} \)	12T293	Trivial
12.2.253613523861504.4	x^12 - 2x^10 + 5x^8 - x^4 + 10x^2 - 1	\( -\,2^{32}\cdot 3^{10} \)	12T293	Trivial
12.0.354408284469289.1	x^12 - 5x^11 + 12x^10 - 19x^9 + 27x^8 - 40x^7 + 59x^6 - 80x^5 + 108x^4 - 152x^3 + 192x^2 - 160x + 64	\( 1009\cdot 592661^{2} \)	12T293	Trivial
12.0.487655109438793.1	x^12 - 6x^11 + 27x^10 - 80x^9 + 187x^8 - 334x^7 + 476x^6 - 529x^5 + 457x^4 - 295x^3 + 134x^2 - 38x + 5	\( 79^{2}\cdot 337\cdot 15227^{2} \)	12T293	Trivial
12.0.565156521021889.1	x^12 - 5x^11 + 14x^10 - 32x^9 + 65x^8 - 111x^7 + 165x^6 - 222x^5 + 260x^4 - 256x^3 + 224x^2 - 160x + 64	\( 1609\cdot 592661^{2} \)	12T293	Trivial
12.12.600281227113989.1	x^12 - 2x^11 - 11x^10 + 23x^9 + 37x^8 - 80x^7 - 53x^6 + 114x^5 + 32x^4 - 64x^3 - 4x^2 + 9x - 1	\( 1709\cdot 592661^{2} \)	12T293	Trivial
12.0.638398317541977.1	x^12 - x^11 + 3x^10 - 4x^9 + 5x^8 - 10x^7 + 3x^6 - 20x^5 + 20x^4 - 32x^3 + 48x^2 - 32x + 64	\( 3^{2}\cdot 97\cdot 855143^{2} \)	12T293	Trivial
12.2.655360000000000.2	x^12 - 2x^10 - 5x^8 - 8x^2 - 4	\( -\,2^{26}\cdot 5^{10} \)	12T293	Trivial
12.0.703575002767673.1	x^12 - 6x^11 + 27x^10 - 80x^9 + 185x^8 - 326x^7 + 451x^6 - 482x^5 + 392x^4 - 234x^3 + 97x^2 - 25x + 3	\( 113\cdot 199^{2}\cdot 12539^{2} \)	12T293	Trivial
12.0.747804992700809.1	x^12 - 3x^11 + 9x^10 - 18x^9 + 31x^8 - 50x^7 + 69x^6 - 100x^5 + 124x^4 - 144x^3 + 144x^2 - 96x + 64	\( 2129\cdot 592661^{2} \)	12T293	Trivial
12.4.760840571584512.1	x^12 - 2x^10 - 3x^8 - 4x^6 + 15x^4 - 18x^2 + 3	\( 2^{32}\cdot 3^{11} \)	12T293	Trivial
12.0.760840571584512.1	x^12 + 2x^10 - 3x^8 + 4x^6 + 15x^4 + 18x^2 + 3	\( 2^{32}\cdot 3^{11} \)	12T293	Trivial
12.4.760840571584512.2	x^12 - 6x^10 + 21x^8 - 32x^6 + 27x^4 - 18x^2 + 3	\( 2^{32}\cdot 3^{11} \)	12T293	Trivial
12.0.760840571584512.2	x^12 + 6x^10 + 21x^8 + 32x^6 + 27x^4 + 18x^2 + 3	\( 2^{32}\cdot 3^{11} \)	12T293	Trivial
12.0.767490870661513.1	x^12 - 6x^11 + 27x^10 - 80x^9 + 188x^8 - 338x^7 + 486x^6 - 545x^5 + 474x^4 - 307x^3 + 139x^2 - 39x + 5	\( 23^{2}\cdot 97\cdot 122299^{2} \)	12T293	Trivial
12.0.800871057112057.1	x^12 - 2x^11 + x^10 + 3x^9 - 4x^8 - 5x^7 + 19x^6 - 10x^5 - 16x^4 + 24x^3 + 16x^2 - 64x + 64	\( 337\cdot 1541581^{2} \)	12T293	Trivial