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 472)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.448196983533.1	x^12 - x^11 + 2x^10 - x^9 + 5x^8 - 7x^7 + 8x^6 - 8x^5 + 2x^4 - x^3 + 1	\( 3^{6}\cdot 13^{3}\cdot 23^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.533806460928.1	x^12 - 5x^11 + 13x^10 - 23x^9 + 31x^8 - 32x^7 + 27x^6 - 17x^5 + 8x^4 - 2x^3 + x - 1	\( -\,2^{12}\cdot 3^{3}\cdot 13^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.1108674957312.1	x^12 - 5x^11 + 6x^10 + 8x^9 - 19x^8 - 6x^7 + 31x^6 - 6x^5 - 19x^4 + 8x^3 + 6x^2 - 5x + 1	\( 2^{12}\cdot 3^{6}\cdot 13^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.2409451520000.1	x^12 - 3x^10 + 7x^8 - 7x^6 + 6x^4 - 2x^2 + 2	\( 2^{15}\cdot 5^{4}\cdot 7^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.2458624000000.1	x^12 + 5x^8 - 16x^6 - 5x^4 - 1	\( -\,2^{16}\cdot 5^{6}\cdot 7^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.4843421142021.1	x^12 - x^11 + 9x^10 - 8x^9 + 34x^8 - 30x^7 + 70x^6 - 60x^5 + 78x^4 - 58x^3 + 40x^2 - 21x + 7	\( 3^{9}\cdot 7^{5}\cdot 11^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.5061276073984.1	x^12 - 2x^10 - 2x^8 + 2x^4 - 2x^2 - 1	\( -\,2^{20}\cdot 13^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.4.6022586125125.1	x^12 - x^9 - 12x^6 - 12x^3 - 1	\( 3^{4}\cdot 5^{3}\cdot 29^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.6229262860288.1	x^12 - 2x^11 + 2x^10 - 2x^9 + 5x^8 - 8x^7 + 12x^6 - 8x^5 + 5x^4 - 2x^3 + 2x^2 - 2x + 1	\( 2^{24}\cdot 13^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.7537191616512.1	x^12 - 2x^11 - x^10 + 8x^9 - 6x^8 - 10x^7 + 21x^6 - 10x^5 - 6x^4 + 8x^3 - x^2 - 2x + 1	\( 2^{16}\cdot 3^{4}\cdot 17^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.7860327022592.2	x^12 - 2x^6 + 4x^4 - 4x^2 + 2	\( 2^{29}\cdot 11^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.7867596800000.1	x^12 - 6x^9 + 3x^8 + 12x^6 - 12x^5 + 5x^4 - 8x^3 + 12x^2 - 10x + 5	\( 2^{20}\cdot 5^{5}\cdot 7^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.8008266092544.1	x^12 - 5x^11 + 9x^10 - 4x^9 - 15x^8 + 35x^7 - 40x^6 + 29x^5 - 17x^4 + 10x^3 - 5x^2 + x - 1	\( -\,2^{12}\cdot 3^{4}\cdot 17^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.10240000000000.1	x^12 - 3x^10 + 5x^8 - 10x^6 - 5x^4 - 3x^2 - 1	\( -\,2^{20}\cdot 5^{10} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.10307264000000.3	x^12 - 2x^11 + 4x^9 - 6x^8 + 10x^7 - 19x^6 + 30x^5 - 29x^4 + 22x^3 - 15x^2 + 6x - 1	\( -\,2^{12}\cdot 5^{6}\cdot 11^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.15045919506432.1	x^12 - 6x^10 + 30x^8 - 48x^6 + 42x^4 - 18x^2 + 3	\( 2^{20}\cdot 3^{15} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.18238415044608.2	x^12 - 2x^11 + x^10 + 10x^9 - 20x^8 + 18x^7 + 19x^6 - 58x^5 + 74x^4 - 50x^3 + 23x^2 - 6x + 1	\( 2^{22}\cdot 3^{3}\cdot 11^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.18238415044608.3	x^12 - 2x^11 + 3x^10 - 8x^9 + 15x^8 - 6x^7 + 17x^6 + 8x^5 - 6x^4 + 12x^2 + 8x + 2	\( 2^{22}\cdot 3^{3}\cdot 11^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.4.19034346272000.1	x^12 - 3x^11 + 4x^10 - 8x^9 + 20x^8 - 35x^7 + 25x^6 + 14x^5 - 49x^4 + 49x^3 - 25x^2 + 7x - 1	\( 2^{8}\cdot 5^{3}\cdot 29^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.20245104295936.2	x^12 - 4x^10 + 3x^8 + 8x^6 - 15x^4 + 10x^2 - 4	\( -\,2^{22}\cdot 13^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.22675980800000.1	x^12 - 5x^11 + 16x^10 - 32x^9 + 49x^8 - 54x^7 + 47x^6 - 29x^5 + 11x^4 + 3x^3 - 5x^2 + 2x + 1	\( 2^{12}\cdot 5^{5}\cdot 11^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.24917051441152.1	x^12 - 4x^11 + 8x^10 - 8x^9 - 7x^8 + 20x^7 + 4x^6 - 20x^5 - 7x^4 + 8x^3 + 8x^2 + 4x + 1	\( 2^{26}\cdot 13^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.4.25959422953125.1	x^12 - 3x^11 + 2x^10 + 5x^8 - 8x^7 + 6x^6 - 4x^5 - 14x^4 + 4x^3 - 11x^2 + 2x + 1	\( 3^{4}\cdot 5^{6}\cdot 29^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.32768000000000.1	x^12 - 2x^11 - 2x^10 + 14x^9 - 11x^8 - 16x^7 + 36x^6 - 16x^5 - 11x^4 + 14x^3 - 2x^2 - 2x + 1	\( 2^{24}\cdot 5^{9} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.33903947994147.1	x^12 - x^11 - x^10 + 3x^9 - 5x^8 + 7x^7 + x^6 + 7x^5 - 5x^4 + 3x^3 - x^2 - x + 1	\( -\,3^{9}\cdot 7^{6}\cdot 11^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.34163613499392.1	x^12 - 4x^11 + 6x^10 + 2x^9 - 10x^8 + 6x^7 - 5x^6 + 14x^5 - 21x^4 + 20x^3 - 11x^2 + 2x + 1	\( -\,2^{18}\cdot 3^{3}\cdot 13^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.37559623221248.2	x^12 - 2x^10 + 2x^8 - 4x^6 + 16x^4 - 16x^2 + 8	\( 2^{27}\cdot 23^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial (GRH)
12.2.39822650441728.1	x^12 - 4x^11 + 5x^10 - 2x^9 - 5x^8 + 10x^7 - 9x^6 - 2x^5 + 2x^4 + 2x^3 - 4x - 2	\( -\,2^{16}\cdot 7^{3}\cdot 11^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.39822650441728.2	x^12 + x^10 - 2x^9 + 4x^8 - 12x^7 + 9x^6 - 12x^5 + 4x^4 - 2x^3 + x^2 + 1	\( -\,2^{16}\cdot 7^{3}\cdot 11^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.40960000000000.1	x^12 - 6x^10 + 15x^8 - 30x^6 + 45x^4 - 16x^2 - 4	\( -\,2^{22}\cdot 5^{10} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.42318822408192.1	x^12 + 3x^10 + x^8 + 11x^6 - 20x^4 + 10x^2 - 2	\( -\,2^{15}\cdot 3^{6}\cdot 11^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.42318822408192.2	x^12 + x^10 - 9x^8 + 21x^6 - 22x^4 + 14x^2 - 2	\( -\,2^{15}\cdot 3^{6}\cdot 11^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.43307615520000.1	x^12 - 3x^11 + 12x^9 - 7x^8 - 18x^7 + 3x^6 + 48x^5 + x^4 - 78x^3 + 30x^2 + 45x + 9	\( 2^{8}\cdot 3^{6}\cdot 5^{4}\cdot 13^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.44058542080000.1	x^12 - 6x^11 + 19x^10 - 38x^9 + 48x^8 - 22x^7 - 51x^6 + 146x^5 - 206x^4 + 190x^3 - 115x^2 + 42x - 7	\( -\,2^{22}\cdot 5^{4}\cdot 7^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.51200000000000.2	x^12 - 5x^10 + 5x^8 + 10x^6 - 25x^4 + 35x^2 - 5	\( -\,2^{20}\cdot 5^{11} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.51840000000000.1	x^12 - 7x^10 + 20x^8 - 15x^6 - 20x^4 - 7x^2 - 1	\( -\,2^{16}\cdot 3^{4}\cdot 5^{10} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.52929948960000.1	x^12 - 5x^11 + 9x^10 - 9x^9 + 7x^8 - 18x^7 + 77x^6 - 162x^5 + 225x^4 - 205x^3 + 122x^2 - 42x + 7	\( 2^{8}\cdot 3^{9}\cdot 5^{4}\cdot 7^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.54203275126125.1	x^12 - x^11 + x^10 - 3x^9 + 9x^8 - x^7 + 13x^6 - x^5 + 9x^4 - 3x^3 + x^2 - x + 1	\( 3^{6}\cdot 5^{3}\cdot 29^{6} \)	$S_3\times D_4$ (as 12T28)	$[2]$
12.0.60183678025728.1	x^12 - 6x^11 + 15x^10 - 10x^9 - 27x^8 + 60x^7 - 18x^6 - 60x^5 + 60x^4 + 8x^3 - 24x^2 + 4	\( 2^{22}\cdot 3^{15} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.60236288000000.1	x^12 - 5x^11 + 9x^10 - 3x^9 - 14x^8 + 36x^7 - 26x^6 - 4x^5 + 46x^4 - 54x^3 + 40x^2 - 16x + 4	\( 2^{15}\cdot 5^{6}\cdot 7^{6} \)	$S_3\times D_4$ (as 12T28)	$[2]$
12.0.61334280470528.1	x^12 - 6x^10 + 20x^8 - 40x^6 + 37x^4 - 10x^2 + 2	\( 2^{31}\cdot 13^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.61737492466944.2	x^12 - 3x^11 + 20x^9 - 27x^8 - 24x^7 + 87x^6 - 24x^5 - 27x^4 + 20x^3 - 3x + 1	\( 2^{8}\cdot 3^{15}\cdot 7^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.2.62882616180736.2	x^12 - 4x^10 - 4x^8 + 28x^6 + 24x^4 - 4	\( -\,2^{32}\cdot 11^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.67834724548608.1	x^12 - 6x^11 + 20x^10 - 44x^9 + 66x^8 - 56x^7 + 4x^6 + 40x^5 - 16x^4 - 40x^3 + 52x^2 - 24x + 4	\( 2^{16}\cdot 3^{6}\cdot 17^{5} \)	$S_3\times D_4$ (as 12T28)	$[2]$
12.0.69965554122752.3	x^12 - 4x^10 + 8x^8 - 6x^6 + 4x^4 - 4x^2 + 2	\( 2^{29}\cdot 19^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial (GRH)
12.0.70955197267968.1	x^12 - 2x^10 - 2x^9 + 6x^8 + 10x^7 - 23x^6 - 10x^5 + 63x^4 - 72x^3 + 39x^2 - 10x + 1	\( 2^{18}\cdot 3^{6}\cdot 13^{5} \)	$S_3\times D_4$ (as 12T28)	$[2]$
12.2.72074394832896.1	x^12 - 5x^11 + 13x^10 - 19x^9 + 10x^8 + 28x^7 - 86x^6 + 140x^5 - 158x^4 + 130x^3 - 80x^2 + 32x - 8	\( -\,2^{12}\cdot 3^{6}\cdot 17^{6} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.77608915349504.1	x^12 - x^11 + 5x^10 - 12x^9 + 21x^8 - 27x^7 + 42x^6 - 27x^5 + 21x^4 - 12x^3 + 5x^2 - x + 1	\( 2^{12}\cdot 7^{6}\cdot 11^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.77608915349504.2	x^12 - 3x^11 + 9x^10 - 13x^9 + 24x^8 - 34x^7 + 56x^6 - 64x^5 + 54x^4 - 42x^3 + 32x^2 - 16x + 4	\( 2^{12}\cdot 7^{6}\cdot 11^{5} \)	$S_3\times D_4$ (as 12T28)	Trivial
12.0.94929648877568.8	x^12 - 4x^10 + 8x^8 - 16x^6 + 4x^4 + 16x^2 + 32	\( 2^{27}\cdot 29^{4} \)	$S_3\times D_4$ (as 12T28)	Trivial (GRH)