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 67)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.389136420864.2	x^12 + x^10 + x^8 + 2x^6 + 4x^4 + 3x^2 + 1	\( 2^{12}\cdot 3^{6}\cdot 19^{4} \)	12T158	Trivial
12.0.479174066176.3	x^12 - x^8 - 2x^6 + 2x^2 + 1	\( 2^{24}\cdot 13^{4} \)	12T158	Trivial
12.0.7044820107264.2	x^12 + 2x^10 + 3x^8 + 2x^6 + 2x^4 + 1	\( 2^{30}\cdot 3^{8} \)	12T158	Trivial
12.4.25542916000000.1	x^12 - 6x^11 + 23x^10 - 60x^9 + 108x^8 - 138x^7 + 109x^6 - 30x^5 - 28x^4 + 32x^3 - 9x^2 - 2x + 1	\( 2^{8}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4} \)	12T158	Trivial
12.4.73108912640625.1	x^12 - 3x^11 + 4x^9 - 2x^8 + x^7 - 3x^6 + x^5 - 2x^4 + 4x^3 - 3x + 1	\( 3^{2}\cdot 5^{6}\cdot 151^{4} \)	12T158	Trivial
12.0.128536820158464.2	x^12 + 6x^10 + 15x^8 + 17x^6 + 6x^4 - 3x^2 + 1	\( 2^{12}\cdot 3^{22} \)	12T158	Trivial
12.8.133448704000000.1	x^12 + x^10 - 18x^8 + 21x^6 + 2x^4 - 7x^2 + 1	\( 2^{16}\cdot 5^{6}\cdot 19^{4} \)	12T158	Trivial
12.0.139931108245504.4	x^12 + 4x^10 + 6x^8 + 6x^6 + 7x^4 + 2x^2 + 1	\( 2^{30}\cdot 19^{4} \)	12T158	Trivial
12.0.406239826673664.3	x^12 + 3x^10 - 25x^6 + 30x^4 - 9x^2 + 1	\( 2^{20}\cdot 3^{18} \)	12T158	Trivial
12.8.408686656000000.1	x^12 - 2x^11 - x^10 - 6x^9 + 12x^8 + 8x^7 + 3x^6 + 2x^5 - 44x^4 + 20x^3 + 13x^2 - 8x + 1	\( 2^{12}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4} \)	12T158	Trivial
12.0.570630428688384.22	x^12 + 6x^6 + 9x^4 - 54x^2 + 81	\( 2^{30}\cdot 3^{12} \)	12T158	$[2]$
12.0.570630428688384.23	x^12 - 6x^6 + 9x^4 + 54x^2 + 81	\( 2^{30}\cdot 3^{12} \)	12T158	$[2]$
12.8.713637796000000.1	x^12 - 2x^11 - 7x^10 + 12x^9 + 36x^8 - 66x^7 - 69x^6 + 190x^5 - 36x^4 - 148x^3 + 113x^2 - 26x + 1	\( 2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 37^{2} \)	12T158	Trivial
12.0.722204136308736.4	x^12 - 6x^10 + 15x^8 - 18x^6 + 18x^4 - 6x^2 + 1	\( 2^{24}\cdot 3^{16} \)	12T158	Trivial
12.0.1624959306694656.9	x^12 + 12x^10 + 48x^8 + 70x^6 + 24x^4 - 12x^2 + 4	\( 2^{22}\cdot 3^{18} \)	12T158	Trivial
12.0.1624959306694656.16	x^12 - 12x^10 + 48x^8 - 70x^6 + 24x^4 + 12x^2 + 4	\( 2^{22}\cdot 3^{18} \)	12T158	Trivial
12.0.6499837226778624.23	x^12 + 9x^8 - 6x^6 + 9	\( 2^{24}\cdot 3^{18} \)	12T158	$[2]$
12.0.6499837226778624.24	x^12 - 6x^10 + 9x^8 + 9	\( 2^{24}\cdot 3^{18} \)	12T158	$[2]$
12.4.6538986496000000.1	x^12 - 2x^11 - 2x^10 + 14x^9 - 30x^8 + 64x^7 - 122x^6 + 236x^5 - 324x^4 + 276x^3 - 184x^2 + 48x - 4	\( 2^{16}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4} \)	12T158	Trivial
12.4.6538986496000000.2	x^12 + 5x^10 - 2x^8 - 39x^6 - 34x^4 + 49x^2 + 49	\( 2^{16}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4} \)	12T158	Trivial
12.0.8226356490141696.27	x^12 + 12x^10 + 60x^8 + 136x^6 + 96x^4 - 96x^2 + 64	\( 2^{18}\cdot 3^{22} \)	12T158	Trivial
12.0.8226356490141696.28	x^12 - 12x^10 + 60x^8 - 136x^6 + 96x^4 + 96x^2 + 64	\( 2^{18}\cdot 3^{22} \)	12T158	Trivial
12.8.8540717056000000.1	x^12 - 4x^10 - 6x^8 + 34x^6 - 28x^4 + 4	\( 2^{22}\cdot 5^{6}\cdot 19^{4} \)	12T158	Trivial
12.0.13685690504052736.29	x^12 - 26x^10 + 299x^8 - 2002x^6 + 8450x^4 - 21970x^2 + 28561	\( 2^{24}\cdot 13^{8} \)	12T158	$[2]$
12.0.13685690504052736.31	x^12 + 39x^8 - 208x^6 + 338x^4 - 4394x^2 + 28561	\( 2^{24}\cdot 13^{8} \)	12T158	$[2]$
12.0.23891266624000000.1	x^12 + 12x^10 + 48x^8 + 80x^6 + 54x^4 + 13x^2 + 1	\( 2^{12}\cdot 5^{6}\cdot 139^{4} \)	12T158	$[2, 4]$
12.0.32905425960566784.13	x^12 + 45x^8 - 6x^6 + 81x^4 - 54x^2 + 9	\( 2^{20}\cdot 3^{22} \)	12T158	Trivial
12.0.32905425960566784.14	x^12 - 9x^10 + 36x^8 - 87x^6 + 108x^4 - 27x^2 + 9	\( 2^{20}\cdot 3^{22} \)	12T158	Trivial
12.12.37993382255263744.1	x^12 - 2x^11 - 17x^10 + 18x^9 + 114x^8 - 10x^7 - 297x^6 - 196x^5 + 85x^4 + 82x^3 - 2x^2 - 8x - 1	\( 2^{18}\cdot 61^{2}\cdot 79^{4} \)	12T158	Trivial
12.0.104623783936000000.1	x^12 + 15x^10 + 86x^8 + 239x^6 + 334x^4 + 217x^2 + 49	\( 2^{20}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4} \)	12T158	$[12]$
12.12.104623783936000000.1	x^12 - 15x^10 + 86x^8 - 239x^6 + 334x^4 - 217x^2 + 49	\( 2^{20}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4} \)	12T158	Trivial (GRH)
12.0.131621703842267136.5	x^12 - 6x^10 + 42x^8 - 74x^6 + 60x^4 - 24x^2 + 4	\( 2^{22}\cdot 3^{22} \)	12T158	Trivial (GRH)
12.0.131621703842267136.8	x^12 + 6x^10 + 42x^8 + 74x^6 + 24x^4 - 12x^2 + 4	\( 2^{22}\cdot 3^{22} \)	12T158	Trivial
12.0.131621703842267136.14	x^12 - 6x^10 + 42x^8 - 74x^6 + 24x^4 + 12x^2 + 4	\( 2^{22}\cdot 3^{22} \)	12T158	Trivial (GRH)
12.0.131621703842267136.20	x^12 + 6x^10 + 42x^8 + 74x^6 + 60x^4 + 24x^2 + 4	\( 2^{22}\cdot 3^{22} \)	12T158	Trivial (GRH)
12.0.415989582513831936.2	x^12 - 6x^8 + 2x^6 + 63x^4 - 6x^2 + 1	\( 2^{30}\cdot 3^{18} \)	12T158	$[2]$
12.0.415989582513831936.19	x^12 + 6x^10 + 9x^8 - 6x^6 + 36x^4 + 9	\( 2^{30}\cdot 3^{18} \)	12T158	$[2]$
12.0.415989582513831936.20	x^12 - 6x^10 + 9x^8 + 6x^6 + 36x^4 + 9	\( 2^{30}\cdot 3^{18} \)	12T158	$[2]$
12.8.526486815369068544.3	x^12 - 6x^10 - 3x^8 + 46x^6 + 6x^4 - 60x^2 + 1	\( 2^{24}\cdot 3^{22} \)	12T158	Trivial (GRH)
12.8.526486815369068544.5	x^12 - 12x^10 + 42x^8 - 22x^6 - 75x^4 + 42x^2 + 25	\( 2^{24}\cdot 3^{22} \)	12T158	Trivial
12.4.526486815369068544.13	x^12 + 6x^10 - 3x^8 - 46x^6 + 6x^4 + 60x^2 + 1	\( 2^{24}\cdot 3^{22} \)	12T158	Trivial
12.0.3357197463473360896.2	x^12 - x^10 + 3x^8 - 11x^6 + 13x^4 - 5x^2 + 1	\( 2^{12}\cdot 31^{10} \)	12T158	$[9]$
12.0.6428888932339941376.2	x^12 + 4x^10 + 13x^8 - 18x^6 + 29x^4 - 10x^2 + 1	\( 2^{20}\cdot 19^{10} \)	12T158	$[3]$
12.0.18235961957662326784.31	x^12 - 38x^10 + 589x^8 - 4978x^6 + 25992x^4 - 82308x^2 + 130321	\( 2^{30}\cdot 19^{8} \)	12T158	$[2]$ (GRH)
12.0.18235961957662326784.35	x^12 + 38x^10 + 589x^8 + 4978x^6 + 25992x^4 + 82308x^2 + 130321	\( 2^{30}\cdot 19^{8} \)	12T158	$[2]$ (GRH)
12.0.25715555729359765504.2	x^12 + 8x^10 + 52x^8 - 144x^6 + 464x^4 - 320x^2 + 64	\( 2^{22}\cdot 19^{10} \)	12T158	$[3]$ (GRH)
12.0.25715555729359765504.3	x^12 - 8x^10 + 52x^8 + 144x^6 + 464x^4 + 320x^2 + 64	\( 2^{22}\cdot 19^{10} \)	12T158	$[3]$ (GRH)
12.8.33695156183620386816.3	x^12 - 12x^10 + 6x^8 + 182x^6 - 273x^4 - 30x^2 + 1	\( 2^{30}\cdot 3^{22} \)	12T158	Trivial (GRH)
12.8.33695156183620386816.4	x^12 + 6x^10 - 57x^8 + 74x^6 - 12x^4 - 12x^2 + 1	\( 2^{30}\cdot 3^{22} \)	12T158	Trivial (GRH)
12.8.33695156183620386816.5	x^12 - 12x^10 + 24x^8 + 62x^6 - 57x^4 + 6x^2 + 1	\( 2^{30}\cdot 3^{22} \)	12T158	Trivial (GRH)