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 80)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.181824635281.1	x^12 - 2x^11 + 3x^10 - x^9 + 2x^6 - x^3 + 3x^2 - 2x + 1	\( 653^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.1267247769841.1	x^12 - 3x^11 + 4x^10 - 2x^9 + 3x^8 - x^7 - 3x^6 - x^5 + 3x^4 - 2x^3 + 4x^2 - 3x + 1	\( 1061^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.5157663560401.1	x^12 - 3x^10 + 9x^8 - 19x^6 + 17x^4 - 7x^2 + 1	\( 11^{4}\cdot 137^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.5282495463424.1	x^12 + 2x^10 + x^8 - 2x^6 + 2x^4 - 4x^2 + 1	\( 2^{18}\cdot 67^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.64000000000000.1	x^12 + 2x^10 + 5x^8 + 10x^6 + 10x^4 + 8x^2 + 1	\( 2^{18}\cdot 5^{12} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.64000000000000.1	x^12 - 2x^10 + 5x^8 - 10x^6 + 10x^4 - 8x^2 + 1	\( 2^{18}\cdot 5^{12} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.625000000000000.1	x^12 - x^11 + 2x^10 - 5x^9 - 5x^8 + 14x^7 - 4x^6 + 28x^5 - 20x^4 - 40x^3 + 32x^2 - 32x + 64	\( 2^{12}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.960472390437121.1	x^12 - 3x^11 + 2x^10 + 7x^9 - 13x^8 - x^7 + 23x^6 - 2x^5 - 52x^4 + 56x^3 + 32x^2 - 96x + 64	\( 19^{4}\cdot 293^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.1600000000000000.2	x^12 - 2x^11 + 6x^10 - 10x^9 - 5x^8 + 12x^7 - 44x^6 + 12x^5 - 5x^4 - 10x^3 + 6x^2 - 2x + 1	\( 2^{18}\cdot 5^{14} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.4.1828652958613504.1	x^12 - 4x^11 + 2x^10 + 18x^9 - 35x^8 - 4x^7 + 78x^6 - 66x^5 - 24x^4 + 62x^3 - 46x^2 + 14x - 1	\( 2^{18}\cdot 17^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.4096000000000000.1	x^12 - 4x^10 + 10x^8 - 20x^6 + 25x^4 - 14x^2 + 1	\( 2^{24}\cdot 5^{12} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.4096000000000000.2	x^12 + 4x^10 + 10x^8 + 20x^6 + 25x^4 + 14x^2 + 1	\( 2^{24}\cdot 5^{12} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.4452139149819904.1	x^12 - 4x^10 + 10x^8 + 10x^6 + 17x^4 - 10x^2 + 1	\( 2^{18}\cdot 19^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.4771040786343841.1	x^12 - 4x^11 + 3x^10 + 9x^9 - 16x^8 - 8x^7 + 41x^6 - 16x^5 - 64x^4 + 72x^3 + 48x^2 - 128x + 64	\( 8311^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.11984637467948161.1	x^12 - 3x^11 + x^10 + 9x^9 - 13x^8 - 9x^7 + 39x^6 - 18x^5 - 52x^4 + 72x^3 + 16x^2 - 96x + 64	\( 10463^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.13044373862856961.1	x^12 - 4x^11 + 4x^10 + 3x^9 - 7x^8 + 4x^7 - 3x^6 + 8x^5 - 28x^4 + 24x^3 + 64x^2 - 128x + 64	\( 10687^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.15625000000000000.1	x^12 - 4x^11 + 9x^10 - 10x^9 + 15x^8 - 6x^7 - x^6 + 6x^5 + 55x^4 - 20x^3 - 31x^2 + 24x + 16	\( 2^{12}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.12.34341192980985361.1	x^12 - 6x^11 + 3x^10 + 40x^9 - 58x^8 - 74x^7 + 160x^6 + 13x^5 - 128x^4 + 35x^3 + 18x^2 - 4x - 1	\( 13613^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.40000000000000000.3	x^12 - 4x^10 - 10x^8 - 30x^6 + 65x^4 - 34x^2 + 1	\( 2^{18}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.40000000000000000.4	x^12 + 6x^10 - 10x^8 - 60x^7 - 130x^6 - 60x^5 - 10x^4 + 6x^2 + 1	\( 2^{18}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.40000000000000000.5	x^12 - 6x^11 + 14x^10 - 10x^9 - 5x^8 + 12x^7 - 12x^6 - 12x^5 - 5x^4 + 10x^3 + 14x^2 + 6x + 1	\( 2^{18}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.40000000000000000.8	x^12 - 4x^11 + 5x^10 + 5x^8 + 38x^7 + 18x^6 + 60x^5 + 70x^4 + 20x^3 + 92x^2 - 8x + 40	\( 2^{18}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.102400000000000000.7	x^12 + 10x^10 + 30x^8 + 10x^6 - 75x^4 - 70x^2 + 25	\( 2^{24}\cdot 5^{14} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.0.102400000000000000.8	x^12 - 10x^10 + 30x^8 - 10x^6 - 75x^4 + 70x^2 + 25	\( 2^{24}\cdot 5^{14} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.0.117033789351264256.2	x^12 + 2x^10 - 7x^8 - 2x^6 + 10x^4 + 2x^2 + 1	\( 2^{24}\cdot 17^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.117033789351264256.2	x^12 - 2x^10 - 7x^8 + 2x^6 + 10x^4 - 2x^2 + 1	\( 2^{24}\cdot 17^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.131136595679248384.4	x^12 + 10x^8 - 22x^6 + 9x^4 - 142x^2 + 9	\( 2^{18}\cdot 29^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.131136595679248384.7	x^12 + 2x^8 - 58x^6 + 301x^4 - 174x^2 + 25	\( 2^{18}\cdot 29^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.160000000000000000.2	x^12 - 6x^11 + 14x^10 - 10x^9 - 5x^8 - 28x^7 + 28x^6 + 28x^5 - 5x^4 + 10x^3 + 14x^2 + 6x + 1	\( 2^{20}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.160000000000000000.7	x^12 - 2x^10 - 10x^8 + 10x^6 + 25x^4 - 68x^2 + 196	\( 2^{20}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial (GRH)
12.12.162268567138729984.1	x^12 - 4x^11 - 10x^10 + 54x^9 + 17x^8 - 248x^7 + 70x^6 + 466x^5 - 172x^4 - 390x^3 + 74x^2 + 122x + 19	\( 2^{18}\cdot 887^{4} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.223580268118933504.4	x^12 - 4x^11 + 12x^10 - 24x^9 + 17x^8 + 2x^7 - 40x^6 + 98x^5 - 96x^4 + 44x^3 - 16x^2 + 18x - 1	\( 2^{18}\cdot 31^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.284936905588473856.7	x^12 + 10x^10 + 34x^8 + 42x^6 + 13x^4 + 16x^2 + 9	\( 2^{24}\cdot 19^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.284936905588473856.14	x^12 - 10x^10 + 34x^8 - 42x^6 + 13x^4 - 16x^2 + 9	\( 2^{24}\cdot 19^{8} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.528480705039302656.1	x^12 - 2x^11 + 6x^10 - 30x^9 + 24x^8 - 66x^7 + 108x^6 + 60x^5 - 75x^4 - 18x^3 + 6x^2 + 8x - 1	\( 2^{18}\cdot 17^{10} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.0.528480705039302656.4	x^12 - 2x^11 + 6x^10 + 4x^9 + 7x^8 + 2x^7 + 74x^6 + 26x^5 - 58x^4 + 186x^3 + 108x^2 - 264x + 271	\( 2^{18}\cdot 17^{10} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.4.640000000000000000.14	x^12 - 10x^10 + 50x^8 - 180x^6 + 345x^4 - 274x^2 + 100	\( 2^{22}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.1000000000000000000.1	x^12 - 6x^11 + 24x^10 - 60x^9 + 110x^8 - 138x^7 + 118x^6 - 42x^5 - 35x^4 + 60x^3 - 24x^2 - 16x + 19	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.4.1000000000000000000.1	x^12 - 2x^11 - 4x^10 - 10x^9 + 20x^8 + 62x^7 + 46x^6 - 158x^5 - 285x^4 + 220x^3 + 406x^2 - 192x - 184	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T76)	$[2]$ (GRH)
12.4.1000000000000000000.2	x^12 - 6x^11 + 14x^10 - 10x^9 - 5x^8 - 4x^7 + 4x^6 + 4x^5 - 5x^4 + 10x^3 + 14x^2 + 6x + 1	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.0.1000000000000000000.4	x^12 - 6x^11 + 14x^10 - 10x^9 - 25x^8 + 52x^7 + 18x^6 + 8x^5 + 40x^4 + 656x^2 - 256x + 64	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T76)	$[2]$ (GRH)
12.4.1000000000000000000.4	x^12 - 6x^11 + 4x^10 + 30x^9 - 50x^8 + 18x^7 + 52x^6 - 188x^5 + 45x^4 - 50x^3 + 36x^2 + 24x + 29	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.0.1000000000000000000.6	x^12 + 10x^10 + 50x^8 + 100x^6 + 25x^4 - 30x^2 + 100	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T76)	$[2, 2]$
12.0.1000000000000000000.14	x^12 - 6x^11 + 24x^10 - 60x^9 + 125x^8 - 192x^7 + 282x^6 - 408x^5 + 510x^4 - 450x^3 + 536x^2 - 646x + 289	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.4.1607222233084985344.2	x^12 - 6x^11 + 6x^10 + 10x^9 + 13x^8 - 8x^7 - 252x^6 + 40x^5 - 29x^4 + 614x^3 + 318x^2 - 602x - 193	\( 2^{18}\cdot 19^{10} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.1607222233084985344.4	x^12 - 6x^11 + 6x^10 + 2x^9 + 49x^8 + 12x^7 - 300x^6 - 108x^5 + 51x^4 + 738x^3 + 1334x^2 + 130x + 83	\( 2^{18}\cdot 19^{10} \)	$C_2\times A_5$ (as 12T76)	$[2]$
12.4.2560000000000000000.2	x^12 - 12x^10 + 55x^8 - 120x^6 + 135x^4 - 68x^2 + 1	\( 2^{24}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.2560000000000000000.3	x^12 + 12x^10 + 55x^8 + 120x^6 + 135x^4 + 68x^2 + 1	\( 2^{24}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.0.2560000000000000000.10	x^12 + 10x^10 + 50x^8 + 130x^6 + 145x^4 + 54x^2 + 25	\( 2^{24}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial
12.4.2560000000000000000.11	x^12 - 10x^10 + 50x^8 - 130x^6 + 145x^4 - 54x^2 + 25	\( 2^{24}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T76)	Trivial