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 103)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.164648481361.1	x^12 - 2x^11 + 3x^10 - 6x^9 + 12x^8 - 18x^7 + 20x^6 - 15x^5 + 6x^4 + x^3 - x^2 - x + 1	\( 7^{8}\cdot 13^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.509831700625.1	x^12 - 2x^11 + 6x^10 - 9x^9 + 15x^8 - 19x^7 + 21x^6 - 19x^5 + 15x^4 - 9x^3 + 6x^2 - 2x + 1	\( 5^{4}\cdot 13^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.1511207993344.1	x^12 - 2x^11 + 4x^9 - 8x^8 + 20x^7 - 28x^6 - 8x^5 + 68x^4 - 72x^3 + 16x^2 + 16x - 8	\( 2^{18}\cdot 7^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.3595305184641.1	x^12 - x^9 + 3x^8 - 3x^7 + 14x^6 - 15x^5 + 12x^4 - 10x^3 + 9x^2 - 3x + 1	\( 3^{16}\cdot 17^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.4077334216081.1	x^12 - x^11 + x^10 + 4x^9 + 5x^8 + 7x^7 + 15x^6 + 14x^5 + 13x^4 + 11x^3 + 9x^2 + 3x + 1	\( 7^{8}\cdot 29^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.5609891727441.1	x^12 - 6x^11 + 18x^10 - 28x^9 + 12x^8 + 36x^7 - 67x^6 + 36x^5 + 12x^4 - 28x^3 + 18x^2 - 6x + 1	\( 3^{16}\cdot 19^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.8067775586689.3	x^12 - 3x^11 + 2x^10 + x^9 + 4x^8 - 5x^7 - 20x^6 + 28x^5 - 21x^4 + 35x^3 - 21x^2 + 7x - 7	\( 7^{10}\cdot 13^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.11284439629824.1	x^12 - 6x^10 - 10x^9 - 9x^8 + 16x^6 + 6x^5 - 6x^3 - 6x^2 + 6x - 1	\( 2^{18}\cdot 3^{16} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.32357746661769.3	x^12 + 3x^10 - 5x^9 + 6x^8 + 3x^7 - 14x^6 + 48x^5 - 24x^4 - 33x^3 + 27x^2 - 3	\( 3^{18}\cdot 17^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.40777534861441.1	x^12 - 6x^11 + 19x^10 - 40x^9 + 59x^8 - 62x^7 + 41x^6 - 8x^5 - 33x^4 + 54x^3 - 35x^2 + 10x - 1	\( 7^{4}\cdot 19^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.74049191673856.4	x^12 - 4x^11 + 6x^10 - 12x^9 + 30x^8 - 56x^7 + 120x^6 - 224x^5 + 284x^4 - 240x^3 + 136x^2 - 48x + 8	\( 2^{18}\cdot 7^{10} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.4.74049191673856.4	x^12 - 4x^11 + 6x^10 - 12x^9 + 30x^8 - 42x^7 + 8x^6 + 56x^5 - 59x^4 - 2x^3 + 10x^2 - 6x + 1	\( 2^{18}\cdot 7^{10} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.86161557405625.3	x^12 - x^11 - 6x^10 + 7x^9 + 13x^8 - 19x^7 - 15x^6 + 14x^5 + 26x^4 + 17x^3 - 44x^2 - 32x + 64	\( 5^{4}\cdot 13^{10} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.4.96717311574016.3	x^12 - 6x^10 + 17x^8 - 28x^6 + 26x^4 - 12x^2 + 1	\( 2^{24}\cdot 7^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.96717311574016.5	x^12 + 6x^10 + 17x^8 + 28x^6 + 26x^4 + 12x^2 + 1	\( 2^{24}\cdot 7^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.101559956668416.4	x^12 - 6x^11 + 18x^10 - 32x^9 + 30x^8 + 12x^7 - 80x^6 + 66x^5 + 33x^4 - 54x^3 + 18x + 3	\( 2^{18}\cdot 3^{18} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.101559956668416.13	x^12 - 6x^11 + 24x^10 - 62x^9 + 129x^8 - 204x^7 + 268x^6 - 258x^5 + 198x^4 - 84x^3 + 36x^2 + 9	\( 2^{18}\cdot 3^{18} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.4.120028742912169.1	x^12 - 4x^11 + 25x^9 - 65x^8 + 101x^7 - 105x^6 + 68x^5 - 43x^4 + 33x^3 - 10x^2 + 8x - 8	\( 3^{6}\cdot 7^{8}\cdot 13^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.213838914125824.1	x^12 - 6x^11 + 16x^10 - 10x^9 - 55x^8 + 164x^7 - 182x^6 + 18x^5 + 70x^4 + 40x^3 - 44x^2 - 12x - 1	\( 2^{18}\cdot 13^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.218340105584896.1	x^12 - 2x^10 - 6x^8 - 2x^6 - 6x^4 - 2x^2 + 1	\( 2^{8}\cdot 31^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.371667309755625.1	x^12 - 2x^11 - 4x^10 + 7x^9 - 5x^8 - 9x^7 - 4x^6 + 3x^5 - 2x^4 + 32x^3 + 29x^2 - 7x + 1	\( 3^{6}\cdot 5^{4}\cdot 13^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.722204136308736.10	x^12 - 3x^8 - 10x^6 + 18x^4 - 18x^2 + 9	\( 2^{24}\cdot 3^{16} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.722204136308736.12	x^12 - 3x^8 + 10x^6 + 18x^4 + 18x^2 + 9	\( 2^{24}\cdot 3^{16} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.1093889542148001.2	x^12 - 6x^11 + 15x^10 - 18x^9 - 3x^8 + 24x^7 + 3x^6 + 6x^5 + 33x^4 + 152x^3 + 273x^2 + 198x + 51	\( 3^{16}\cdot 71^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.1101670627147776.1	x^12 - 4x^11 - 2x^10 + 14x^9 + 47x^8 - 134x^7 - 60x^6 + 304x^5 + 130x^4 - 638x^3 + 70x^2 + 728x - 497	\( 2^{18}\cdot 3^{6}\cdot 7^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.1101670627147776.3	x^12 - 4x^11 + 16x^10 - 46x^9 + 134x^8 - 242x^7 + 420x^6 - 542x^5 + 673x^4 - 416x^3 + 142x^2 - 10x + 1	\( 2^{18}\cdot 3^{6}\cdot 7^{8} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.4.1363454074150441.1	x^12 - 4x^11 - x^10 + 30x^9 - 75x^8 + 140x^7 - 293x^6 + 518x^5 - 605x^4 + 460x^3 - 235x^2 + 78x - 13	\( 7^{10}\cdot 13^{6} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.0.2154038935140625.1	x^12 - 2x^10 + 19x^8 - 65x^7 + 149x^6 - 195x^5 + 174x^4 - 65x^3 + 8x^2 + 1	\( 5^{6}\cdot 13^{10} \)	$A_4\times C_2$ (as 12T6)	$[2, 2]$
12.0.2572632521265625.3	x^12 - 4x^11 + 15x^10 - 34x^9 + 81x^8 - 100x^7 + 83x^6 + 54x^5 - 165x^4 + 96x^3 + 89x^2 - 138x + 71	\( 5^{6}\cdot 7^{8}\cdot 13^{4} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.0.3493441689358336.1	x^12 - 5x^11 + 10x^10 - 11x^9 + 13x^8 - 28x^7 + 50x^6 - 56x^5 + 52x^4 - 88x^3 + 160x^2 - 160x + 64	\( 2^{12}\cdot 31^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.3493441689358336.8	x^12 + 3x^10 - 7x^8 - 19x^6 + 106x^4 + 364x^2 + 64	\( 2^{12}\cdot 31^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.3980505700380001.2	x^12 + 17x^10 + 101x^8 + 257x^6 + 277x^4 + 101x^2 + 1	\( 13^{8}\cdot 47^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.4452139149819904.3	x^12 - 58x^8 - 190x^6 - 215x^4 - 38x^2 + 121	\( 2^{18}\cdot 19^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.4483841009097121.1	x^12 + 20x^10 + 122x^8 + 266x^6 + 145x^4 + 26x^2 + 1	\( 7^{8}\cdot 167^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.4739148267126784.11	x^12 - 14x^8 + 84x^6 - 147x^4 + 98x^2 + 49	\( 2^{24}\cdot 7^{10} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.4.4739148267126784.23	x^12 - 14x^8 - 84x^6 - 147x^4 - 98x^2 + 49	\( 2^{24}\cdot 7^{10} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.12.6187263609223921.1	x^12 - x^11 - 20x^10 + 12x^9 + 105x^8 - 23x^7 - 197x^6 - 23x^5 + 105x^4 + 12x^3 - 20x^2 - x + 1	\( 7^{8}\cdot 181^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.6499837226778624.42	x^12 + 6x^10 + 18x^8 + 30x^6 + 81x^4 + 162x^2 + 81	\( 2^{24}\cdot 3^{18} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.4.6499837226778624.44	x^12 - 6x^10 + 18x^8 - 30x^6 + 81x^4 - 162x^2 + 81	\( 2^{24}\cdot 3^{18} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.9291682743890625.1	x^12 - 5x^11 + 19x^10 - 26x^9 - 7x^8 + 17x^7 + 9x^6 - 49x^5 + 31x^4 - 13x^3 + 28x^2 - 11x + 1	\( 3^{6}\cdot 5^{6}\cdot 13^{8} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.4.9351388785251241.1	x^12 - 12x^10 - 4x^9 + 69x^8 + 3x^7 - 143x^6 - 93x^5 + 276x^4 + 189x^3 - 540x^2 + 306x - 51	\( 3^{18}\cdot 17^{6} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.12.9845005879332009.1	x^12 - 3x^11 - 15x^10 + 59x^9 + 27x^8 - 315x^7 + 304x^6 + 246x^5 - 561x^4 + 300x^3 - 27x^2 - 18x + 3	\( 3^{18}\cdot 71^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.13685690504052736.4	x^12 + 4x^10 - 3x^8 - 42x^6 - 74x^4 - 42x^2 + 1	\( 2^{24}\cdot 13^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.13685690504052736.9	x^12 - 4x^10 - 3x^8 + 42x^6 - 74x^4 + 42x^2 + 1	\( 2^{24}\cdot 13^{8} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.0.31772777657138401.1	x^12 - 4x^11 + 17x^10 - 37x^9 + 88x^8 - 154x^7 + 204x^6 - 187x^5 - 39x^4 + 119x^3 + 154x^2 - 257x + 103	\( 13^{8}\cdot 79^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial
12.4.36138776487264256.2	x^12 - 6x^11 + 4x^10 + 22x^9 - 11x^8 - 76x^7 + 2x^6 + 174x^5 + 110x^4 - 160x^3 - 276x^2 - 148x - 25	\( 2^{18}\cdot 13^{10} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.0.36138776487264256.4	x^12 - 6x^11 + 30x^10 - 82x^9 + 197x^8 - 284x^7 + 340x^6 - 164x^5 - 33x^4 + 74x^3 - 42x^2 - 18x + 27	\( 2^{18}\cdot 13^{10} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.12.116452742545489441.3	x^12 - 27x^10 + 241x^8 - 819x^6 + 957x^4 - 355x^2 + 1	\( 7^{8}\cdot 13^{4}\cdot 29^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial (GRH)
12.0.209824841467085056.2	x^12 + 4x^10 + 17x^8 + 84x^6 + 197x^4 + 160x^2 + 4	\( 2^{8}\cdot 31^{10} \)	$A_4\times C_2$ (as 12T6)	$[2]$
12.12.219708209445758929.1	x^12 - 3x^11 - 26x^10 + 50x^9 + 207x^8 - 327x^7 - 685x^6 + 987x^5 + 973x^4 - 1323x^3 - 490x^2 + 588x + 56	\( 7^{10}\cdot 167^{4} \)	$A_4\times C_2$ (as 12T6)	Trivial (GRH)