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 7291)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.205924456521.1	x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1	\( 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.1157018619904.1	x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1	\( 2^{12}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.1586874322944.1	x^12 - x^6 + 1	\( 2^{12}\cdot 3^{18} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.4413675765625.1	x^12 - x^11 + 2x^10 - 3x^9 + 5x^8 - 8x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2x^2 + x + 1	\( 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.6053445140625.1	x^12 - 4x^9 + 17x^6 + 4x^3 + 1	\( 3^{18}\cdot 5^{6} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.17213603549184.1	x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6x^2 + 1	\( 2^{12}\cdot 3^{6}\cdot 7^{8} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.45579633110361.1	x^12 - 5x^9 + 17x^6 - 40x^3 + 64	\( 3^{18}\cdot 7^{6} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.65664686390625.1	x^12 - x^11 + 8x^10 + 3x^9 + 44x^8 - 2x^7 + 49x^6 - 13x^5 + 46x^4 - 10x^3 + 11x^2 + 2x + 1	\( 3^{6}\cdot 5^{6}\cdot 7^{8} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.74049191673856.1	x^12 - 2x^10 + 4x^8 - 8x^6 + 16x^4 - 32x^2 + 64	\( 2^{18}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.74049191673856.2	x^12 + 2x^10 + 4x^8 + 8x^6 + 16x^4 + 32x^2 + 64	\( 2^{18}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.0.96717311574016.1	x^12 + 13x^8 + 26x^4 + 1	\( 2^{24}\cdot 7^{8} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.100498840557921.1	x^12 - x^11 + 6x^10 - 3x^9 + 23x^8 - 11x^7 + 41x^6 - 5x^5 + 43x^4 - 10x^3 + 15x^2 + 3x + 1	\( 3^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.0.101559956668416.1	x^12 - 8x^6 + 64	\( 2^{18}\cdot 3^{18} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.101559956668416.2	x^12 + 8x^6 + 64	\( 2^{18}\cdot 3^{18} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.368947264000000.1	x^12 + 15x^10 + 67x^8 + 108x^6 + 71x^4 + 18x^2 + 1	\( 2^{12}\cdot 5^{6}\cdot 7^{8} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.500422134593689.1	x^12 - x^11 - 2x^10 + 5x^9 + x^8 - 16x^7 + 13x^6 - 48x^5 + 9x^4 + 135x^3 - 162x^2 - 243x + 729	\( 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.564668382613504.1	x^12 + 11x^10 + 45x^8 + 84x^6 + 70x^4 + 21x^2 + 1	\( 2^{12}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.686339028913329.1	x^12 - 8x^9 + 37x^6 - 216x^3 + 729	\( 3^{18}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.722204136308736.1	x^12 + 18x^8 + 69x^4 + 1	\( 2^{24}\cdot 3^{16} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.843466573910016.1	x^12 + 13x^10 + 64x^8 + 146x^6 + 148x^4 + 48x^2 + 1	\( 2^{12}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.12.843466573910016.1	x^12 - 11x^10 + 44x^8 - 78x^6 + 60x^4 - 16x^2 + 1	\( 2^{12}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.843466573910016.2	x^12 + 7x^10 + 35x^8 + 84x^6 + 147x^4 + 98x^2 + 49	\( 2^{12}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.0.843466573910016.3	x^12 + 3x^10 + 9x^8 + 27x^6 + 81x^4 + 243x^2 + 729	\( 2^{12}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.0.1101670627147776.1	x^12 - 10x^10 + 76x^8 - 224x^6 + 496x^4 - 192x^2 + 64	\( 2^{18}\cdot 3^{6}\cdot 7^{8} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.1101670627147776.2	x^12 + 10x^10 + 76x^8 + 224x^6 + 496x^4 + 192x^2 + 64	\( 2^{18}\cdot 3^{6}\cdot 7^{8} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.1363454074150441.1	x^12 - x^11 + 4x^10 - 7x^9 + 19x^8 - 40x^7 + 97x^6 + 120x^5 + 171x^4 + 189x^3 + 324x^2 + 243x + 729	\( 7^{10}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2]$
12.0.1870004703089601.1	x^12 - 10x^9 + 127x^6 + 270x^3 + 729	\( 3^{18}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.12.2154038935140625.1	x^12 - x^11 - 16x^10 + 11x^9 + 79x^8 - 29x^7 - 145x^6 + 25x^5 + 107x^4 - 2x^3 - 27x^2 - 3x + 1	\( 5^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.2435758881214464.1	x^12 - 9x^10 + 67x^8 - 124x^6 + 187x^4 - 14x^2 + 1	\( 2^{12}\cdot 3^{6}\cdot 13^{8} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.2754990144000000.1	x^12 + 18x^10 + 99x^8 + 180x^6 + 123x^4 + 27x^2 + 1	\( 2^{12}\cdot 3^{16}\cdot 5^{6} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.3217569633140625.1	x^12 - x^11 + 11x^10 - 7x^9 + 40x^8 - 12x^7 + 62x^6 + 15x^5 + 31x^4 + 112x^3 - 40x^2 - 2x + 211	\( 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.12.3217569633140625.1	x^12 - x^11 - 19x^10 + 18x^9 + 110x^8 - 92x^7 - 218x^6 + 155x^5 + 166x^4 - 88x^3 - 40x^2 + 8x + 1	\( 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.3217569633140625.2	x^12 - x^11 - 7x^10 + 8x^9 + 34x^8 - 42x^7 - 76x^6 + 147x^5 + 76x^4 - 20x^3 - 154x^2 - 638x + 841	\( 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.0.3217569633140625.3	x^12 - x^11 - 3x^10 + 7x^9 + 5x^8 - 33x^7 + 13x^6 - 132x^5 + 80x^4 + 448x^3 - 768x^2 - 1024x + 4096	\( 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.0.4469547301936929.1	x^12 - x^11 - x^10 - 18x^9 + 13x^8 + 9x^7 + 75x^6 + 5x^5 + 27x^4 - 107x^3 + 32x^2 - 35x + 49	\( 3^{6}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.4739148267126784.1	x^12 + 12x^10 + 53x^8 + 104x^6 + 86x^4 + 24x^2 + 1	\( 2^{24}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[4]$
12.12.4739148267126784.1	x^12 - 12x^10 + 53x^8 - 104x^6 + 86x^4 - 24x^2 + 1	\( 2^{24}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.4739148267126784.2	x^12 + 21x^8 + 98x^4 + 49	\( 2^{24}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[4]$
12.0.6499837226778624.1	x^12 + 12x^10 + 54x^8 + 112x^6 + 105x^4 + 36x^2 + 1	\( 2^{24}\cdot 3^{18} \)	$C_6\times C_2$ (as 12T2)	$[6]$
12.12.6499837226778624.1	x^12 - 12x^10 + 54x^8 - 112x^6 + 105x^4 - 36x^2 + 1	\( 2^{24}\cdot 3^{18} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.6499837226778624.2	x^12 + 18x^8 + 45x^4 + 9	\( 2^{24}\cdot 3^{18} \)	$C_6\times C_2$ (as 12T2)	$[2]$
12.0.6818265813529681.1	x^12 - x^11 + 5x^10 - 9x^9 + 29x^8 - 65x^7 + 181x^6 + 260x^5 + 464x^4 + 576x^3 + 1280x^2 + 1024x + 4096	\( 7^{10}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[5]$
12.0.7445055839159169.1	x^12 - x^11 - 3x^10 + 2x^9 - 16x^8 + 42x^7 + 31x^6 - 126x^5 + 545x^4 + 310x^3 - 2043x^2 - 284x + 5041	\( 3^{6}\cdot 7^{8}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.0.9291682743890625.1	x^12 - x^11 + 13x^10 - 14x^9 + 138x^8 - 128x^7 + 377x^6 + 12x^5 + 431x^4 - 60x^3 + 195x^2 + 50x + 25	\( 3^{6}\cdot 5^{6}\cdot 13^{8} \)	$C_6\times C_2$ (as 12T2)	$[2, 2]$
12.0.9351388785251241.1	x^12 - 13x^9 + 233x^6 + 832x^3 + 4096	\( 3^{18}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2]$
12.0.13289296949899369.1	x^12 - x^11 - 4x^10 + 9x^9 + 11x^8 - 56x^7 + x^6 - 280x^5 + 275x^4 + 1125x^3 - 2500x^2 - 3125x + 15625	\( 7^{10}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.13685690504052736.1	x^12 + 53x^8 + 178x^4 + 1	\( 2^{24}\cdot 13^{8} \)	$C_6\times C_2$ (as 12T2)	$[3]$
12.0.16218913707543001.1	x^12 - x^11 + 17x^10 - 10x^9 + 130x^8 - 53x^7 + 485x^6 - 86x^5 + 884x^4 - 128x^3 + 576x^2 + 96x + 64	\( 7^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[7]$
12.0.18078415936000000.1	x^12 + 9x^10 + 32x^8 + 50x^6 + 44x^4 - 24x^2 + 169	\( 2^{12}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[6]$
12.12.18078415936000000.1	x^12 - 21x^10 + 147x^8 - 420x^6 + 539x^4 - 294x^2 + 49	\( 2^{12}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial