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 168)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.117236328125.1	x^12 - 4x^11 + 9x^10 - 20x^9 + 40x^8 - 64x^7 + 81x^6 - 81x^5 + 65x^4 - 40x^3 + 19x^2 - 6x + 1	\( 5^{11}\cdot 7^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.200000000000.1	x^12 - 4x^11 + 9x^10 - 15x^9 + 15x^8 + x^7 - 19x^6 + 14x^5 + 5x^4 - 10x^3 + 4x^2 - x + 1	\( 2^{12}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.546564453125.1	x^12 - x^11 + x^10 - x^8 - 2x^7 + 2x^6 - 3x^5 + x^4 + x^3 + x^2 + 1	\( 5^{9}\cdot 23^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.1012500000000.1	x^12 - 3x^11 + 11x^10 - 25x^9 + 55x^8 - 88x^7 + 119x^6 - 118x^5 + 95x^4 - 55x^3 + 26x^2 - 8x + 1	\( 2^{8}\cdot 3^{4}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.1037970703125.1	x^12 - 2x^9 + 4x^6 - 3x^3 + 1	\( 3^{12}\cdot 5^{9} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.1200500000000.1	x^12 - 2x^11 + 2x^10 - x^9 + 5x^8 + 2x^7 - 3x^6 + 2x^5 + 5x^4 + 9x^3 + 7x^2 + 3x + 1	\( 2^{8}\cdot 5^{9}\cdot 7^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.1803751953125.3	x^12 - x^10 - x^9 + x^8 - 3x^7 + 2x^5 + 3x^4 - 2x^3 + x^2 - x + 1	\( 5^{9}\cdot 31^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.5744580078125.1	x^12 - 2x^11 + x^10 + 5x^9 - 12x^7 - x^6 + 18x^5 - 20x^4 - 5x^3 + 16x^2 - 7x + 1	\( 5^{11}\cdot 7^{6} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.7320500000000.2	x^12 - x^11 + 2x^9 - 3x^8 + 2x^7 + 3x^6 - 8x^5 + 7x^4 + 4x^3 + 2x^2 + x + 1	\( 2^{8}\cdot 5^{9}\cdot 11^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.9112500000000.1	x^12 - 6x^11 + 14x^10 - 15x^9 + 5x^8 + 4x^7 - 9x^6 + 16x^5 - 15x^4 + 5x^3 - x^2 + x + 1	\( 2^{8}\cdot 3^{6}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.9341736328125.1	x^12 - 6x^11 + 15x^10 - 11x^9 - 27x^8 + 69x^7 - 40x^6 - 45x^5 + 57x^4 + 8x^3 - 24x^2 - 3x + 1	\( 3^{14}\cdot 5^{9} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.12800000000000.1	x^12 - 2x^11 + x^10 - 10x^8 + 18x^7 - 26x^6 + 8x^5 + 15x^4 - 20x^3 + 6x^2 + 8x - 4	\( 2^{18}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.25949267578125.1	x^12 - 5x^9 + 15x^6 - 15x^3 + 5	\( 3^{12}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.43436029431808.1	x^12 - 6x^11 + 19x^10 - 39x^9 + 63x^8 - 77x^7 + 71x^6 - 44x^5 + 39x^4 - 10x^3 + 8x^2 + x + 1	\( 2^{12}\cdot 13^{9} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.51200000000000.2	x^12 + 10x^6 - 20x^2 + 5	\( 2^{20}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.58824500000000.1	x^12 - x^11 - 2x^10 + 8x^9 - 5x^8 - 14x^7 + 33x^6 + 24x^5 - 25x^4 + 12x^3 + 18x^2 - 29x - 19	\( 2^{8}\cdot 5^{9}\cdot 7^{6} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.85465283203125.1	x^12 - 4x^11 + 9x^10 - 10x^9 + 16x^7 - 24x^6 - 41x^5 + 45x^4 - 10x^3 - 6x^2 + 14x + 1	\( 3^{6}\cdot 5^{11}\cdot 7^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.145800000000000.1	x^12 - 4x^11 + 9x^10 - 5x^9 - 10x^8 + 21x^7 - 24x^6 - 31x^5 + 10x^4 + 15x^3 - 31x^2 - 11x + 1	\( 2^{12}\cdot 3^{6}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.204800000000000.2	x^12 + 10x^10 + 35x^8 + 70x^6 + 85x^4 + 60x^2 + 20	\( 2^{22}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	$[2]$
12.4.233543408203125.2	x^12 - 6x^11 + 9x^10 - 6x^7 - 4x^6 + 6x^5 + 9x^2 + 6x + 1	\( 3^{14}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.259200000000000.1	x^12 - 10x^10 + 35x^8 - 60x^6 + 55x^4 - 10x^2 + 5	\( 2^{16}\cdot 3^{4}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.265720500000000.3	x^12 - 2x^9 + 4x^6 - 8x^3 + 16	\( 2^{8}\cdot 3^{12}\cdot 5^{9} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.289132595703125.1	x^12 - 2x^11 + 3x^10 - 5x^9 - 6x^8 + 6x^7 - 51x^6 + 87x^5 - 104x^4 + 172x^3 - 181x^2 + 94x - 19	\( 5^{9}\cdot 23^{6} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.307328000000000.1	x^12 - 4x^11 + x^10 + 14x^9 - 28x^8 + 4x^7 + 61x^6 - 68x^5 - 36x^4 + 122x^3 + 53x^2 - 60x - 19	\( 2^{16}\cdot 5^{9}\cdot 7^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.357012500000000.1	x^12 - x^11 - x^10 + 25x^9 - 15x^8 - 86x^7 + 141x^6 + 76x^5 - 365x^4 + 195x^3 + 244x^2 - 384x + 181	\( 2^{8}\cdot 5^{11}\cdot 13^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.458793060873472.1	x^12 - 3x^11 + 9x^10 - 27x^9 + 55x^8 - 100x^7 + 157x^6 - 185x^5 + 152x^4 - 40x^3 - 36x^2 - 9x + 27	\( 2^{8}\cdot 13^{11} \)	$S_3 \times C_4$ (as 12T11)	$[3]$
12.0.503060929445888.2	x^12 - 12x^8 + 20x^6 + 4x^4 - 8x^2 + 2	\( 2^{35}\cdot 11^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.503060929445888.6	x^12 - 12x^8 - 20x^6 + 4x^4 + 8x^2 + 2	\( 2^{35}\cdot 11^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.885780500000000.1	x^12 - x^11 + 3x^10 + x^9 + 9x^8 - 18x^7 - 33x^6 + 46x^5 - 15x^4 - 21x^3 + 20x^2 - 22x + 11	\( 2^{8}\cdot 5^{9}\cdot 11^{6} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.937080500000000.1	x^12 - x^11 + 4x^10 - 6x^9 + 17x^8 + 10x^7 + 35x^6 + 12x^5 + 103x^4 - 32x^3 + 10x^2 - 3x + 1	\( 2^{8}\cdot 5^{9}\cdot 37^{4} \)	$S_3 \times C_4$ (as 12T11)	$[2]$
12.4.981348487528448.4	x^12 - 4x^10 + 6x^8 + 8x^6 - 7x^4 - 4x^2 + 2	\( 2^{35}\cdot 13^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.981348487528448.5	x^12 + 4x^10 + 6x^8 - 8x^6 - 7x^4 + 4x^2 + 2	\( 2^{35}\cdot 13^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.1119448865964032.6	x^12 - 16x^8 - 40x^6 - 32x^4 + 8	\( 2^{33}\cdot 19^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.1119448865964032.15	x^12 - 16x^8 + 40x^6 - 32x^4 + 8	\( 2^{33}\cdot 19^{4} \)	$S_3 \times C_4$ (as 12T11)	$[2]$
12.0.1175078824045389.1	x^12 - 2x^11 + 3x^9 - 3x^8 + 17x^7 + 22x^6 - 25x^5 - 20x^4 + 91x^3 + 230x^2 + 228x + 83	\( 3^{4}\cdot 29^{9} \)	$S_3 \times C_4$ (as 12T11)	$[2]$
12.4.1733405626953125.1	x^12 - 6x^10 - x^9 + 11x^8 + 17x^7 - 60x^6 - 43x^5 + 118x^4 + 138x^3 - 44x^2 - 31x + 31	\( 5^{9}\cdot 31^{6} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.2332800000000000.1	x^12 + 5x^10 - 10x^8 - 35x^6 + 10x^4 + 105x^2 + 45	\( 2^{16}\cdot 3^{6}\cdot 5^{11} \)	$S_3 \times C_4$ (as 12T11)	$[2, 2]$
12.4.2391484500000000.1	x^12 - 3x^11 - 3x^10 - x^9 - 3x^8 + 42x^7 + 41x^6 + 126x^5 + 153x^4 + 193x^3 + 156x^2 + 108x + 31	\( 2^{8}\cdot 3^{14}\cdot 5^{9} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.2403815886159872.6	x^12 - 4x^10 + 26x^8 - 56x^6 + 40x^4 - 32x^2 + 8	\( 2^{33}\cdot 23^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.2403815886159872.11	x^12 + 4x^10 + 26x^8 + 56x^6 + 40x^4 + 32x^2 + 8	\( 2^{33}\cdot 23^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.2779905883635712.5	x^12 - 4x^10 - 14x^9 + 6x^8 + 42x^7 + 11x^6 - 42x^5 - 29x^4 + 148x^3 + 15x^2 - 134x + 107	\( 2^{18}\cdot 13^{9} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.3713829369822464.1	x^12 - 2x^11 + 5x^10 + 9x^9 + 6x^8 + 23x^7 + 12x^6 + 61x^5 + 74x^4 + 41x^3 + 91x^2 + 15x + 7	\( 2^{8}\cdot 29^{9} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.4187798876953125.1	x^12 - 2x^11 + 11x^10 - 15x^9 + 30x^8 - 22x^7 - x^6 - 7x^5 + 50x^4 - 160x^3 + 501x^2 - 282x + 751	\( 3^{6}\cdot 5^{11}\cdot 7^{6} \)	$S_3 \times C_4$ (as 12T11)	$[2, 2]$
12.4.4477795463856128.9	x^12 - 8x^10 + 20x^8 - 36x^6 + 28x^4 - 8x^2 + 2	\( 2^{35}\cdot 19^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.0.4477795463856128.16	x^12 + 8x^10 + 20x^8 + 36x^6 + 28x^4 + 8x^2 + 2	\( 2^{35}\cdot 19^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.4565043429507072.8	x^12 - 8x^6 + 8	\( 2^{33}\cdot 3^{12} \)	$S_3 \times C_4$ (as 12T11)	$[2]$
12.0.4565043429507072.19	x^12 + 8x^6 + 8	\( 2^{33}\cdot 3^{12} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.12.4638867626953125.1	x^12 - 6x^11 + 4x^10 + 35x^9 - 55x^8 - 56x^7 + 136x^6 + x^5 - 105x^4 + 40x^3 + 14x^2 - 9x + 1	\( 3^{6}\cdot 5^{11}\cdot 19^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.4.7340688973975552.4	x^12 - 4x^11 + 3x^10 + 14x^9 - 56x^8 + 94x^7 - 12x^6 - 212x^5 + 341x^4 - 298x^3 + 282x^2 - 244x + 92	\( 2^{12}\cdot 13^{11} \)	$S_3 \times C_4$ (as 12T11)	$[3]$
12.4.7932984984338432.3	x^12 + 8x^10 + 20x^8 - 24x^6 - 44x^4 - 16x^2 + 8	\( 2^{33}\cdot 31^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial