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 347)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.66468114161.1	x^12 - x^11 - 2x^10 + 4x^9 + x^8 - 5x^7 + x^6 + 5x^5 + x^4 - 4x^3 - 2x^2 + x + 1	\( 23^{6}\cdot 449 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.200884701373.1	x^12 - 3x^11 + 5x^10 - 3x^9 - 2x^8 + 4x^7 + 2x^6 - 11x^5 + 15x^4 - 12x^3 + 8x^2 - 4x + 1	\( 23^{7}\cdot 59 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.217908828608.1	x^12 - 4x^11 + 10x^10 - 20x^9 + 30x^8 - 35x^7 + 31x^6 - 19x^5 + 10x^4 - 6x^3 + x^2 + x + 1	\( 2^{6}\cdot 23^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.1743270628864.1	x^12 - 4x^11 + 7x^10 - 7x^9 + 2x^8 + 8x^7 - 16x^6 + 23x^5 - 21x^4 + 3x^3 + 12x^2 - 23x + 23	\( 2^{9}\cdot 23^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.1760807303104.1	x^12 - 4x^11 + 6x^10 - x^9 - 11x^8 + 17x^7 - x^6 - 36x^5 + 73x^4 - 85x^3 + 66x^2 - 32x + 8	\( 2^{6}\cdot 31^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.13946165030912.1	x^12 - 2x^10 + 4x^8 - 3x^6 + 8x^4 - 23x^2 + 23	\( 2^{12}\cdot 23^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.14086458424832.1	x^12 - x^11 + 3x^10 + 7x^9 + 2x^8 + 10x^7 + 27x^6 + 4x^5 + 38x^4 + 14x^3 + 12x^2 + 3x + 1	\( 2^{9}\cdot 31^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.20433779818496.2	x^12 - 7x^10 + 22x^8 - 41x^6 + 48x^4 - 33x^2 + 11	\( 2^{20}\cdot 11^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.20433779818496.4	x^12 + 7x^10 + 22x^8 + 41x^6 + 48x^4 + 33x^2 + 11	\( 2^{20}\cdot 11^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.22568879259648.1	x^12 + 3x^10 - 4x^9 + 6x^8 - 18x^7 + 47x^6 - 78x^5 + 87x^4 - 68x^3 + 36x^2 - 12x + 2	\( 2^{19}\cdot 3^{16} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.40095224463872.1	x^12 - 4x^11 + 5x^10 - 4x^9 + 16x^8 - 57x^7 + 60x^6 + 13x^5 + 37x^4 - 100x^3 + 158x^2 - 147x + 49	\( 2^{9}\cdot 23^{8} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.2.44007339367168.1	x^12 - 3x^11 + 4x^10 - 6x^9 + 7x^8 - 8x^7 + 9x^6 - 8x^5 + 7x^4 - 6x^3 + 4x^2 - 3x + 1	\( -\,2^{8}\cdot 37^{6}\cdot 67 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.52428800000000.1	x^12 + 4x^10 + 6x^8 - 4x^6 + 3x^4 - 4x^2 + 2	\( 2^{27}\cdot 5^{8} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.6.70280377795328.1	x^12 - 3x^11 - 4x^10 + 22x^9 - 13x^8 - 40x^7 + 59x^6 - 4x^5 - 33x^4 + 8x^3 + 10x^2 - x - 1	\( -\,2^{8}\cdot 37^{6}\cdot 107 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.81735119273984.3	x^12 + 2x^10 - 12x^6 - 8x^4 + 44	\( 2^{22}\cdot 11^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.81735119273984.4	x^12 - 2x^10 + 12x^6 - 8x^4 + 44	\( 2^{22}\cdot 11^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.4.89985156616448.1	x^12 - 5x^11 + 8x^10 - 7x^9 + 10x^8 - 7x^7 - x^6 + 6x^5 - 2x^4 - 8x^3 - 8x^2 + 8x + 4	\( 2^{8}\cdot 37^{6}\cdot 137 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.6.91298808537856.1	x^12 - 2x^11 + 11x^9 - 17x^8 - 8x^7 + 27x^6 - 10x^5 - 5x^4 + 9x^3 - 7x^2 - x + 1	\( -\,2^{8}\cdot 37^{6}\cdot 139 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.96402615118848.2	x^12 - 9x^8 + 6x^6 + 27x^4 - 36x^2 + 12	\( 2^{10}\cdot 3^{23} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.111569320247296.1	x^12 - 9x^10 + 44x^8 - 127x^6 + 242x^4 - 276x^2 + 184	\( 2^{15}\cdot 23^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.111569320247296.3	x^12 - 2x^10 + 7x^8 - 29x^6 + 32x^4 - 92x^2 + 184	\( 2^{15}\cdot 23^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.111569320247296.6	x^12 + 2x^10 + 7x^8 + 29x^6 + 32x^4 + 92x^2 + 184	\( 2^{15}\cdot 23^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	$[2]$
12.0.112691667398656.3	x^12 + 9x^10 + 37x^8 + 87x^6 + 121x^4 + 93x^2 + 31	\( 2^{12}\cdot 31^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.4.153040448844032.1	x^12 - 3x^11 + 7x^10 - 10x^9 + 11x^8 - 3x^7 + 3x^5 - 27x^4 + 54x^3 - 39x^2 + 11x - 1	\( 2^{8}\cdot 37^{6}\cdot 233 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.4.176686183429376.1	x^12 - x^11 - 4x^10 + 16x^9 - 35x^8 + 52x^7 - 59x^6 + 52x^5 - 35x^4 + 16x^3 - 4x^2 - x + 1	\( 2^{8}\cdot 37^{6}\cdot 269 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.8.192450006486272.1	x^12 - 3x^11 + 4x^10 + 2x^9 - 15x^8 + 20x^7 - x^6 - 36x^5 + 17x^4 + 20x^3 - 8x^2 - 3x + 1	\( 2^{8}\cdot 37^{6}\cdot 293 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.203119913336832.1	x^12 - 6x^11 + 15x^10 - 12x^9 - 27x^8 + 90x^7 - 103x^6 + 12x^5 + 132x^4 - 204x^3 + 162x^2 - 72x + 16	\( 2^{19}\cdot 3^{18} \)	$C_2^4:C_3.D_4$ (as 12T135)	$[2]$
12.8.208213829543168.1	x^12 - x^11 - 3x^10 - x^9 + 11x^8 - 26x^7 + 41x^6 + 10x^5 - 55x^4 + 7x^3 + 18x^2 - 2x - 1	\( 2^{8}\cdot 37^{6}\cdot 317 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.209715200000000.3	x^12 - 4x^10 + 6x^8 + 4x^6 + 3x^4 + 4x^2 + 2	\( 2^{29}\cdot 5^{8} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.8.229232260285696.1	x^12 - x^11 - 7x^10 + 7x^9 + 21x^8 - 6x^7 - 31x^6 - 18x^5 + 27x^4 + 21x^3 - 12x^2 - 2x + 1	\( 2^{8}\cdot 37^{6}\cdot 349 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.2.241055127578368.1	x^12 - 6x^11 + 19x^10 - 40x^9 + 49x^8 - 22x^7 - 59x^6 + 152x^5 - 198x^4 + 164x^3 - 88x^2 + 28x - 4	\( -\,2^{8}\cdot 37^{6}\cdot 367 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.385610460475392.6	x^12 + 9x^10 + 45x^8 + 120x^6 + 180x^4 + 144x^2 + 48	\( 2^{12}\cdot 3^{23} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.8.394752402383104.1	x^12 - 6x^11 + 13x^10 - 10x^9 - 16x^8 + 58x^7 - 75x^6 + 46x^5 - 22x^3 + 9x^2 + 2x - 1	\( 2^{8}\cdot 37^{6}\cdot 601 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.427677828251648.1	x^12 - 4x^11 + 3x^10 + 10x^9 - 22x^8 + 2x^7 + 41x^6 - 26x^5 - 35x^4 + 30x^3 + 2x^2 - 12x + 18	\( 2^{19}\cdot 13^{8} \)	$C_2^4:C_3.D_4$ (as 12T135)	$[3]$
12.0.436680211169792.1	x^12 - 4x^11 + 17x^10 - 44x^9 + 99x^8 - 176x^7 + 285x^6 - 392x^5 + 563x^4 - 634x^3 + 775x^2 - 534x + 423	\( 2^{9}\cdot 31^{8} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.449543156006912.1	x^12 - 6x^10 + 9x^8 + 4x^6 - 20x^4 + 16x^2 + 32	\( 2^{21}\cdot 11^{8} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.526372711694336.2	x^12 - 4x^11 + 12x^10 - 26x^9 + 40x^8 - 44x^7 + 55x^6 - 48x^5 + 46x^4 - 24x^3 + 22x^2 - 8x + 4	\( 2^{23}\cdot 13^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	$[2]$
12.0.526372711694336.4	x^12 - 2x^11 + x^10 - 4x^9 + 22x^8 - 28x^7 + 6x^6 + 24x^5 - 16x^4 - 48x^3 + 96x^2 - 64x + 16	\( 2^{23}\cdot 13^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	$[2]$
12.10.704117429874688.1	x^12 - 4x^11 - 3x^10 + 28x^9 - 20x^8 - 32x^7 + 35x^6 - 8x^5 - 6x^4 + 26x^3 - 7x^2 - 10x + 1	\( -\,2^{12}\cdot 37^{6}\cdot 67 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.4.812493713390848.1	x^12 - x^11 + 6x^9 - 9x^8 + 5x^6 - 54x^5 + 39x^4 - 58x^3 + 20x^2 + 13x + 1	\( 2^{8}\cdot 37^{6}\cdot 1237 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.892554561978368.1	x^12 - 4x^10 + 16x^8 - 24x^6 + 128x^4 - 736x^2 + 1472	\( 2^{18}\cdot 23^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.892554561978368.4	x^12 + 4x^10 + 16x^8 + 24x^6 + 128x^4 + 736x^2 + 1472	\( 2^{18}\cdot 23^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	$[2]$
12.0.901533339189248.1	x^12 - 8x^10 + 41x^8 - 131x^6 + 288x^4 - 372x^2 + 248	\( 2^{15}\cdot 31^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	$[2]$
12.0.901533339189248.5	x^12 + 5x^10 + x^8 - 17x^6 + 50x^4 + 248x^2 + 248	\( 2^{15}\cdot 31^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.901533339189248.7	x^12 + 8x^10 + 41x^8 + 131x^6 + 288x^4 + 372x^2 + 248	\( 2^{15}\cdot 31^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.937292452593664.3	x^12 - 9x^10 + 34x^8 - 69x^6 + 82x^4 - 57x^2 + 19	\( 2^{20}\cdot 19^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.937292452593664.8	x^12 + 9x^10 + 34x^8 + 69x^6 + 82x^4 + 57x^2 + 19	\( 2^{20}\cdot 19^{7} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.10.1100183484179200.1	x^12 - x^11 - 12x^10 + 10x^9 + 59x^8 - 46x^7 - 141x^6 + 114x^5 + 149x^4 - 130x^3 - 42x^2 + 39x - 1	\( -\,2^{8}\cdot 5^{2}\cdot 37^{6}\cdot 67 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.0.1310720000000000.2	x^12 - 10x^8 + 75x^4 + 100x^2 + 50	\( 2^{27}\cdot 5^{10} \)	$C_2^4:C_3.D_4$ (as 12T135)	$[2]$
12.0.1444408272617472.1	x^12 - 6x^10 + 24x^8 - 56x^6 + 57x^4 - 18x^2 + 2	\( 2^{25}\cdot 3^{16} \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial