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 180)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.126548911552.1	x^12 - 4x^11 + 5x^10 + 3x^9 - 11x^8 - 3x^7 + 35x^6 - 47x^5 + 27x^4 - 4x^3 - x^2 - x + 1	\( 2^{6}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.144627327488.1	x^12 - 3x^11 + 3x^10 + 2x^9 - 10x^8 + 11x^7 - x^6 - 11x^5 + 18x^4 - 16x^3 + 10x^2 - 4x + 1	\( 2^{9}\cdot 7^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.398655683181.1	x^12 - 2x^9 + 12x^6 + 7x^3 + 1	\( 3^{19}\cdot 7^{3} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.794280046581.1	x^12 - 3x^11 + 2x^10 + 2x^9 - 3x^7 - x^6 - 6x^5 + 28x^4 - 33x^3 + 18x^2 - 5x + 1	\( 3^{9}\cdot 7^{9} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.851162814333.2	x^12 - 4x^9 + 8x^6 - 5x^3 + 1	\( 3^{18}\cdot 13^{3} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.1012391292416.1	x^12 - 3x^11 + 5x^10 - 17x^9 + 38x^8 - 46x^7 + 49x^6 - 44x^5 + 20x^4 - 10x^3 + 6x^2 + x + 1	\( 2^{9}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.2631821894933.1	x^12 - 4x^11 + 5x^10 + 3x^9 - 25x^8 + 46x^7 - 21x^6 - 68x^5 + 181x^4 - 242x^3 + 202x^2 - 106x + 29	\( 7^{11}\cdot 11^{3} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.3722179279923.1	x^12 - 3x^11 - x^10 + 11x^9 - 10x^8 - 14x^7 + 24x^6 + 10x^5 - 12x^4 - 2x^3 - 3x^2 - x + 1	\( -\,3^{3}\cdot 13^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.4760622968832.2	x^12 - 9x^10 + 33x^8 - 54x^6 + 45x^4 - 18x^2 + 3	\( 2^{12}\cdot 3^{19} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.5559960326067.1	x^12 - 5x^11 + 6x^10 + 9x^9 - 26x^8 + 15x^7 - x^6 + 12x^5 - 6x^4 - 16x^3 + 5x^2 + 6x + 1	\( -\,3^{9}\cdot 7^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.7730680042917.1	x^12 - 3x^11 + 7x^10 - 11x^9 + 18x^8 - 9x^7 - 9x^6 + 27x^5 - x^4 - 12x^3 + 14x^2 + 8x + 1	\( 3^{6}\cdot 13^{9} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.8099130339328.1	x^12 - 2x^11 - 4x^10 - 4x^9 - 2x^8 + 8x^7 + 7x^6 + 8x^5 - 2x^4 - 4x^3 - 4x^2 - 2x + 1	\( -\,2^{12}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.9256148959232.2	x^12 - 3x^10 + 2x^8 + x^6 + 4x^4 - 12x^2 + 8	\( 2^{15}\cdot 7^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.10578455953408.1	x^12 - 2x^11 - x^10 - 2x^9 + 3x^8 + 14x^7 - 20x^6 + 34x^4 + 12x^3 - x^2 + 2x + 1	\( -\,2^{18}\cdot 7^{9} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.48388330638999.1	x^12 - 4x^11 + 3x^10 + x^9 + 9x^8 - 23x^7 + 27x^6 - 17x^5 - 10x^4 + 14x^3 - 4x^2 + 3x + 1	\( -\,3^{3}\cdot 13^{11} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.64793042714624.1	x^12 - 14x^10 + 77x^8 - 203x^6 + 280x^4 - 196x^2 + 56	\( 2^{15}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	$[2]$
12.0.92254156521408.1	x^12 - 3x^11 - 2x^10 + 4x^9 + 66x^8 - 214x^7 + 273x^6 - 212x^5 + 216x^4 - 157x^3 - 71x^2 + 99x + 43	\( 2^{6}\cdot 3^{6}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	$[2]$
12.6.136738899331083.1	x^12 + 9x^10 + 3x^8 - 36x^6 - 9x^4 + 18x^2 - 3	\( -\,3^{19}\cdot 7^{6} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.304679870005248.2	x^12 - 12x^10 - 16x^9 + 21x^8 + 66x^7 - 18x^6 - 78x^5 + 12x^4 + 20x^3 - 6x^2 + 6x + 1	\( -\,2^{18}\cdot 3^{19} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.304679870005248.1	x^12 - 18x^10 + 132x^8 - 432x^6 + 720x^4 - 576x^2 + 192	\( 2^{18}\cdot 3^{19} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.518344341716992.1	x^12 - 6x^11 + 27x^10 - 80x^9 + 153x^8 - 198x^7 + 147x^6 - 18x^5 - 81x^4 + 88x^3 - 23x^2 - 10x + 1	\( -\,2^{18}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.518344341716992.1	x^12 + 28x^8 - 224x^6 + 672x^4 - 896x^2 + 448	\( 2^{18}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	$[2]$
12.6.564668382613504.4	x^12 - x^10 - 18x^8 - 22x^6 + 6x^4 + 10x^2 - 1	\( -\,2^{12}\cdot 13^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.623334901029867.1	x^12 - 3x^10 - 8x^9 - 9x^8 + 21x^7 - 2x^6 - 27x^5 + 12x^4 + 45x^3 + 72x^2 + 60x + 17	\( -\,3^{17}\cdot 13^{6} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.677021181018112.2	x^12 - 8x^10 - 4x^9 + 11x^8 - 16x^7 - 28x^6 + 80x^5 + 182x^4 + 144x^3 + 58x^2 + 12x + 1	\( -\,2^{24}\cdot 7^{9} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.677298770454137.1	x^12 - x^11 - 2x^10 - 5x^9 + 16x^8 + 7x^7 + 26x^6 - 3x^5 + 108x^4 + 183x^3 + 294x^2 + 184x + 103	\( 13^{10}\cdot 17^{3} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.773738492592128.1	x^12 - 10x^10 + 50x^8 - 116x^6 + 144x^4 - 48x^2 + 8	\( 2^{27}\cdot 7^{8} \)	$D_4 \times C_3$ (as 12T14)	Trivial (GRH)
12.0.1306484927252973.1	x^12 - 6x^11 + 10x^10 + 5x^9 - 17x^8 - 28x^7 + 51x^6 + 32x^5 - 49x^4 - 31x^3 + 4x^2 + 28x + 40	\( 3^{6}\cdot 13^{11} \)	$D_4 \times C_3$ (as 12T14)	$[4]$
12.12.2196839556078125.1	x^12 - x^11 - 17x^10 + 8x^9 + 79x^8 - 32x^7 - 126x^6 + 37x^5 + 81x^4 - 15x^3 - 19x^2 + 2x + 1	\( 5^{6}\cdot 7^{8}\cdot 29^{3} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.2779905883635712.6	x^12 - 2x^11 - 6x^10 + 30x^9 - 17x^8 - 50x^7 + 172x^6 - 204x^5 + 266x^4 - 228x^3 + 384x^2 - 206x + 125	\( 2^{18}\cdot 13^{9} \)	$D_4 \times C_3$ (as 12T14)	$[3]$
12.6.3502954942155823.1	x^12 + 14x^10 + 35x^8 - 28x^6 - 77x^4 + 49x^2 - 7	\( -\,7^{11}\cdot 11^{6} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.12.4864965285308625.1	x^12 - 4x^11 - 9x^10 + 45x^9 + 10x^8 - 150x^7 + 56x^6 + 135x^5 - 36x^4 - 53x^3 - x^2 + 6x + 1	\( 3^{9}\cdot 5^{3}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.5777633090469888.6	x^12 - 12x^10 + 72x^8 - 212x^6 + 324x^4 - 72x^2 + 8	\( 2^{27}\cdot 3^{16} \)	$D_4 \times C_3$ (as 12T14)	Trivial (GRH)
12.6.5904266017370112.1	x^12 - 2x^11 - 4x^10 + 38x^9 - 16x^8 - 216x^7 + 126x^6 + 540x^5 - 289x^4 - 676x^3 + 332x^2 + 418x - 251	\( -\,2^{12}\cdot 3^{6}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	$[2]$
12.0.5904266017370112.1	x^12 + 14x^10 + 63x^8 + 126x^6 + 119x^4 + 49x^2 + 7	\( 2^{12}\cdot 3^{6}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	$[4]$
12.6.6189907940737024.2	x^12 - 10x^10 + 11x^8 + 46x^6 + 6x^4 - 12x^2 - 1	\( -\,2^{30}\cdot 7^{8} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.7340688973975552.3	x^12 - 26x^8 + 117x^4 - 13	\( -\,2^{12}\cdot 13^{11} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.19499511680335872.4	x^12 - 15x^8 + 18x^4 - 3	\( -\,2^{24}\cdot 3^{19} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.33174037869887488.6	x^12 - 14x^8 + 21x^4 - 7	\( -\,2^{24}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	$[2]$
12.6.33174037869887488.9	x^12 - 28x^9 - 21x^8 + 112x^7 + 140x^6 - 168x^5 - 413x^4 + 672x^3 - 364x^2 + 84x - 7	\( -\,2^{24}\cdot 7^{11} \)	$D_4 \times C_3$ (as 12T14)	$[2]$
12.6.36138776487264256.4	x^12 - 2x^10 - 72x^8 - 176x^6 + 96x^4 + 320x^2 - 64	\( -\,2^{18}\cdot 13^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.12.37913186137014272.1	x^12 - 16x^10 + 88x^8 - 204x^6 + 212x^4 - 88x^2 + 8	\( 2^{27}\cdot 7^{10} \)	$D_4 \times C_3$ (as 12T14)	Trivial (GRH)
12.0.37913186137014272.8	x^12 + 16x^10 + 88x^8 + 204x^6 + 212x^4 + 88x^2 + 8	\( 2^{27}\cdot 7^{10} \)	$D_4 \times C_3$ (as 12T14)	$[6]$
12.0.37913186137014272.9	x^12 - 14x^10 + 98x^8 - 364x^6 + 784x^4 - 784x^2 + 392	\( 2^{27}\cdot 7^{10} \)	$D_4 \times C_3$ (as 12T14)	$[2]$
12.12.43329355585159168.1	x^12 - 16x^10 + 90x^8 - 230x^6 + 273x^4 - 126x^2 + 7	\( 2^{30}\cdot 7^{9} \)	$D_4 \times C_3$ (as 12T14)	Trivial (GRH)
12.0.43329355585159168.5	x^12 + 16x^10 + 90x^8 + 230x^6 + 273x^4 + 126x^2 + 7	\( 2^{30}\cdot 7^{9} \)	$D_4 \times C_3$ (as 12T14)	$[6]$
12.6.46221064723759104.5	x^12 - 12x^10 + 18x^8 + 94x^6 + 45x^4 - 18x^2 - 1	\( -\,2^{30}\cdot 3^{16} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.49519263525896192.5	x^12 - 26x^8 + 104x^4 - 8	\( -\,2^{33}\cdot 7^{8} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.0.49519263525896192.7	x^12 + 26x^8 + 104x^4 + 8	\( 2^{33}\cdot 7^{8} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.6.51998697814228992.7	x^12 + 12x^10 - 212x^6 + 276x^4 - 72x^2 - 8	\( -\,2^{27}\cdot 3^{18} \)	$D_4 \times C_3$ (as 12T14)	Trivial