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 780)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.606024705125.1	x^12 - 2x^11 + 7x^10 - 8x^9 + 16x^8 - 11x^7 + 19x^6 - 6x^5 + 15x^4 + x^3 + 7x^2 + x + 1	\( 5^{3}\cdot 7^{8}\cdot 29^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.1211328810125.1	x^12 - 5x^11 + 13x^10 - 23x^9 + 28x^8 - 22x^7 + 10x^6 - 3x^5 + 7x^4 - 12x^3 + 10x^2 - 4x + 1	\( 5^{3}\cdot 7^{8}\cdot 41^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.1942483285125.1	x^12 - 3x^11 + 5x^9 + 3x^8 - 9x^7 - 8x^6 + 18x^5 - 13x^3 + 3x^2 + 3x + 1	\( 3^{16}\cdot 5^{3}\cdot 19^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.3632545230125.1	x^12 - 5x^10 - 2x^9 + 8x^8 + 9x^7 - 4x^6 - 16x^5 - 7x^4 + 14x^3 + 8x^2 + 3x - 1	\( 5^{3}\cdot 7^{8}\cdot 71^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.4786496975897.1	x^12 - 4x^11 + 3x^10 + 13x^9 - 33x^8 + 17x^7 + 33x^6 - 51x^5 + 18x^4 + 6x^3 - 2x^2 - x + 1	\( 7^{8}\cdot 13^{2}\cdot 17^{3} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.4961602806272.1	x^12 - x^11 + 4x^10 - 6x^9 + 16x^8 - 18x^7 + 28x^6 - 33x^5 + 39x^4 - 29x^3 + 16x^2 - 5x + 1	\( 2^{9}\cdot 7^{8}\cdot 41^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.6.5099237430147.1	x^12 - x^11 - 7x^10 + 8x^9 + 16x^8 - 16x^7 - 18x^6 + 13x^5 + 10x^4 - 8x^3 - 3x^2 + 3x + 1	\( -\,3^{3}\cdot 7^{8}\cdot 181^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.6369537212928.1	x^12 - 3x^11 + 6x^10 - 5x^9 + 3x^8 - 3x^7 + 16x^6 - 30x^5 + 36x^4 - 23x^3 + 9x^2 + 1	\( 2^{9}\cdot 3^{16}\cdot 17^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.6.19829802833407.1	x^12 - 3x^11 - 2x^10 + 13x^9 - 11x^8 - 12x^7 + 27x^6 - 12x^5 - 11x^4 + 13x^3 - 2x^2 - 3x + 1	\( -\,7^{9}\cdot 701^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.23607580695125.1	x^12 - x^11 - 4x^10 + 4x^9 - x^8 - 14x^7 - 2x^4 + 3x^3 - 2x^2 + 2x + 1	\( 5^{3}\cdot 7^{8}\cdot 181^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.27124815070125.1	x^12 + 6x^10 - 2x^9 + 18x^8 - 6x^7 + 25x^6 - 12x^5 + 21x^4 - 7x^3 + 9x^2 - 3x + 1	\( 3^{16}\cdot 5^{3}\cdot 71^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.29695210551125.1	x^12 - 5x^10 - 7x^9 + 11x^8 + 28x^7 + x^6 - 42x^5 - 40x^4 - 7x^3 + 11x^2 + 7x + 1	\( 5^{3}\cdot 7^{10}\cdot 29^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.30386387131821.1	x^12 - 2x^11 + 4x^10 - 2x^9 + 7x^8 - 8x^7 + 13x^6 - 4x^5 + 7x^4 - 9x^3 + 9x^2 - 4x + 1	\( 3^{3}\cdot 7^{9}\cdot 167^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.44044027432128.1	x^12 - 3x^11 + 14x^9 - 33x^8 + 45x^7 - 40x^6 + 15x^5 + 12x^4 - 18x^3 + 9x^2 - 3	\( 2^{6}\cdot 3^{17}\cdot 73^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.45398528475125.1	x^12 - 2x^11 + 8x^10 - 12x^9 + 29x^8 - 34x^7 + 49x^6 - 45x^5 + 51x^4 - 33x^3 + 18x^2 - 4x + 1	\( 5^{3}\cdot 7^{8}\cdot 251^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.57325834916352.1	x^12 + 3x^10 - x^9 + 9x^8 - 9x^7 - 9x^6 + 27x^5 - 45x^4 + 26x^3 - 9x^2 - 3x + 1	\( 2^{9}\cdot 3^{18}\cdot 17^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.126509278545125.1	x^12 - x^11 + 2x^10 + 6x^8 - 4x^7 + 12x^6 + 2x^5 - 2x^4 - 7x^3 + x^2 + 2x + 1	\( 5^{3}\cdot 7^{8}\cdot 419^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.172407498445125.1	x^12 - 7x^9 + 16x^6 + 15x^4 - 2x^3 + 6x^2 - 3x + 1	\( 3^{16}\cdot 5^{3}\cdot 179^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.8.188900999168000.1	x^12 - 2x^11 - 8x^10 + 16x^9 + 17x^8 - 38x^7 + 2x^6 + 54x^5 - 124x^4 + 58x^3 + 50x^2 - 12x - 1	\( 2^{18}\cdot 5^{3}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.213086649790125.1	x^12 - 3x^11 + 9x^10 - 11x^9 + 9x^8 - 3x^7 + 7x^6 + 6x^5 - 6x^4 - 11x^3 + 15x^2 - 6x + 1	\( 3^{16}\cdot 5^{3}\cdot 199^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.8.354103622025125.1	x^12 - 4x^11 - 2x^10 + 30x^9 - 51x^8 + 26x^7 + 33x^6 - 75x^5 + 47x^4 + 19x^3 - 30x^2 + 4x + 1	\( 5^{3}\cdot 7^{8}\cdot 701^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.8.370012674167213.1	x^12 - 2x^10 - 3x^9 - 11x^8 + 32x^7 + 29x^6 - 77x^5 - 26x^4 + 58x^3 + 9x^2 - 10x - 1	\( 7^{9}\cdot 11^{3}\cdot 83^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.8.559301713620125.1	x^12 - x^11 - 11x^10 + 6x^9 + 53x^8 - 16x^7 - 121x^6 + 33x^5 + 95x^4 - 15x^3 - 25x^2 - x + 1	\( 5^{3}\cdot 7^{8}\cdot 881^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.8.773738492592128.1	x^12 - 8x^10 + 18x^8 - 24x^6 + 36x^4 - 32x^2 + 8	\( 2^{27}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.773738492592128.1	x^12 + 2x^10 + 2x^8 - 4x^6 - 40x^4 - 40x^2 + 8	\( 2^{27}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.773738492592128.5	x^12 + 8x^10 + 18x^8 + 24x^6 + 36x^4 + 32x^2 + 8	\( 2^{27}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.773738492592128.7	x^12 - 2x^10 + 2x^8 + 4x^6 - 40x^4 + 40x^2 + 8	\( 2^{27}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.2591394083414528.1	x^12 + 14x^10 + 73x^8 + 175x^6 + 192x^4 + 84x^2 + 8	\( 2^{9}\cdot 7^{8}\cdot 937^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.8.2779905883635712.1	x^12 - 6x^11 + 8x^10 + 4x^9 - 8x^8 + 20x^7 - 40x^6 - 10x^5 + 57x^4 + 6x^3 - 26x^2 - 10x - 1	\( 2^{18}\cdot 13^{9} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial (GRH)
12.4.2779905883635712.3	x^12 - 2x^11 - 4x^10 + 10x^9 + 17x^8 - 66x^7 + 32x^6 + 108x^5 - 170x^4 + 88x^3 - 10x^2 - 6x + 1	\( 2^{18}\cdot 13^{9} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.2779905883635712.3	x^12 - 6x^11 + 24x^10 - 54x^9 + 95x^8 - 100x^7 + 100x^6 - 30x^5 + 24x^4 + 56x^3 + 28x^2 + 8x + 5	\( 2^{18}\cdot 13^{9} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.2779905883635712.4	x^12 - 2x^11 - 14x^9 + 23x^8 - 8x^7 + 8x^6 - 8x^5 + 23x^4 - 14x^3 - 2x + 1	\( 2^{18}\cdot 13^{9} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.12.3989681137476125.1	x^12 - x^11 - 17x^10 + 13x^9 + 96x^8 - 53x^7 - 212x^6 + 62x^5 + 175x^4 - 15x^3 - 44x^2 - 5x + 1	\( 5^{3}\cdot 7^{8}\cdot 13^{2}\cdot 181^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.8.5777633090469888.1	x^12 - 6x^10 + 12x^8 - 28x^6 + 60x^4 - 48x^2 + 8	\( 2^{27}\cdot 3^{16} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial (GRH)
12.4.5777633090469888.9	x^12 - 6x^8 - 8x^6 - 12x^4 + 8	\( 2^{27}\cdot 3^{16} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.5777633090469888.10	x^12 - 6x^8 + 8x^6 - 12x^4 + 8	\( 2^{27}\cdot 3^{16} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.5777633090469888.19	x^12 + 6x^10 + 12x^8 + 28x^6 + 60x^4 + 48x^2 + 8	\( 2^{27}\cdot 3^{16} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.6787085019525657.1	x^12 - 6x^11 + 15x^10 - 4x^9 - 68x^8 + 201x^7 - 297x^6 + 260x^5 - 164x^4 + 27x^3 + 10x^2 - 45x - 1	\( 3^{3}\cdot 7^{8}\cdot 11^{3}\cdot 181^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.12.18674283107881408.1	x^12 - 16x^10 - 4x^9 + 94x^8 + 45x^7 - 237x^6 - 161x^5 + 212x^4 + 180x^3 - 5x^2 - 11x - 1	\( 2^{6}\cdot 7^{9}\cdot 2689^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.19499511680335872.1	x^12 + 6x^10 + 15x^8 + 12x^6 - 54x^4 - 90x^2 + 3	\( 2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.8.19499511680335872.1	x^12 - 6x^10 + 6x^8 - 12x^6 + 45x^4 - 36x^2 + 3	\( 2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.19499511680335872.2	x^12 + 6x^10 + 6x^8 - 6x^6 + 9x^4 + 18x^2 + 3	\( 2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	$[2]$
12.8.19499511680335872.2	x^12 - 6x^10 + 6x^8 + 6x^6 + 9x^4 - 18x^2 + 3	\( 2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.19499511680335872.3	x^12 + 6x^10 + 6x^8 + 12x^6 + 45x^4 + 36x^2 + 3	\( 2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	$[2]$
12.4.19499511680335872.4	x^12 + 6x^10 + 6x^8 - 6x^6 - 27x^4 + 3	\( 2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.19499511680335872.5	x^12 - 6x^10 + 6x^8 + 6x^6 - 27x^4 + 3	\( 2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.4.19499511680335872.12	x^12 - 6x^10 + 15x^8 - 12x^6 - 54x^4 + 90x^2 + 3	\( 2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.20886476513882112.1	x^12 + 15x^10 + 83x^8 + 212x^6 + 261x^4 + 144x^2 + 27	\( 2^{12}\cdot 3^{3}\cdot 7^{8}\cdot 181^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	$[6]$
12.8.33174037869887488.1	x^12 - 14x^10 + 70x^8 - 154x^6 + 161x^4 - 84x^2 + 7	\( 2^{24}\cdot 7^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.0.33174037869887488.1	x^12 - 14x^8 + 14x^6 + 105x^4 + 56x^2 + 7	\( 2^{24}\cdot 7^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	$[2]$