Global number field search results

Further refine search

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 109)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.48737056617.1	x^12 - 2x^11 + 5x^10 - 10x^9 + 16x^8 - 22x^7 + 30x^6 - 31x^5 + 28x^4 - 27x^3 + 19x^2 - 7x + 1	\( 3^{9}\cdot 19^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.50551744653.1	x^12 - 4x^11 + 11x^10 - 21x^9 + 32x^8 - 40x^7 + 45x^6 - 46x^5 + 40x^4 - 26x^3 + 12x^2 - 4x + 1	\( 3^{6}\cdot 37^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.84687918336.1	x^12 - 4x^11 + 8x^10 - 11x^9 + 13x^8 - 14x^7 + 15x^6 - 14x^5 + 7x^4 + 3x^3 - 5x^2 + x + 1	\( 2^{8}\cdot 3^{9}\cdot 7^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.97332232192.1	x^12 - 4x^11 + 6x^10 - 4x^9 + 4x^8 - 18x^7 + 44x^6 - 64x^5 + 63x^4 - 42x^3 + 20x^2 - 6x + 1	\( 2^{18}\cdot 13^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.241162079949.1	x^12 - 6x^11 + 18x^10 - 35x^9 + 54x^8 - 72x^7 + 84x^6 - 81x^5 + 66x^4 - 44x^3 + 21x^2 - 6x + 1	\( 3^{15}\cdot 7^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.3833392529408.2	x^12 - 6x^10 + 18x^8 - 36x^6 + 48x^4 - 32x^2 + 8	\( 2^{27}\cdot 13^{4} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial (GRH)
12.0.3833392529408.5	x^12 - 2x^10 + 2x^8 - 12x^6 + 16x^4 + 8	\( 2^{27}\cdot 13^{4} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial (GRH)
12.0.4149707998464.1	x^12 - 3x^11 + 5x^10 - x^9 - 15x^8 + 6x^7 + 11x^6 + 6x^5 + 19x^4 + 9x^3 - 6x^2 - 2x + 1	\( 2^{8}\cdot 3^{9}\cdot 7^{7} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.6229262860288.5	x^12 + 6x^8 - 4x^6 + 13x^4 + 13	\( 2^{24}\cdot 13^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.6.9904396000000.1	x^12 - 3x^11 - x^10 + 7x^9 - x^8 - 2x^7 + 7x^6 - 16x^5 - 9x^4 + 19x^3 + 4x^2 - 4x - 1	\( -\,2^{8}\cdot 5^{6}\cdot 19^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.11816941917501.1	x^12 - 6x^11 + 18x^10 - 30x^9 + 30x^8 - 24x^7 + 30x^6 - 36x^5 + 21x^4 + 9x^2 - 9x + 3	\( 3^{15}\cdot 7^{7} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.16449147240448.2	x^12 - 2x^11 - 8x^10 + 20x^9 + 34x^8 - 100x^7 + 8x^6 + 72x^5 + 40x^4 - 56x^3 - 32x^2 + 16x + 8	\( 2^{18}\cdot 13^{7} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.21134460321792.2	x^12 + 2x^10 + 3x^8 - 2x^6 - 6x^4 + 3	\( 2^{30}\cdot 3^{9} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.21134460321792.3	x^12 - 2x^10 + 3x^8 + 2x^6 - 6x^4 + 3	\( 2^{30}\cdot 3^{9} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.6.24321556876032.1	x^12 - 6x^11 + 12x^10 - 5x^9 - 31x^8 + 88x^7 - 105x^6 + 52x^5 + 23x^4 - 53x^3 + 35x^2 - 11x + 1	\( -\,2^{8}\cdot 3^{9}\cdot 13^{6} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.49834102882304.4	x^12 + 8x^8 - 20x^6 + 52x^4 - 104x^2 + 104	\( 2^{27}\cdot 13^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.49834102882304.5	x^12 - 8x^8 - 4x^6 + 52x^4 - 104x^2 + 104	\( 2^{27}\cdot 13^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.56358560858112.2	x^12 - 8x^10 + 26x^8 - 48x^6 + 56x^4 - 32x^2 + 8	\( 2^{33}\cdot 3^{8} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.56358560858112.5	x^12 + 8x^10 + 26x^8 + 48x^6 + 56x^4 + 32x^2 + 8	\( 2^{33}\cdot 3^{8} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.69205338429957.1	x^12 - 2x^10 - 8x^9 - 8x^8 - 22x^7 + 40x^6 + 114x^5 + 123x^4 - 72x^3 - 45x^2 - 27x + 27	\( 3^{6}\cdot 37^{7} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.76169967501312.2	x^12 - 8x^9 + 30x^6 - 20x^3 + 4	\( 2^{16}\cdot 3^{19} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.76169967501312.3	x^12 - 10x^9 + 30x^6 - 16x^3 + 4	\( 2^{16}\cdot 3^{19} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.169075682574336.3	x^12 - 4x^10 + 6x^8 - 8x^6 + 24x^4 + 24	\( 2^{33}\cdot 3^{9} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.169075682574336.4	x^12 + 4x^10 + 6x^8 + 8x^6 + 24x^4 + 24	\( 2^{33}\cdot 3^{9} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.190210142896128.2	x^12 - 6x^10 + 15x^8 - 26x^6 + 66x^4 - 36x^2 + 27	\( 2^{30}\cdot 3^{11} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.190210142896128.5	x^12 + 6x^10 + 15x^8 + 26x^6 + 66x^4 + 36x^2 + 27	\( 2^{30}\cdot 3^{11} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.385610460475392.2	x^12 - 3x^6 + 3	\( 2^{12}\cdot 3^{23} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.385610460475392.4	x^12 + 3x^6 + 3	\( 2^{12}\cdot 3^{23} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.1052745423388672.9	x^12 - 16x^10 + 133x^8 - 664x^6 + 2106x^4 - 3380x^2 + 2197	\( 2^{24}\cdot 13^{7} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.1119448865964032.21	x^12 - 8x^10 + 18x^8 - 24x^4 - 32x^2 + 72	\( 2^{33}\cdot 19^{4} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.1119448865964032.22	x^12 + 8x^10 + 18x^8 - 24x^4 + 32x^2 + 72	\( 2^{33}\cdot 19^{4} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.1521681143169024.4	x^12 - 12x^10 + 78x^8 - 296x^6 + 600x^4 - 576x^2 + 216	\( 2^{33}\cdot 3^{11} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.1521681143169024.7	x^12 + 12x^10 + 78x^8 + 296x^6 + 600x^4 + 576x^2 + 216	\( 2^{33}\cdot 3^{11} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.2535525376000000.1	x^12 - 2x^11 + 4x^10 + 3x^8 - 24x^7 + 70x^6 - 12x^5 + 33x^4 + 82x^3 + 134x^2 - 44x + 71	\( 2^{16}\cdot 5^{6}\cdot 19^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	$[2]$
12.12.2535525376000000.1	x^12 - 2x^11 - 14x^10 + 22x^9 + 67x^8 - 64x^7 - 138x^6 + 48x^5 + 109x^4 + 6x^3 - 28x^2 - 10x - 1	\( 2^{16}\cdot 5^{6}\cdot 19^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.2658691056664576.6	x^12 - 10x^8 - 2x^6 + 57x^4 - 38x^2 + 19	\( 2^{30}\cdot 19^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.2658691056664576.18	x^12 - 10x^8 + 2x^6 + 57x^4 + 38x^2 + 19	\( 2^{30}\cdot 19^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.3378385204000000.1	x^12 - 3x^11 + 7x^10 - 5x^9 + 13x^8 + 10x^7 + 29x^6 + 76x^5 + 127x^4 + 169x^3 + 166x^2 + 108x + 31	\( 2^{8}\cdot 5^{6}\cdot 61^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.4565043429507072.30	x^12 + 18x^8 - 48x^6 - 72x^4 + 648	\( 2^{33}\cdot 3^{12} \)	$C_3\times C_3:D_4$ (as 12T42)	$[2]$
12.0.4565043429507072.31	x^12 + 18x^8 + 48x^6 - 72x^4 + 648	\( 2^{33}\cdot 3^{12} \)	$C_3\times C_3:D_4$ (as 12T42)	$[2]$
12.0.4874877920083968.11	x^12 - 18x^6 + 108	\( 2^{22}\cdot 3^{19} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.4874877920083968.12	x^12 + 18x^6 + 108	\( 2^{22}\cdot 3^{19} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.5777633090469888.26	x^12 - 12x^10 + 72x^8 - 212x^6 + 468x^4 - 504x^2 + 200	\( 2^{27}\cdot 3^{16} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.5777633090469888.27	x^12 - 12x^10 + 72x^8 - 188x^6 + 180x^4 - 72x^2 + 200	\( 2^{27}\cdot 3^{16} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.6169767367606272.2	x^12 - 6x^9 + 42x^6 + 12	\( 2^{16}\cdot 3^{23} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.6169767367606272.3	x^12 - 12x^9 + 30x^6 + 36x^3 + 12	\( 2^{16}\cdot 3^{23} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.6169767367606272.8	x^12 - 12x^6 + 48	\( 2^{16}\cdot 3^{23} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.6169767367606272.10	x^12 + 12x^6 + 48	\( 2^{16}\cdot 3^{23} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.12.6226318560264192.1	x^12 - 13x^10 + 60x^8 - 125x^6 + 120x^4 - 45x^2 + 3	\( 2^{16}\cdot 3^{9}\cdot 13^{6} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.0.8421963387109376.23	x^12 - 14x^10 + 74x^8 - 612x^6 + 5200x^4 - 16224x^2 + 17576	\( 2^{27}\cdot 13^{7} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial