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 1141)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.46574387721.1	x^12 - x^11 - x^10 + x^9 + 2x^8 - 3x^6 + 2x^4 + x^3 - x^2 - x + 1	\( 3^{6}\cdot 7993^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.54507773961.1	x^12 - x^11 - 2x^10 + 5x^9 - x^8 - 4x^7 + 5x^6 - 4x^5 - x^4 + 5x^3 - 2x^2 - x + 1	\( 3^{6}\cdot 8647^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.67030763409.1	x^12 - x^11 - 2x^10 + 6x^8 - x^7 - 5x^6 - x^5 + 6x^4 - 2x^2 - x + 1	\( 3^{6}\cdot 43^{2}\cdot 223^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.119831591889.1	x^12 - x^11 + x^10 - x^9 - x^8 + 2x^7 - x^6 + 2x^5 - x^4 - x^3 + x^2 - x + 1	\( 3^{6}\cdot 12821^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.144716333056.1	x^12 - 2x^11 + 2x^10 - 2x^8 + 4x^7 - 4x^6 + 2x^5 + x^4 - 2x^3 + 2x^2 - 2x + 1	\( 2^{18}\cdot 743^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.158194721169.1	x^12 - x^11 + x^10 - 2x^9 + 2x^8 - 2x^7 + 3x^6 - 2x^5 + x^4 - 2x^3 + x^2 + 1	\( 3^{6}\cdot 14731^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.259972515625.1	x^12 - x^11 - x^10 + x^9 + 2x^8 - x^7 + x^5 + 2x^4 - x^3 - x^2 + x + 1	\( 5^{6}\cdot 4079^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.364212250000.1	x^12 - x^11 - 2x^10 + 2x^9 + 3x^8 - x^7 - 3x^6 + x^5 + 3x^4 - 2x^3 - 2x^2 + x + 1	\( 2^{4}\cdot 5^{6}\cdot 17^{2}\cdot 71^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.4.1459264000000.1	x^12 - 4x^11 + 8x^10 - 8x^9 - 2x^8 + 18x^7 - 27x^6 + 18x^5 - 2x^4 - 8x^3 + 8x^2 - 4x + 1	\( 2^{12}\cdot 5^{6}\cdot 151^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.4.2673633765625.1	x^12 - x^11 - x^10 - 4x^9 + 8x^8 - 6x^7 + 10x^6 - 13x^5 + 20x^4 - 28x^3 + 22x^2 - 8x + 1	\( 5^{6}\cdot 103^{2}\cdot 127^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.3962711310336.1	x^12 + 2x^10 + 3x^8 + 8x^6 - x^4 + 6x^2 + 1	\( 2^{26}\cdot 3^{10} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.4.15850845241344.1	x^12 - 6x^10 - 4x^9 + 18x^8 + 8x^7 - 20x^6 - 12x^5 + 10x^4 + 16x^3 - 8x - 2	\( 2^{28}\cdot 3^{10} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.15850845241344.2	x^12 - 4x^10 - 4x^9 + 5x^8 + 8x^7 - 4x^6 - 4x^5 + 15x^4 + 16x^3 + 9	\( 2^{28}\cdot 3^{10} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.20061226008576.2	x^12 - 2x^11 + 3x^10 - 2x^9 + 2x^7 - 7x^6 + 6x^5 + 2x^4 - 2x^3 + 5x^2 + 2x + 1	\( 2^{22}\cdot 3^{14} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.8.45358541265625.1	x^12 - 5x^11 + 3x^10 + 14x^9 - 11x^8 - 19x^7 + 3x^6 + 26x^5 + 9x^4 - 21x^3 - 7x^2 + 5x + 1	\( 5^{6}\cdot 7^{2}\cdot 43^{2}\cdot 179^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.57127475625984.2	x^12 - 3x^10 - 2x^9 + 3x^8 - 6x^7 + 10x^6 + 6x^5 + 9x^4 + 6x^3 + 9x^2 + 3	\( 2^{14}\cdot 3^{20} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.8.76483770250000.1	x^12 - 3x^11 - x^10 + 10x^9 - 5x^8 - 2x^7 - 5x^6 - 13x^5 + 26x^4 + 6x^3 - 16x^2 + 2x + 1	\( 2^{4}\cdot 5^{6}\cdot 17491^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.93166065194049.1	x^12 - 2x^11 - 3x^10 + 7x^9 + 5x^8 - 6x^7 - 11x^6 - 12x^5 + 20x^4 + 56x^3 - 48x^2 - 64x + 64	\( 3^{6}\cdot 389^{2}\cdot 919^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.101559956668416.14	x^12 - 4x^9 + 3x^8 - 6x^7 - 2x^6 - 6x^5 + 21x^4 + 30x^3 + 27x^2 + 18x + 9	\( 2^{18}\cdot 3^{18} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.157365759791601.1	x^12 - 3x^11 + x^10 + 11x^8 - 6x^7 - 17x^6 - 12x^5 + 44x^4 + 16x^2 - 96x + 64	\( 3^{8}\cdot 154871^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.163199832950961.1	x^12 - 5x^11 + 15x^10 - 35x^9 + 68x^8 - 114x^7 + 169x^6 - 228x^5 + 272x^4 - 280x^3 + 240x^2 - 160x + 64	\( 3^{6}\cdot 473147^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.176848639418025.1	x^12 - 4x^11 + 11x^10 - 24x^9 + 47x^8 - 79x^7 + 119x^6 - 158x^5 + 188x^4 - 192x^3 + 176x^2 - 128x + 64	\( 3^{6}\cdot 5^{2}\cdot 98507^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.192526503153664.1	x^12 - 2x^11 - x^10 + 2x^9 + 6x^8 - 20x^6 + 24x^4 + 16x^3 - 16x^2 - 64x + 64	\( 2^{12}\cdot 216803^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.221124989353984.1	x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64x + 64	\( 2^{16}\cdot 29^{2}\cdot 2003^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.253930089113856.1	x^12 - 5x^11 + 14x^10 - 29x^9 + 52x^8 - 87x^7 + 131x^6 - 174x^5 + 208x^4 - 232x^3 + 224x^2 - 160x + 64	\( 2^{8}\cdot 3^{6}\cdot 36887^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.256059107411409.1	x^12 - x^11 + 6x^10 - 3x^9 + 24x^8 - 12x^7 + 37x^6 + x^5 + 28x^4 - 2x^3 + 9x^2 + 2x + 1	\( 3^{6}\cdot 592661^{2} \)	$S_6\times C_2$ (as 12T219)	$[3]$
12.0.266126138637129.1	x^12 - 2x^11 + 6x^10 - 11x^9 + 20x^8 - 36x^7 + 49x^6 - 72x^5 + 80x^4 - 88x^3 + 96x^2 - 64x + 64	\( 3^{6}\cdot 197^{2}\cdot 3067^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.298306404859401.1	x^12 - 5x^11 + 12x^10 - 22x^9 + 37x^8 - 53x^7 + 71x^6 - 106x^5 + 148x^4 - 176x^3 + 192x^2 - 160x + 64	\( 3^{8}\cdot 213229^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.4.320979616137216.1	x^12 - 4x^11 + 2x^10 + 12x^9 - 9x^8 - 20x^7 + 10x^6 + 12x^5 - 3x^4 + 12x^3 - 12x - 3	\( 2^{26}\cdot 3^{14} \)	$S_6\times C_2$ (as 12T219)	Trivial (GRH)
12.0.331264497652929.1	x^12 + 13x^10 + 57x^8 + 98x^6 + 66x^4 + 16x^2 + 1	\( 3^{6}\cdot 674099^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.357596912114289.1	x^12 - 5x^11 + 11x^10 - 11x^9 - 5x^8 + 36x^7 - 67x^6 + 72x^5 - 20x^4 - 88x^3 + 176x^2 - 160x + 64	\( 3^{6}\cdot 29^{2}\cdot 24151^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.362042445472569.1	x^12 - 4x^11 + 5x^10 - x^8 - 19x^7 + 47x^6 - 38x^5 - 4x^4 + 80x^2 - 128x + 64	\( 3^{6}\cdot 704719^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.385355941335225.1	x^12 - 5x^11 + 14x^10 - 29x^9 + 49x^8 - 72x^7 + 101x^6 - 144x^5 + 196x^4 - 232x^3 + 224x^2 - 160x + 64	\( 3^{6}\cdot 5^{2}\cdot 7^{2}\cdot 20773^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.388253172547881.1	x^12 - 3x^11 + 6x^9 - 6x^7 + x^6 - 12x^5 + 48x^3 - 96x + 64	\( 3^{12}\cdot 151^{2}\cdot 179^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.413288082342144.1	x^12 - 3x^11 + x^10 + 8x^9 - 12x^8 - 8x^7 + 36x^6 - 16x^5 - 48x^4 + 64x^3 + 16x^2 - 96x + 64	\( 2^{8}\cdot 3^{6}\cdot 47059^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.435705715809225.1	x^12 + 12x^10 + 52x^8 + 98x^6 + 76x^4 + 19x^2 + 1	\( 3^{6}\cdot 5^{2}\cdot 154619^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.466269611598729.1	x^12 - 5x^11 + 12x^10 - 14x^9 - 4x^8 + 48x^7 - 95x^6 + 96x^5 - 16x^4 - 112x^3 + 192x^2 - 160x + 64	\( 3^{6}\cdot 433^{2}\cdot 1847^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.498025279590400.1	x^12 - 2x^11 - x^10 + 2x^9 + 2x^8 - 2x^7 + x^6 - 4x^5 + 8x^4 + 16x^3 - 16x^2 - 64x + 64	\( 2^{12}\cdot 5^{2}\cdot 69739^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.533095502277321.1	x^12 - x^11 + 3x^10 + 13x^7 - 13x^6 + 26x^5 + 48x^2 - 32x + 64	\( 3^{6}\cdot 855143^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.535084982665216.1	x^12 - 4x^11 + 5x^10 - 2x^9 - x^8 + 14x^7 - 35x^6 + 28x^5 - 4x^4 - 16x^3 + 80x^2 - 128x + 64	\( 2^{16}\cdot 90359^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.537122757976281.1	x^12 - 5x^11 + 11x^10 - 12x^9 - 4x^8 + 43x^7 - 85x^6 + 86x^5 - 16x^4 - 96x^3 + 176x^2 - 160x + 64	\( 3^{6}\cdot 599^{2}\cdot 1433^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.548345023565824.1	x^12 - 4x^11 + 7x^10 - 8x^9 + 10x^8 - 22x^7 + 41x^6 - 44x^5 + 40x^4 - 64x^3 + 112x^2 - 128x + 64	\( 2^{12}\cdot 43^{2}\cdot 67^{2}\cdot 127^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.562472514549009.1	x^12 - 5x^11 + 11x^10 - 16x^9 + 26x^8 - 53x^7 + 89x^6 - 106x^5 + 104x^4 - 128x^3 + 176x^2 - 160x + 64	\( 3^{6}\cdot 19^{2}\cdot 83^{2}\cdot 557^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.565111264540761.1	x^12 + 12x^10 + 52x^8 + 101x^6 + 88x^4 + 28x^2 + 1	\( 3^{6}\cdot 17^{2}\cdot 67^{2}\cdot 773^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.599366022694209.1	x^12 - 5x^11 + 11x^10 - 15x^9 + 20x^8 - 38x^7 + 65x^6 - 76x^5 + 80x^4 - 120x^3 + 176x^2 - 160x + 64	\( 3^{6}\cdot 853^{2}\cdot 1063^{2} \)	$S_6\times C_2$ (as 12T219)	$[2]$
12.0.603515084103936.1	x^12 - x^11 - 3x^10 + 2x^9 + 8x^8 - 20x^6 + 32x^4 + 16x^3 - 48x^2 - 32x + 64	\( 2^{8}\cdot 3^{6}\cdot 19^{2}\cdot 41^{2}\cdot 73^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.4.655360000000000.1	x^12 - 2x^11 - x^10 + 12x^7 - 4x^6 + 8x^5 - 50x^4 + 60x^3 - 42x^2 + 24x - 8	\( 2^{26}\cdot 5^{10} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.655360000000000.4	x^12 - 4x^11 + 8x^10 - 20x^9 + 35x^8 - 32x^7 + 48x^6 - 56x^5 + 15x^4 - 60x^3 + 72x^2 + 12x + 1	\( 2^{26}\cdot 5^{10} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.655360000000000.13	x^12 - 4x^11 + 8x^10 - 10x^8 + 24x^7 - 16x^6 - 8x^5 + 25x^4 - 20x^3 + 8x^2 + 8x + 4	\( 2^{26}\cdot 5^{10} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.0.722204136308736.11	x^12 - 6x^10 + 9x^8 + 14x^6 - 18x^4 + 9	\( 2^{24}\cdot 3^{16} \)	$S_6\times C_2$ (as 12T219)	Trivial