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 90)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.49519263525896192.1	x^12 - 12x^10 + 68x^8 - 224x^6 + 388x^4 - 272x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.49519263525896192.2	x^12 + 4x^10 - 22x^8 - 8x^4 + 144x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.4.49519263525896192.2	x^12 - 4x^10 - 22x^8 - 8x^4 - 144x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.49519263525896192.3	x^12 + 12x^10 + 68x^8 + 224x^6 + 388x^4 + 272x^2 + 8	\( 2^{33}\cdot 7^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.250348290616922112.1	x^12 + 6x^10 - 4x^9 + 21x^8 - 30x^7 + 3x^6 - 72x^5 + 42x^4 + 124x^3 + 393x^2 + 324x + 199	\( 2^{12}\cdot 3^{16}\cdot 17^{5} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.4.250348290616922112.1	x^12 - 3x^10 - 32x^9 - 30x^8 - 108x^7 - 111x^6 - 24x^5 - 54x^4 - 72x^3 + 45x^2 + 84x - 19	\( 2^{12}\cdot 3^{16}\cdot 17^{5} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.4.369768517790072832.1	x^12 - 12x^10 + 60x^8 - 160x^6 + 228x^4 - 144x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.369768517790072832.2	x^12 - 30x^8 + 56x^6 + 120x^4 + 96x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.4.369768517790072832.10	x^12 - 30x^8 - 56x^6 + 120x^4 - 96x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.369768517790072832.39	x^12 + 12x^10 + 60x^8 + 160x^6 + 228x^4 + 144x^2 + 8	\( 2^{33}\cdot 3^{16} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.469804094334435328.2	x^12 - 6x^11 + 36x^10 - 112x^9 + 334x^8 - 600x^7 + 1052x^6 - 982x^5 + 965x^4 - 122x^3 + 56x^2 + 2x + 1	\( 2^{18}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T99)	$[4]$
12.0.469804094334435328.4	x^12 - 26x^8 + 234x^6 - 507x^4 + 910x^2 + 13	\( 2^{18}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T99)	$[4]$
12.4.469804094334435328.4	x^12 - 26x^8 - 234x^6 - 507x^4 - 910x^2 + 13	\( 2^{18}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.4.469804094334435328.9	x^12 - 6x^11 + 10x^10 - 8x^9 + 48x^8 - 80x^7 - 144x^6 + 240x^5 + 172x^4 + 632x^3 - 1920x^2 - 336x + 2120	\( 2^{18}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.0.2354201409964503125.1	x^12 - 4x^11 + 10x^10 - 19x^9 + 31x^8 - 23x^7 + 67x^6 - 250x^5 + 252x^4 - 98x^3 + 140x^2 - 425x + 625	\( 5^{5}\cdot 13^{8}\cdot 31^{4} \)	$C_2^5.C_6$ (as 12T99)	$[2, 2]$
12.12.2354201409964503125.1	x^12 - 3x^11 - 20x^10 + 40x^9 + 150x^8 - 130x^7 - 402x^6 + 169x^5 + 421x^4 - 96x^3 - 180x^2 + 20x + 25	\( 5^{5}\cdot 13^{8}\cdot 31^{4} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.4.2354201409964503125.1	x^12 - 2x^11 - 5x^10 + 19x^8 + 3x^7 - 19x^6 + 31x^5 + 21x^4 - 195x^3 - 110x^2 + 100x + 25	\( 5^{5}\cdot 13^{8}\cdot 31^{4} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.8.2354201409964503125.1	x^12 - 2x^11 - 5x^10 + 33x^9 - 41x^8 - 122x^7 + 281x^6 + 62x^5 - 433x^4 + 150x^3 + 121x^2 - 41x + 1	\( 5^{5}\cdot 13^{8}\cdot 31^{4} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.4.2354201409964503125.2	x^12 - 2x^11 - 15x^10 + 33x^9 + 33x^8 - 212x^7 + 95x^6 + 425x^5 + 95x^4 - 310x^3 - 450x^2 - 675x + 125	\( 5^{5}\cdot 13^{8}\cdot 31^{4} \)	$C_2^5.C_6$ (as 12T99)	$[2, 2]$
12.8.2354201409964503125.2	x^12 - 76x^8 + 325x^6 - 380x^4 + 125	\( 5^{5}\cdot 13^{8}\cdot 31^{4} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.2426443912768913408.16	x^12 - 70x^8 + 672x^6 - 2744x^4 + 3920x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.0.2426443912768913408.17	x^12 - 28x^8 - 280x^6 + 196x^4 + 9408x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.4.2426443912768913408.24	x^12 - 28x^8 + 280x^6 + 196x^4 - 9408x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.4.2426443912768913408.25	x^12 - 70x^8 - 672x^6 - 2744x^4 - 3920x^2 + 392	\( 2^{33}\cdot 7^{10} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.4.3327916660110655488.25	x^12 + 12x^10 + 54x^8 - 48x^6 - 756x^4 - 1296x^2 + 72	\( 2^{33}\cdot 3^{18} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.4.3327916660110655488.26	x^12 - 12x^10 + 36x^8 + 48x^6 - 108x^4 - 864x^2 + 72	\( 2^{33}\cdot 3^{18} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.3327916660110655488.54	x^12 + 12x^10 + 36x^8 - 48x^6 - 108x^4 + 864x^2 + 72	\( 2^{33}\cdot 3^{18} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.0.3327916660110655488.55	x^12 - 12x^10 + 54x^8 + 48x^6 - 756x^4 + 1296x^2 + 72	\( 2^{33}\cdot 3^{18} \)	$C_2^5.C_6$ (as 12T99)	$[2]$
12.4.7007073538075000832.37	x^12 - 12x^10 + 68x^8 - 224x^6 + 436x^4 - 464x^2 + 200	\( 2^{33}\cdot 13^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.4.7007073538075000832.38	x^12 - 16x^10 + 66x^8 - 88x^6 + 8x^4 + 224x^2 + 200	\( 2^{33}\cdot 13^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.7007073538075000832.88	x^12 + 16x^10 + 66x^8 + 88x^6 + 8x^4 - 224x^2 + 200	\( 2^{33}\cdot 13^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.7007073538075000832.91	x^12 + 12x^10 + 68x^8 + 224x^6 + 436x^4 + 464x^2 + 200	\( 2^{33}\cdot 13^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.0.7154568579805872128.1	x^12 + 7x^10 + 12x^8 + 12x^6 + 24x^4 + 28x^2 + 8	\( 2^{23}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	$[2]$ (GRH)
12.0.7154568579805872128.12	x^12 - 12x^10 + 8x^8 + 132x^6 + 844x^4 + 760x^2 + 128	\( 2^{23}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	$[2]$ (GRH)
12.0.7154568579805872128.14	x^12 - 8x^10 + 38x^8 + 108x^6 - 464x^4 + 96x^2 + 512	\( 2^{23}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	$[2]$ (GRH)
12.0.7154568579805872128.16	x^12 + 17x^10 + 128x^8 + 542x^6 + 1296x^4 + 1472x^2 + 512	\( 2^{23}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	$[2]$ (GRH)
12.4.7154568579805872128.29	x^12 - 15x^10 + 88x^8 - 286x^6 + 588x^4 - 416x^2 + 32	\( 2^{23}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.4.7154568579805872128.57	x^12 - 22x^10 + 178x^8 - 648x^6 + 1168x^4 - 1472x^2 + 512	\( 2^{23}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.4.7154568579805872128.58	x^12 - 9x^10 + 20x^8 - 16x^6 + 160x^4 - 576x^2 + 512	\( 2^{23}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial
12.4.7154568579805872128.61	x^12 - 14x^10 + 66x^8 - 140x^6 - 192x^4 + 480x^2 + 512	\( 2^{23}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.12.7317705105431086093.1	x^12 - 4x^11 - 21x^10 + 99x^9 + 104x^8 - 771x^7 + 89x^6 + 2330x^5 - 1374x^4 - 2406x^3 + 1728x^2 + 689x - 421	\( 7^{8}\cdot 13^{5}\cdot 43^{4} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.0.28618274319223488512.9	x^12 + 15x^10 + 88x^8 + 286x^6 + 588x^4 + 416x^2 + 32	\( 2^{25}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	$[2, 4]$ (GRH)
12.4.28618274319223488512.9	x^12 - 7x^10 + 12x^8 - 12x^6 + 24x^4 - 28x^2 + 8	\( 2^{25}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.0.28618274319223488512.15	x^12 + 14x^10 + 66x^8 + 140x^6 - 192x^4 - 480x^2 + 512	\( 2^{25}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	$[2, 2]$ (GRH)
12.0.28618274319223488512.16	x^12 + 9x^10 + 20x^8 + 16x^6 + 160x^4 + 576x^2 + 512	\( 2^{25}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	$[2, 2]$ (GRH)
12.0.28618274319223488512.19	x^12 + 22x^10 + 178x^8 + 648x^6 + 1168x^4 + 1472x^2 + 512	\( 2^{25}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	$[2, 2]$ (GRH)
12.4.28618274319223488512.48	x^12 + 12x^10 + 8x^8 - 132x^6 + 844x^4 - 760x^2 + 128	\( 2^{25}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.4.28618274319223488512.64	x^12 - 17x^10 + 128x^8 - 542x^6 + 1296x^4 - 1472x^2 + 512	\( 2^{25}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.4.28618274319223488512.69	x^12 + 8x^10 + 38x^8 - 108x^6 - 464x^4 - 96x^2 + 512	\( 2^{25}\cdot 31^{8} \)	$C_2^5.C_6$ (as 12T99)	Trivial (GRH)
12.0.30067462037403860992.13	x^12 - 13x^8 + 208x^6 - 169x^4 - 312x^2 + 325	\( 2^{24}\cdot 13^{11} \)	$C_2^5.C_6$ (as 12T99)	$[4]$ (GRH)