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 112)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.19708707423601.1	x^12 - 4x^11 + 7x^10 - 6x^9 + x^8 + 10x^7 - 11x^6 + 10x^5 - 8x^4 + 6x^3 - 5x^2 - x + 1	\( 7^{8}\cdot 43^{4} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.19708707423601.2	x^12 - 3x^11 + 4x^10 - 6x^9 + 10x^8 + x^7 - 11x^6 - 5x^5 + 2x^4 + 6x^3 + x + 1	\( 7^{8}\cdot 43^{4} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.96717311574016.5	x^12 - 2x^10 - 5x^8 + 18x^6 - 12x^4 - 2x^2 + 1	\( 2^{24}\cdot 7^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.96717311574016.8	x^12 - 6x^10 + 11x^8 - 4x^6 - 6x^4 + 4x^2 + 1	\( 2^{24}\cdot 7^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.722204136308736.6	x^12 - 15x^8 - 2x^6 + 6x^2 + 1	\( 2^{24}\cdot 3^{16} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.722204136308736.8	x^12 - 6x^10 + 15x^8 - 20x^6 + 6x^4 + 12x^2 + 1	\( 2^{24}\cdot 3^{16} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.3493441689358336.3	x^12 - 4x^10 - 19x^8 + 12x^6 + 37x^4 - 32x^2 + 4	\( 2^{12}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.3493441689358336.4	x^12 - 14x^8 - 7x^4 + 4	\( 2^{12}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.4739148267126784.14	x^12 + 2x^10 - 10x^8 - 6x^6 - 5x^4 + 4x^2 + 1	\( 2^{24}\cdot 7^{10} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.4739148267126784.16	x^12 - 6x^10 + 15x^8 - 20x^6 + 8x^4 + 8x^2 + 1	\( 2^{24}\cdot 7^{10} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.6189907940737024.3	x^12 + 4x^10 - 6x^8 - 18x^6 - 17x^4 - 6x^2 + 1	\( 2^{30}\cdot 7^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.6189907940737024.7	x^12 - 6x^10 + 11x^8 - 4x^6 - 13x^4 + 18x^2 + 1	\( 2^{30}\cdot 7^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.6499837226778624.5	x^12 - 9x^8 + 10x^6 + 18x^4 - 18x^2 + 1	\( 2^{24}\cdot 3^{18} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.6499837226778624.10	x^12 + 6x^10 - 3x^8 - 26x^6 - 24x^4 - 6x^2 + 1	\( 2^{24}\cdot 3^{18} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.13685690504052736.7	x^12 - 4x^10 - 11x^8 + 46x^6 - 60x^4 + 14x^2 + 1	\( 2^{24}\cdot 13^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.13685690504052736.11	x^12 - 6x^10 + 3x^8 + 28x^6 - 22x^4 - 28x^2 + 25	\( 2^{24}\cdot 13^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.46221064723759104.21	x^12 + 6x^10 + 3x^8 - 28x^6 - 45x^4 - 18x^2 + 9	\( 2^{30}\cdot 3^{16} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.46221064723759104.22	x^12 - 12x^8 + 26x^6 - 9x^4 - 18x^2 + 9	\( 2^{30}\cdot 3^{16} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.55895067029733376.10	x^12 - 6x^10 + 5x^8 + 20x^6 - 84x^4 + 112x^2 + 16	\( 2^{16}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.55895067029733376.11	x^12 - 8x^10 - 27x^8 + 62x^6 + 280x^4 + 232x^2 + 16	\( 2^{16}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.64834322978970801.1	x^12 - x^9 - 24x^8 - 30x^7 - 29x^6 + 6x^5 + 30x^4 + 210x^3 + 261x^2 + 135x + 17	\( 3^{16}\cdot 197^{4} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.64834322978970801.2	x^12 - 3x^11 - 3x^10 + 30x^9 - 54x^8 - 84x^7 + 191x^6 + 108x^5 - 369x^4 + 188x^3 + 393x^2 + 198x + 107	\( 3^{16}\cdot 197^{4} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.223580268118933504.14	x^12 - 8x^8 + 11x^4 + 4	\( 2^{18}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.223580268118933504.15	x^12 - 40x^8 + 27x^4 + 4	\( 2^{18}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.223580268118933504.16	x^12 - 7x^10 - 2x^8 + 43x^6 + 57x^4 + 26x^2 + 4	\( 2^{18}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.223580268118933504.25	x^12 - x^10 + x^8 + 42x^6 - 48x^4 - 72x^2 + 16	\( 2^{18}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.284936905588473856.17	x^12 - 6x^10 + 27x^8 - 68x^6 + 2x^4 + 116x^2 + 49	\( 2^{24}\cdot 19^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.284936905588473856.19	x^12 + 8x^8 - 80x^4 + 64	\( 2^{24}\cdot 19^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.0.303175916851972129.3	x^12 - 2x^11 - 3x^10 + 6x^9 + 51x^8 + 24x^7 - 41x^6 - 14x^5 + 609x^4 + 742x^3 + 749x^2 + 1267	\( 7^{10}\cdot 181^{4} \)	$C_4:D_4:C_3$ (as 12T60)	$[4]$
12.0.303175916851972129.4	x^12 - x^11 - x^10 - 4x^9 + 6x^8 + 37x^7 - 21x^6 - 143x^5 + 332x^4 + 346x^3 - 352x^2 - 242x + 1331	\( 7^{10}\cdot 181^{4} \)	$C_4:D_4:C_3$ (as 12T60)	$[4]$
12.4.303305489096114176.19	x^12 - 6x^10 + x^8 + 78x^6 - 48x^4 - 188x^2 + 169	\( 2^{30}\cdot 7^{10} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.303305489096114176.21	x^12 + 2x^10 - 17x^8 - 62x^6 - 26x^4 + 144x^2 + 169	\( 2^{30}\cdot 7^{10} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.415989582513831936.32	x^12 + 6x^10 + 9x^8 + 66x^6 + 144x^4 - 108x^2 + 9	\( 2^{30}\cdot 3^{18} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.415989582513831936.38	x^12 + 6x^10 + 27x^8 + 66x^6 - 288x^4 + 9	\( 2^{30}\cdot 3^{18} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.875884192259375104.9	x^12 + 6x^10 - 5x^8 - 60x^6 - 93x^4 - 50x^2 + 1	\( 2^{30}\cdot 13^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.875884192259375104.10	x^12 + 2x^10 - 15x^8 + 18x^6 + 8x^4 - 20x^2 + 1	\( 2^{30}\cdot 13^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.2312881695184912384.7	x^12 - 2x^10 - 20x^8 + 6x^6 + 5x^4 + 8x^2 + 1	\( 2^{24}\cdot 13^{10} \)	$C_4:D_4:C_3$ (as 12T60)	$[2]$
12.4.2312881695184912384.8	x^12 - 6x^10 + 15x^8 - 20x^6 + 2x^4 + 20x^2 + 1	\( 2^{24}\cdot 13^{10} \)	$C_4:D_4:C_3$ (as 12T60)	$[2]$
12.4.3577284289902936064.23	x^12 - 6x^10 + 5x^8 + 20x^6 - 22x^4 - 12x^2 + 16	\( 2^{22}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial (GRH)
12.4.3577284289902936064.46	x^12 - 4x^10 - 77x^8 - 226x^6 - 136x^4 + 176x^2 + 64	\( 2^{22}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.3577284289902936064.54	x^12 + x^10 - 28x^8 + 42x^6 - 328x^4 + 904x^2 + 1024	\( 2^{22}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial (GRH)
12.4.3577284289902936064.60	x^12 - 15x^10 + 70x^8 - 44x^6 - 344x^4 + 320x^2 + 256	\( 2^{22}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial (GRH)
12.4.14309137159611744256.12	x^12 - 9x^10 + 19x^8 + 21x^6 - 30x^4 - 2x^2 + 4	\( 2^{24}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial (GRH)
12.4.14309137159611744256.13	x^12 + 23x^8 - 20x^4 + 4	\( 2^{24}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial (GRH)
12.4.14309137159611744256.14	x^12 - 9x^8 - 4x^4 + 4	\( 2^{24}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.14309137159611744256.28	x^12 + 5x^10 - 37x^8 - 11x^6 + 70x^4 + 64x^2 + 16	\( 2^{24}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial (GRH)
12.4.14309137159611744256.43	x^12 - 7x^10 - 13x^8 + 53x^6 + 10x^4 - 112x^2 + 64	\( 2^{24}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	$[2]$
12.4.14309137159611744256.44	x^12 - 41x^8 - 256x^4 + 64	\( 2^{24}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial (GRH)
12.4.14309137159611744256.45	x^12 + 29x^8 - 102x^4 + 64	\( 2^{24}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial
12.4.14309137159611744256.46	x^12 - 19x^8 - 14x^4 + 64	\( 2^{24}\cdot 31^{8} \)	$C_4:D_4:C_3$ (as 12T60)	Trivial (GRH)