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 1011)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.109061760025.1	x^12 - 3x^11 + 5x^10 - 7x^9 + 10x^8 - 10x^7 + 9x^6 - 10x^5 + 10x^4 - 7x^3 + 5x^2 - 3x + 1	\( 5^{2}\cdot 257^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.176003742784.1	x^12 - x^11 + 2x^10 + 4x^8 + x^7 + 2x^6 + x^5 + 4x^4 + 2x^2 - x + 1	\( 2^{6}\cdot 229^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.413788573696.3	x^12 + 2x^10 + 4x^8 + 5x^6 + 4x^4 + 2x^2 + 1	\( 2^{12}\cdot 19^{2}\cdot 23^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.457711783936.2	x^12 + 2x^10 + 2x^8 + x^6 + 2x^4 + 2x^2 + 1	\( 2^{12}\cdot 11^{2}\cdot 31^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.704014971136.1	x^12 - x^8 + x^6 - x^4 + 1	\( 2^{8}\cdot 229^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.1833965977600.1	x^12 - 4x^11 + 4x^10 + 6x^9 - 15x^8 - 8x^7 + 20x^6 + 10x^5 - 10x^4 - 2x^3 - 2x^2 - 2x + 1	\( 2^{18}\cdot 5^{2}\cdot 23^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.1923849446841.1	x^12 - 4x^10 + 4x^8 - 3x^6 + 4x^4 - 4x^2 + 1	\( 3^{2}\cdot 7^{2}\cdot 257^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.2178859401216.1	x^12 - 6x^11 + 16x^10 - 24x^9 + 10x^8 + 20x^7 - 34x^6 + 14x^5 + 9x^4 - 2x^3 - 8x^2 + 2x + 1	\( 2^{18}\cdot 3^{2}\cdot 31^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.2771239407616.1	x^12 - x^10 - 6x^8 + 11x^6 - 6x^4 - x^2 + 1	\( 2^{12}\cdot 19^{2}\cdot 37^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.2966551527424.1	x^12 + x^10 - x^8 + 6x^6 - x^4 + x^2 + 1	\( 2^{22}\cdot 29^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.3018430193769.1	x^12 - 2x^11 - 4x^10 + 7x^9 + 7x^8 - 5x^7 - 9x^6 - 5x^5 + 7x^4 + 7x^3 - 4x^2 - 2x + 1	\( 3^{2}\cdot 761^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.4060902068224.1	x^12 - 2x^11 - 2x^10 + 4x^9 + 7x^8 - 10x^7 - 4x^6 + 10x^5 + 7x^4 - 4x^3 - 2x^2 + 2x + 1	\( 2^{12}\cdot 23^{2}\cdot 37^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.6455989866496.1	x^12 - 5x^10 + 6x^8 - 5x^6 + 6x^4 - 5x^2 + 1	\( 2^{12}\cdot 29^{2}\cdot 37^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.29721861554176.2	x^12 - 4x^11 + 10x^10 - 12x^9 + x^8 - 14x^6 + 4x^5 + 17x^4 - 4x^3 - 4x^2 + 4x - 1	\( 2^{24}\cdot 11^{6} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.30667140235264.2	x^12 - 5x^10 - 5x^8 - 14x^6 - 5x^4 - 5x^2 + 1	\( 2^{30}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.30667140235264.6	x^12 - 4x^11 + 15x^10 - 34x^9 + 64x^8 - 88x^7 + 110x^6 - 108x^5 + 95x^4 - 60x^3 + 37x^2 - 14x + 2	\( 2^{30}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.38806720086016.1	x^12 - 4x^11 + 6x^10 + 2x^9 - 38x^8 + 18x^7 + 74x^6 - 10x^5 - 63x^4 - 24x^3 + 8x^2 + 6x + 1	\( 2^{18}\cdot 23^{6} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.47464824438784.1	x^12 - x^10 - x^8 - 6x^6 - x^4 - x^2 + 1	\( 2^{26}\cdot 29^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.47464824438784.3	x^12 + 5x^8 - 4x^6 + 5x^4 + 1	\( 2^{26}\cdot 29^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.47464824438784.12	x^12 + 6x^10 + 16x^8 + 6x^6 + 9x^4 + 4x^2 + 4	\( 2^{26}\cdot 29^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.80980417183744.11	x^12 + 4x^6 + 19x^4 + 24x^2 + 16	\( 2^{24}\cdot 13^{6} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.122668560941056.2	x^12 - 6x^10 + 18x^8 - 32x^6 + 65x^4 - 82x^2 + 4	\( 2^{32}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.122668560941056.6	x^12 - 6x^10 + 14x^8 - 16x^6 + 9x^4 - 2x^2 + 4	\( 2^{32}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	$[2]$
12.0.122668560941056.9	x^12 + 6x^10 + 14x^8 + 16x^6 + 9x^4 + 2x^2 + 4	\( 2^{32}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.122668560941056.14	x^12 - 6x^10 + 14x^8 - 16x^6 - 7x^4 + 30x^2 + 16	\( 2^{32}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.139931108245504.2	x^12 - 5x^10 + 3x^8 - 14x^6 + 3x^4 - 5x^2 + 1	\( 2^{30}\cdot 19^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.139931108245504.6	x^12 + 7x^10 + 11x^8 - 6x^6 + 11x^4 + 7x^2 + 1	\( 2^{30}\cdot 19^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.155929364660224.1	x^12 - x^11 - 3x^10 + 4x^9 + 2x^8 - 12x^7 + 10x^6 - 6x^5 - 5x^4 + 23x^3 - 9x^2 - 10x + 4	\( 2^{18}\cdot 29^{6} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial (GRH)
12.8.180227832610816.1	x^12 - 11x^10 + 42x^8 - 79x^6 + 70x^4 - 23x^2 + 1	\( 2^{16}\cdot 229^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.180227832610816.1	x^12 - 2x^10 - 2x^8 - 2x^6 - 2x^4 - 2x^2 + 1	\( 2^{16}\cdot 229^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.180227832610816.2	x^12 - x^10 - 2x^8 - 4x^6 - 2x^4 - x^2 + 1	\( 2^{16}\cdot 229^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.180551034077184.1	x^12 - 3x^10 + 3x^8 - 18x^6 + 3x^4 - 3x^2 + 1	\( 2^{22}\cdot 3^{16} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.189859297755136.1	x^12 + x^8 + 16x^6 + 9x^4 - 36x^2 + 1	\( 2^{28}\cdot 29^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.189859297755136.3	x^12 + 4x^10 - 3x^8 - 20x^6 - 3x^4 + 4x^2 + 1	\( 2^{28}\cdot 29^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.189859297755136.8	x^12 + 6x^10 + 14x^8 + 16x^6 + 17x^4 + 18x^2 + 4	\( 2^{28}\cdot 29^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.228509902503936.1	x^12 - 3x^10 + 6x^8 - 16x^6 + 6x^4 - 3x^2 + 1	\( 2^{16}\cdot 3^{20} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.228509902503936.5	x^12 - 3x^10 - 3x^8 + 17x^6 - 3x^4 - 21x^2 + 16	\( 2^{16}\cdot 3^{20} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.232653764952064.2	x^12 - 2x^11 - 8x^10 + 2x^9 + 74x^8 - 142x^7 + 92x^6 + 28x^5 - 51x^4 - 10x^3 + 16x^2 + 8x + 1	\( 2^{18}\cdot 31^{6} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.8.234683893804816.2	x^12 - x^10 - 16x^8 + 36x^6 - 16x^4 - x^2 + 1	\( 2^{4}\cdot 19^{4}\cdot 103^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.323921668734976.3	x^12 - 5x^10 - 3x^8 + 12x^6 + 4x^4 - 12x^2 + 4	\( 2^{26}\cdot 13^{6} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.419430400000000.2	x^12 - 2x^11 - x^10 + 10x^9 - 4x^8 - 20x^7 - 6x^6 + 44x^5 + 31x^4 - 30x^3 - 27x^2 - 2x + 2	\( 2^{30}\cdot 5^{8} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.4.475549784866816.1	x^12 - 10x^10 - 4x^9 + 24x^8 + 72x^7 + 40x^6 - 156x^5 - 150x^4 + 72x^3 + 128x^2 + 40x - 58	\( 2^{28}\cdot 11^{6} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.475549784866816.30	x^12 + 6x^10 - 4x^9 + 4x^8 - 16x^7 - 24x^6 - 68x^5 - 40x^4 + 248x^3 + 512x^2 + 392x + 122	\( 2^{28}\cdot 11^{6} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.490674243764224.1	x^12 - 8x^10 + 23x^8 + 23x^4 - 8x^2 + 1	\( 2^{34}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	$[2]$
12.4.490674243764224.2	x^12 - 4x^10 + 7x^8 - 40x^6 + 7x^4 - 4x^2 + 1	\( 2^{34}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.490674243764224.2	x^12 - x^8 + 16x^6 - x^4 + 1	\( 2^{34}\cdot 13^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	$[2]$
12.4.559724432982016.3	x^12 - 2x^10 + 7x^8 - 44x^6 + 7x^4 - 2x^2 + 1	\( 2^{32}\cdot 19^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial
12.0.559724432982016.12	x^12 - 2x^11 - x^10 + 6x^9 + 7x^8 - 40x^7 + 40x^6 + 8x^5 - 38x^4 + 28x^3 - 6x^2 - 12x + 10	\( 2^{32}\cdot 19^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	$[2]$
12.0.559724432982016.14	x^12 - 6x^10 + 18x^8 - 32x^6 + 41x^4 - 34x^2 + 16	\( 2^{32}\cdot 19^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	$[2]$
12.0.559724432982016.16	x^12 + 6x^10 + 18x^8 + 32x^6 + 41x^4 + 34x^2 + 16	\( 2^{32}\cdot 19^{4} \)	$C_2\times C_2^2:S_4$ (as 12T101)	Trivial