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 77)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.5282495463424.1	x^12 - 2x^10 - 3x^8 + 14x^6 - 18x^4 + 8x^2 + 1	\( 2^{18}\cdot 67^{4} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.7444428488704.1	x^12 - 2x^11 + 2x^10 - 4x^9 + 10x^8 - 10x^7 + 8x^6 - 14x^5 + 17x^4 - 4x^3 + 1	\( 2^{18}\cdot 73^{4} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.25000000000000.1	x^12 - 4x^11 + 4x^10 + 6x^7 - 9x^6 - 6x^5 + 4x^2 + 4x + 1	\( 2^{12}\cdot 5^{14} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.64000000000000.2	x^12 - 4x^11 + 8x^10 - 10x^9 + 10x^8 - 16x^7 + 34x^6 - 38x^5 + 25x^4 - 10x^3 + 8x^2 - 12x + 9	\( 2^{18}\cdot 5^{12} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.174322509765625.1	x^12 - 2x^11 + x^10 + 5x^9 - 15x^8 + 27x^7 + 21x^6 - 33x^5 + 20x^4 - 5x^3 + 11x^2 - 7x + 1	\( 5^{14}\cdot 13^{4} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.1600000000000000.3	x^12 - 10x^8 + 10x^6 + 25x^4 + 30x^2 + 25	\( 2^{18}\cdot 5^{14} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.0.1828652958613504.4	x^12 - 2x^10 + x^8 + 14x^6 - 2x^4 - 8x^2 + 9	\( 2^{18}\cdot 17^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.4096000000000000.2	x^12 - 8x^10 + 30x^8 - 60x^6 + 65x^4 - 38x^2 + 9	\( 2^{24}\cdot 5^{12} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.4096000000000000.4	x^12 + 8x^10 + 30x^8 + 60x^6 + 65x^4 + 38x^2 + 9	\( 2^{24}\cdot 5^{12} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.4452139149819904.1	x^12 - 4x^11 + 8x^10 - 16x^9 + 37x^8 - 54x^7 + 48x^6 - 26x^5 + 22x^4 - 24x^3 + 18x^2 - 6x + 1	\( 2^{18}\cdot 19^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.8257511016239104.2	x^12 - 4x^11 + 6x^10 - 10x^9 + 9x^8 + 54x^7 - 166x^6 + 164x^5 + 2x^4 - 158x^3 + 164x^2 - 76x + 13	\( 2^{12}\cdot 17^{10} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.15625000000000000.1	x^12 - 2x^11 - 4x^10 + 2x^7 - 14x^6 + 2x^5 - 4x^2 - 2x + 1	\( 2^{12}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.15625000000000000.2	x^12 - 2x^11 - 4x^10 + 2x^7 + 11x^6 + 2x^5 - 4x^2 - 2x + 1	\( 2^{12}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.15625000000000000.3	x^12 - 4x^11 + 4x^10 - 6x^7 + 9x^6 + 6x^5 + 4x^2 + 4x + 1	\( 2^{12}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.25112847391952896.4	x^12 - 6x^11 + 22x^10 - 42x^9 + 55x^8 - 6x^7 - 19x^6 + 48x^5 + 186x^4 - 218x^3 + 417x^2 - 146x + 283	\( 2^{12}\cdot 19^{10} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.40000000000000000.1	x^12 - 2x^11 + 2x^10 + 10x^8 - 16x^7 + 12x^6 - 2x^5 + 25x^4 - 30x^3 + 18x^2 - 6x + 1	\( 2^{18}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.40000000000000000.3	x^12 - 6x^11 + 18x^10 - 30x^9 + 25x^8 + 2x^7 - 22x^6 + 36x^5 - 20x^4 + 10x^2 - 10x + 5	\( 2^{18}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.40000000000000000.6	x^12 + 2x^10 + 10x^8 + 60x^6 + 65x^4 - 78x^2 + 4	\( 2^{18}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.102400000000000000.6	x^12 - 10x^10 + 10x^8 - 70x^6 + 25x^4 - 140x^2 + 25	\( 2^{24}\cdot 5^{14} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.0.102400000000000000.9	x^12 + 10x^10 + 10x^8 + 70x^6 + 25x^4 + 140x^2 + 25	\( 2^{24}\cdot 5^{14} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.0.117033789351264256.9	x^12 + 12x^10 + 54x^8 + 112x^6 + 125x^4 + 82x^2 + 25	\( 2^{24}\cdot 17^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.117033789351264256.9	x^12 - 12x^10 + 54x^8 - 112x^6 + 125x^4 - 82x^2 + 25	\( 2^{24}\cdot 17^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.131136595679248384.2	x^12 - 10x^10 + 29x^8 - 6x^6 - 58x^4 + 40x^2 + 9	\( 2^{18}\cdot 29^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.131136595679248384.4	x^12 - 2x^11 + 2x^10 + 6x^9 + x^8 - 2x^7 + 20x^6 + 36x^5 + 34x^4 + 40x^3 + 50x^2 + 30x + 9	\( 2^{18}\cdot 29^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.160000000000000000.4	x^12 - 4x^11 + 8x^10 + 10x^8 - 32x^7 + 48x^6 - 16x^5 + 25x^4 - 60x^3 + 72x^2 - 48x + 16	\( 2^{20}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	$[2]$ (GRH)
12.0.160000000000000000.7	x^12 - 6x^11 + 18x^10 - 30x^9 + 25x^8 - 4x^7 - 16x^6 + 48x^5 - 20x^4 + 40x^2 - 40x + 20	\( 2^{20}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.0.162268567138729984.1	x^12 + 18x^10 + 121x^8 + 366x^6 + 450x^4 + 104x^2 + 1	\( 2^{18}\cdot 887^{4} \)	$C_2\times A_5$ (as 12T75)	$[2, 4]$
12.0.223580268118933504.2	x^12 + 2x^10 + 21x^8 - 6x^6 - 26x^4 + 12x^2 + 1	\( 2^{18}\cdot 31^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.250000000000000000.1	x^12 - 2x^11 - 4x^10 - 58x^7 + 206x^6 - 58x^5 - 4x^2 - 2x + 1	\( 2^{16}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	Trivial (GRH)
12.0.284936905588473856.5	x^12 - 6x^10 + 13x^8 + 10x^6 - 22x^4 + 6x^2 + 1	\( 2^{24}\cdot 19^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.284936905588473856.7	x^12 + 6x^10 + 13x^8 - 10x^6 - 22x^4 - 6x^2 + 1	\( 2^{24}\cdot 19^{8} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.346730532947800681.1	x^12 - 3x^11 + 7x^10 + 8x^9 - 80x^8 + 81x^7 + 269x^6 - 419x^5 - 201x^4 + 574x^3 - 405x^2 + 548x + 1565	\( 19^{6}\cdot 293^{4} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.0.528480705039302656.6	x^12 + 34x^8 + 102x^6 + 289x^4 + 578x^2 + 289	\( 2^{18}\cdot 17^{10} \)	$C_2\times A_5$ (as 12T75)	$[4]$
12.0.640000000000000000.4	x^12 - 2x^10 + 10x^8 - 60x^6 + 65x^4 + 78x^2 + 4	\( 2^{22}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.4.640000000000000000.6	x^12 - 8x^10 - 10x^8 + 40x^6 + 25x^4 - 32x^2 + 16	\( 2^{22}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.0.640000000000000000.8	x^12 + 8x^10 - 10x^8 - 40x^6 + 25x^4 + 32x^2 + 16	\( 2^{22}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.0.1000000000000000000.3	x^12 - 2x^11 + 6x^10 + 10x^8 + 4x^7 + 42x^6 + 14x^5 + 25x^4 + 70x^3 + 204x^2 + 142x + 29	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.4.1000000000000000000.6	x^12 - 6x^11 + 9x^10 - 10x^9 + 60x^8 - 78x^7 - 67x^6 + 18x^5 - 85x^4 + 760x^3 - 294x^2 - 696x + 424	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.0.1000000000000000000.13	x^12 - 50x^8 + 250x^6 - 475x^4 + 230x^2 + 225	\( 2^{18}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	$[2]$
12.4.1607222233084985344.1	x^12 + 2x^10 - 10x^9 - 64x^8 + 150x^7 + 344x^6 - 370x^5 - 837x^4 + 100x^3 + 1254x^2 + 130x - 775	\( 2^{18}\cdot 19^{10} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.1723216827597623296.1	x^12 - 2x^11 - 2x^10 + 32x^9 - 32x^8 - 72x^7 + 336x^6 - 48x^5 - 736x^4 + 800x^3 + 1088x^2 - 512x - 448	\( 2^{12}\cdot 29^{10} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.1723216827597623296.4	x^12 - 2x^11 - 4x^10 - 16x^9 - 22x^8 + 150x^7 + 246x^6 + 622x^5 + 45x^4 - 980x^3 - 1826x^2 - 1092x + 45	\( 2^{12}\cdot 29^{10} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.2560000000000000000.2	x^12 + 2x^10 - 10x^8 - 10x^6 + 25x^4 + 8x^2 + 1	\( 2^{24}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.2560000000000000000.3	x^12 - 2x^10 - 10x^8 + 10x^6 + 25x^4 - 8x^2 + 1	\( 2^{24}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.4.2560000000000000000.4	x^12 + 2x^10 + 10x^8 + 10x^6 - 35x^4 - 38x^2 + 9	\( 2^{24}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.2560000000000000000.5	x^12 - 2x^10 + 10x^8 - 10x^6 - 35x^4 + 38x^2 + 9	\( 2^{24}\cdot 5^{16} \)	$C_2\times A_5$ (as 12T75)	Trivial
12.0.3357197463473360896.9	x^12 - 2x^11 - 10x^10 - 20x^9 + 60x^8 + 296x^7 + 568x^6 + 592x^5 + 240x^4 - 160x^3 - 160x^2 - 64x + 64	\( 2^{12}\cdot 31^{10} \)	$C_2\times A_5$ (as 12T75)	$[3]$
12.0.4000000000000000000.9	x^12 - 50x^8 + 200x^6 - 175x^4 - 280x^2 + 400	\( 2^{20}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	$[2, 2]$
12.0.4000000000000000000.14	x^12 - 2x^11 + x^10 + 10x^9 - 10x^8 - 26x^7 + 77x^6 - 166x^5 - 105x^4 + 480x^3 - 356x^2 - 288x + 2614	\( 2^{20}\cdot 5^{18} \)	$C_2\times A_5$ (as 12T75)	$[2, 2]$
12.12.4126077869684353969.1	x^12 - 3x^11 - 13x^10 + 37x^9 + 70x^8 - 166x^7 - 205x^6 + 323x^5 + 329x^4 - 241x^3 - 235x^2 + 31x + 38	\( 17^{6}\cdot 643^{4} \)	$C_2\times A_5$ (as 12T75)	Trivial