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 76)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.11709207984384.1	x^12 - 6x^11 + 15x^10 - 20x^9 + 22x^8 - 34x^7 + 47x^6 - 40x^5 + 38x^4 - 42x^3 + 27x^2 - 8x + 1	\( 2^{8}\cdot 3^{6}\cdot 89^{4} \)	$S_5$ (as 12T74)	$[2]$
12.0.42681865994496.1	x^12 - 6x^11 + 13x^10 - 8x^9 - 16x^8 + 32x^7 + 9x^6 - 106x^5 + 160x^4 - 114x^3 + 63x^2 - 54x + 27	\( 2^{8}\cdot 3^{8}\cdot 71^{4} \)	$S_5$ (as 12T74)	Trivial
12.4.107495424000000.1	x^12 + 3x^10 - 8x^9 - 6x^8 - 12x^7 + 45x^6 - 12x^5 - 6x^4 - 8x^3 + 3x^2 + 1	\( 2^{20}\cdot 3^{8}\cdot 5^{6} \)	$S_5$ (as 12T74)	Trivial
12.4.115157043765625.1	x^12 - x^10 + 2x^8 + 4x^6 - 3x^4 - 3x^2 + 1	\( 5^{6}\cdot 293^{4} \)	$S_5$ (as 12T74)	Trivial
12.4.256000000000000.1	x^12 - 2x^11 - 4x^10 + 10x^9 - 5x^8 - 20x^7 + 40x^6 - 25x^4 + 30x^3 - 10x + 5	\( 2^{20}\cdot 5^{12} \)	$S_5$ (as 12T74)	Trivial
12.0.386869246296064.2	x^12 - 2x^10 + 3x^8 - 4x^6 + 19x^4 - 34x^2 + 49	\( 2^{26}\cdot 7^{8} \)	$S_5$ (as 12T74)	Trivial
12.4.625000000000000.1	x^12 - 6x^11 + 9x^10 + 10x^9 - 40x^8 + 28x^7 + 37x^6 - 78x^5 + 40x^4 + 40x^3 - 59x^2 + 24x - 1	\( 2^{12}\cdot 5^{16} \)	$S_5$ (as 12T74)	Trivial
12.4.1024000000000000.4	x^12 - 6x^11 + 11x^10 - 15x^8 - 6x^7 + 21x^6 + 24x^5 - 50x^4 + 20x^3 - 16x^2 + 16x + 4	\( 2^{22}\cdot 5^{12} \)	$S_5$ (as 12T74)	Trivial
12.4.3421422626013184.4	x^12 + 2x^10 + 11x^8 + 7x^4 - 18x^2 + 1	\( 2^{22}\cdot 13^{8} \)	$S_5$ (as 12T74)	Trivial
12.0.10000000000000000.1	x^12 - 6x^11 + 13x^10 - 10x^9 + 5x^8 - 26x^7 + 41x^6 - 8x^5 + 20x^4 - 70x^3 + 8x^2 + 32x + 74	\( 2^{16}\cdot 5^{16} \)	$S_5$ (as 12T74)	$[2]$
12.4.10000000000000000.1	x^12 - 4x^11 + 14x^10 - 20x^9 + 10x^8 + 24x^7 - 66x^6 - 24x^5 + 10x^4 + 20x^3 + 14x^2 + 4x + 1	\( 2^{16}\cdot 5^{16} \)	$S_5$ (as 12T74)	Trivial
12.0.16384000000000000.6	x^12 - 4x^11 + 14x^10 - 40x^9 + 85x^8 - 156x^7 + 244x^6 - 344x^5 + 460x^4 - 480x^3 + 464x^2 - 256x + 96	\( 2^{26}\cdot 5^{12} \)	$S_5$ (as 12T74)	$[2]$
12.0.16384000000000000.7	x^12 - 4x^11 + 8x^10 - 20x^9 + 25x^8 - 8x^7 + 32x^6 + 16x^5 - 140x^4 + 32x^2 + 112x + 196	\( 2^{26}\cdot 5^{12} \)	$S_5$ (as 12T74)	Trivial (GRH)
12.0.16384000000000000.8	x^12 + 15x^8 - 8x^7 + 40x^5 + 175x^4 + 40x^3 + 32x^2 + 120x + 225	\( 2^{26}\cdot 5^{12} \)	$S_5$ (as 12T74)	Trivial (GRH)
12.4.24414062500000000.1	x^12 - x^11 - x^10 + 20x^9 - 15x^8 - 7x^7 - 28x^6 + 197x^5 + 155x^4 - 60x^3 - 39x^2 - x - 1	\( 2^{8}\cdot 5^{20} \)	$S_5$ (as 12T74)	$[2]$
12.4.40000000000000000.1	x^12 - 4x^11 + 4x^10 - 20x^9 + 25x^8 - 8x^7 + 2x^6 - 32x^5 + 30x^4 + 6x^2 - 4x - 1	\( 2^{18}\cdot 5^{16} \)	$S_5$ (as 12T74)	$[4]$
12.0.57541523968884736.5	x^12 - 2x^11 + 7x^10 - 20x^9 + 44x^8 - 76x^7 + 210x^6 - 216x^5 + 228x^4 - 176x^3 + 184x^2 - 96x + 16	\( 2^{28}\cdot 11^{8} \)	$S_5$ (as 12T74)	$[2]$
12.4.57541523968884736.6	x^12 - 2x^11 - 3x^10 - 6x^9 - 2x^8 + 14x^7 - 31x^6 + 58x^5 + 317x^4 + 220x^3 - 154x^2 - 220x - 66	\( 2^{28}\cdot 11^{8} \)	$S_5$ (as 12T74)	Trivial
12.4.65536000000000000.4	x^12 - 32x^7 - 40x^6 - 80x^5 - 25x^4 + 80x^3 + 116x^2 + 160x + 60	\( 2^{28}\cdot 5^{12} \)	$S_5$ (as 12T74)	$[2]$
12.0.65536000000000000.10	x^12 - 10x^10 + 5x^8 - 32x^7 + 100x^6 + 160x^5 + 190x^4 + 200x^3 + 176x^2 + 80x + 40	\( 2^{28}\cdot 5^{12} \)	$S_5$ (as 12T74)	$[2]$
12.0.65536000000000000.15	x^12 + 8x^10 + 10x^8 - 100x^6 + 25x^4 + 100x^2 + 100	\( 2^{28}\cdot 5^{12} \)	$S_5$ (as 12T74)	Trivial (GRH)
12.4.75826372274028544.3	x^12 - 2x^11 - 7x^10 + 22x^9 + 5x^8 - 84x^7 + 50x^6 + 140x^5 - 130x^4 - 160x^3 + 112x^2 + 80x + 8	\( 2^{28}\cdot 7^{10} \)	$S_5$ (as 12T74)	$[3]$
12.0.82115019702009856.11	x^12 - 4x^11 + 9x^10 - 22x^9 + 45x^8 - 40x^7 + 27x^6 - 86x^5 + 22x^4 + 48x^3 + 96x^2 + 48x + 16	\( 2^{20}\cdot 23^{8} \)	$S_5$ (as 12T74)	$[2]$ (GRH)
12.4.160000000000000000.4	x^12 - 2x^11 - 14x^10 + 30x^9 + 55x^8 - 120x^7 - 120x^6 + 340x^5 - 225x^4 + 50x^3 + 30x^2 - 10x + 5	\( 2^{20}\cdot 5^{16} \)	$S_5$ (as 12T74)	Trivial
12.0.218971048064843776.81	x^12 - 6x^11 + 13x^10 - 2x^9 - 36x^8 + 30x^7 + 187x^6 - 726x^5 + 1395x^4 - 1700x^3 + 1378x^2 - 716x + 194	\( 2^{28}\cdot 13^{8} \)	$S_5$ (as 12T74)	$[3]$ (GRH)
12.0.262144000000000000.4	x^12 - 8x^10 + 45x^8 - 120x^6 + 160x^4 - 112x^2 + 36	\( 2^{30}\cdot 5^{12} \)	$S_5$ (as 12T74)	Trivial (GRH)
12.4.262144000000000000.4	x^12 + 8x^10 + 5x^8 - 80x^6 + 160x^4 - 128x^2 + 36	\( 2^{30}\cdot 5^{12} \)	$S_5$ (as 12T74)	Trivial
12.4.262144000000000000.6	x^12 - 4x^11 + 4x^10 - 20x^9 + 70x^8 - 76x^7 + 164x^6 - 364x^5 + 25x^4 + 400x^3 + 144x^2 - 576x + 216	\( 2^{30}\cdot 5^{12} \)	$S_5$ (as 12T74)	$[2]$
12.4.390625000000000000.1	x^12 - 2x^11 - 4x^10 + 40x^7 - 80x^6 + 40x^5 + 320x^2 + 160x - 80	\( 2^{12}\cdot 5^{20} \)	$S_5$ (as 12T74)	Trivial (GRH)
12.4.390625000000000000.2	x^12 - 2x^11 - 4x^10 + 25x^8 - 10x^7 - 30x^6 + 40x^5 - 125x^4 + 150x^3 + 30x^2 - 60x - 20	\( 2^{12}\cdot 5^{20} \)	$S_5$ (as 12T74)	Trivial (GRH)
12.4.401805558271246336.1	x^12 - 2x^11 - 4x^10 + 8x^9 + 18x^8 - 16x^7 - 64x^6 + 32x^5 + 72x^4 - 64x^3 - 64x^2 + 64x + 64	\( 2^{16}\cdot 19^{10} \)	$S_5$ (as 12T74)	$[3]$
12.4.415989582513831936.56	x^12 - 12x^10 + 90x^8 - 308x^6 + 633x^4 - 432x^2 + 64	\( 2^{30}\cdot 3^{18} \)	$S_5$ (as 12T74)	$[3]$
12.0.524546382716993536.12	x^12 - 4x^11 + 5x^10 + 2x^9 + 5x^8 - 72x^7 + 119x^6 + 82x^5 - 362x^4 + 48x^3 + 768x^2 - 976x + 400	\( 2^{20}\cdot 29^{8} \)	$S_5$ (as 12T74)	$[2]$ (GRH)
12.4.638686677648277504.23	x^12 - 12x^10 + 2x^8 + 172x^6 + 481x^4 - 384x^2 + 256	\( 2^{30}\cdot 29^{6} \)	$S_5$ (as 12T74)	$[2]$
12.0.640000000000000000.11	x^12 - 2x^11 + 11x^10 - 20x^9 + 35x^8 - 58x^7 + 21x^6 - 28x^5 - 20x^4 + 60x^3 + 56x^2 - 32x + 76	\( 2^{22}\cdot 5^{16} \)	$S_5$ (as 12T74)	$[4]$
12.4.640000000000000000.13	x^12 - 18x^10 + 115x^8 - 360x^6 + 575x^4 - 422x^2 + 81	\( 2^{22}\cdot 5^{16} \)	$S_5$ (as 12T74)	Trivial
12.4.935976560656121856.66	x^12 - 6x^10 - 12x^9 + 48x^8 - 236x^6 + 648x^5 - 252x^4 - 1152x^3 + 1728x^2 - 864x + 144	\( 2^{28}\cdot 3^{20} \)	$S_5$ (as 12T74)	Trivial
12.4.1723216827597623296.3	x^12 + 6x^10 + 15x^8 + 20x^6 + 15x^4 - 110x^2 + 1	\( 2^{12}\cdot 29^{10} \)	$S_5$ (as 12T74)	Trivial
12.12.1844033634304000000.1	x^12 - 24x^10 + 192x^8 - 664x^6 + 992x^4 - 512x^2 + 16	\( 2^{20}\cdot 5^{6}\cdot 103^{4} \)	$S_5$ (as 12T74)	Trivial (GRH)
12.0.2098185530867974144.3	x^12 + 14x^10 - 28x^9 + 89x^8 - 52x^7 - 226x^6 + 216x^5 + 285x^4 - 516x^3 + 308x^2 - 84x + 9	\( 2^{22}\cdot 29^{8} \)	$S_5$ (as 12T74)	$[4]$ (GRH)
12.4.2105947261476274176.1	x^12 - 6x^10 - 12x^9 - 21x^8 + 144x^7 + 316x^6 - 288x^5 - 1101x^4 + 48x^3 + 1506x^2 + 108x - 599	\( 2^{26}\cdot 3^{22} \)	$S_5$ (as 12T74)	Trivial
12.0.3577284289902936064.30	x^12 + 6x^10 - 4x^9 + 32x^8 - 64x^7 + 82x^6 - 16x^5 + 612x^4 + 128x^3 + 2872x^2 + 2432x + 1392	\( 2^{22}\cdot 31^{8} \)	$S_5$ (as 12T74)	$[8]$
12.4.3743906242624487424.135	x^12 + 54x^8 - 324x^6 + 729x^4 - 972x^2 + 324	\( 2^{30}\cdot 3^{20} \)	$S_5$ (as 12T74)	Trivial
12.4.5255361260928630784.1	x^12 - 4x^11 + 2x^10 - 16x^9 + 64x^8 + 76x^7 - 436x^6 + 792x^5 - 2183x^4 + 4608x^3 - 5702x^2 + 4504x - 1654	\( 2^{26}\cdot 23^{8} \)	$S_5$ (as 12T74)	Trivial (GRH)
12.0.6250000000000000000.6	x^12 - 4x^11 - x^10 + 60x^9 - 205x^8 + 198x^7 + 758x^6 - 3508x^5 + 7390x^4 - 9520x^3 + 7856x^2 - 4224x + 1504	\( 2^{16}\cdot 5^{20} \)	$S_5$ (as 12T74)	$[2, 2]$ (GRH)
12.4.7490162518480912384.4	x^12 - 4x^11 + 2x^10 - 4x^9 + 101x^8 - 480x^7 + 996x^6 - 960x^5 + 404x^4 - 32x^3 + 32x^2 - 128x + 64	\( 2^{30}\cdot 17^{8} \)	$S_5$ (as 12T74)	Trivial
12.0.8423789045905096704.125	x^12 - 6x^10 + 51x^8 - 72x^7 - 200x^6 + 216x^5 + 1338x^4 - 1488x^3 - 1032x^2 - 288x + 2920	\( 2^{28}\cdot 3^{22} \)	$S_5$ (as 12T74)	$[4]$ (GRH)
12.0.10240000000000000000.17	x^12 - 4x^11 + 14x^10 - 20x^9 + 115x^8 - 192x^7 + 138x^6 - 568x^5 + 770x^4 + 360x^3 + 1496x^2 - 1904x + 824	\( 2^{26}\cdot 5^{16} \)	$S_5$ (as 12T74)	$[2]$ (GRH)
12.12.20525657038395450841.1	x^12 - x^11 - 20x^10 + 17x^9 + 140x^8 - 87x^7 - 408x^6 + 113x^5 + 464x^4 + 55x^3 - 106x^2 - 18x + 1	\( 29^{6}\cdot 431^{4} \)	$S_5$ (as 12T74)	Trivial
12.4.21021445043714523136.19	x^12 - 4x^10 - 50x^8 - 184x^7 + 32x^6 + 368x^5 - 200x^4 - 64x^2 + 64	\( 2^{28}\cdot 23^{8} \)	$S_5$ (as 12T74)	Trivial (GRH)