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 250)

Label	Polynomial	Discriminant	Galois group	Class group
12.2.644204000000.2	x^12 - 3x^11 + 2x^10 + 4x^9 - 7x^8 + 2x^7 + 3x^6 + 2x^5 - 7x^4 + 4x^3 + 2x^2 - 3x + 1	\( -\,2^{8}\cdot 5^{6}\cdot 11^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.3133812796875.1	x^12 - x^11 - 4x^10 + 6x^9 + 2x^8 - 11x^7 + 11x^6 - x^5 - 9x^4 + 10x^3 - 2x^2 - 2x + 1	\( -\,3^{4}\cdot 5^{6}\cdot 19^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.13963577987072.1	x^12 - 2x^11 + 2x^10 + 10x^8 - 6x^7 + x^6 - 10x^5 + 6x^4 + 2x^3 + 2x^2 - 2x + 1	\( 2^{12}\cdot 7^{4}\cdot 17^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.26995979190272.1	x^12 - 2x^11 - 3x^10 + 10x^9 - 9x^8 - 8x^7 + 18x^6 - 12x^5 - 7x^4 + 10x^3 - 3x^2 + 2x - 1	\( -\,2^{22}\cdot 23^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.30148766466048.1	x^12 - 2x^11 + 5x^10 - 6x^9 + 12x^8 - 18x^7 + 31x^6 - 46x^5 + 55x^4 - 52x^3 + 36x^2 - 16x + 4	\( 2^{18}\cdot 3^{4}\cdot 17^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.36322536628125.1	x^12 - 3x^6 + 5	\( 3^{8}\cdot 5^{5}\cdot 11^{6} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.107983916761088.12	x^12 + 2x^10 - 12x^9 + 2x^8 + 26x^6 - 16x^5 + 2x^4 - 4x^2 - 4x + 1	\( -\,2^{24}\cdot 23^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.164916224000000.1	x^12 + x^10 - 3x^8 + 6x^6 - 33x^4 + 33x^2 + 11	\( 2^{16}\cdot 5^{6}\cdot 11^{5} \)	$D_6:D_6$ (as 12T81)	$[2]$
12.4.164916224000000.1	x^12 - x^10 - 3x^8 - 6x^6 - 33x^4 - 33x^2 + 11	\( 2^{16}\cdot 5^{6}\cdot 11^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.4.207746946367488.1	x^12 - 4x^11 - x^10 + 20x^9 - 14x^8 - 20x^7 - x^6 + 46x^5 - 8x^4 - 30x^3 - 15x^2 + 18x + 9	\( 2^{16}\cdot 3^{9}\cdot 11^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.344119977181184.1	x^12 - 6x^11 + 14x^10 - 10x^9 - 19x^8 + 24x^7 + 28x^6 - 24x^5 - 19x^4 + 10x^3 + 14x^2 + 6x + 1	\( 2^{24}\cdot 29^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.559724432982016.10	x^12 - 6x^10 + 17x^8 - 29x^4 - 10x^2 - 1	\( -\,2^{32}\cdot 19^{4} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.559724432982016.16	x^12 + 6x^10 + 17x^8 - 29x^4 + 10x^2 - 1	\( -\,2^{32}\cdot 19^{4} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.1376479908724736.14	x^12 + 2x^8 - 20x^6 + 145x^4 - 116x^2 + 116	\( 2^{26}\cdot 29^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.2282521714753536.6	x^12 - 4x^6 - 4	\( -\,2^{32}\cdot 3^{12} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.2282521714753536.7	x^12 + 4x^6 - 4	\( -\,2^{32}\cdot 3^{12} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.4477795463856128.7	x^12 - 18x^8 - 24x^6 - 20x^4 - 8x^2 - 2	\( -\,2^{35}\cdot 19^{4} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.4477795463856128.16	x^12 - 18x^8 + 24x^6 - 20x^4 + 8x^2 - 2	\( -\,2^{35}\cdot 19^{4} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.6847565144260608.3	x^12 + 2x^10 - 11x^8 - 4x^6 + 55x^4 - 22x^2 + 3	\( 2^{32}\cdot 3^{13} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.6847565144260608.13	x^12 - 2x^10 - 11x^8 + 4x^6 + 55x^4 + 22x^2 + 3	\( 2^{32}\cdot 3^{13} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.6847565144260608.20	x^12 - 4x^6 + 12	\( 2^{32}\cdot 3^{13} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.6847565144260608.21	x^12 + 4x^6 + 12	\( 2^{32}\cdot 3^{13} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.14280872991653888.2	x^12 - 4x^11 - 4x^10 + 28x^9 + 3x^8 - 64x^7 + 28x^6 + 44x^5 - 63x^4 + 52x^3 + 116x^2 + 16x - 16	\( -\,2^{22}\cdot 23^{7} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.18260173718028288.28	x^12 - 8x^6 - 2	\( -\,2^{35}\cdot 3^{12} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.18260173718028288.33	x^12 + 8x^6 - 2	\( -\,2^{35}\cdot 3^{12} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.18260173718028288.49	x^12 - 8x^6 + 18	\( 2^{35}\cdot 3^{12} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.18260173718028288.50	x^12 + 8x^6 + 18	\( 2^{35}\cdot 3^{12} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.19499511680335872.7	x^12 + 6x^10 - 4x^9 - 36x^7 + 78x^6 - 216x^5 + 297x^4 - 256x^3 + 216x^2 - 24x - 8	\( -\,2^{24}\cdot 3^{19} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.19499511680335872.20	x^12 - 6x^10 - 8x^9 - 24x^8 - 84x^7 - 174x^6 - 300x^5 - 375x^4 - 320x^3 - 204x^2 - 72x + 4	\( -\,2^{24}\cdot 3^{19} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.20542695432781824.14	x^12 - 6x^10 - 3x^8 - 24x^6 - 9x^4 - 18x^2 - 9	\( -\,2^{32}\cdot 3^{14} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.20542695432781824.18	x^12 + 6x^10 - 3x^8 + 24x^6 - 9x^4 + 18x^2 - 9	\( -\,2^{32}\cdot 3^{14} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.27643882690838528.1	x^12 + 14x^8 + 20x^6 - 23x^4 + 92x^2 + 92	\( 2^{32}\cdot 23^{5} \)	$D_6:D_6$ (as 12T81)	$[2]$
12.4.27643882690838528.3	x^12 + 14x^8 - 20x^6 - 23x^4 - 92x^2 + 92	\( 2^{32}\cdot 23^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.44047357079191552.2	x^12 - 4x^11 + 10x^10 - 8x^9 - 56x^8 + 144x^7 + 24x^6 - 512x^5 + 838x^4 - 640x^3 + 252x^2 - 48x + 4	\( 2^{31}\cdot 29^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.44047357079191552.4	x^12 - 4x^11 + 10x^10 - 36x^9 + 98x^8 - 180x^7 + 400x^6 - 1012x^5 + 1721x^4 - 1720x^3 + 1018x^2 - 336x + 50	\( 2^{31}\cdot 29^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.6.45755155136000000.1	x^12 - 6x^11 + 4x^10 + 32x^9 - 19x^8 - 68x^7 - 73x^6 - 28x^5 + 109x^4 + 188x^3 + 126x^2 + 40x + 5	\( -\,2^{12}\cdot 5^{6}\cdot 59^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.6.53804562284000000.1	x^12 - 2x^11 - 8x^10 + 17x^9 - 33x^8 + 12x^7 + 139x^6 + 42x^5 - 303x^4 - 347x^3 + 1131x^2 + 23x - 1061	\( -\,2^{8}\cdot 5^{6}\cdot 11^{5}\cdot 17^{4} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.57123491966615552.53	x^12 - 4x^11 + 2x^10 + 12x^9 - 62x^8 + 88x^7 + 210x^6 - 84x^5 - 23x^4 + 388x^3 + 140x^2 - 16x - 8	\( -\,2^{24}\cdot 23^{7} \)	$D_6:D_6$ (as 12T81)	Trivial
12.12.62328574510453125.1	x^12 - 3x^11 - 15x^10 + 45x^9 + 69x^8 - 216x^7 - 118x^6 + 400x^5 + 67x^4 - 233x^3 - 30x^2 + 13x + 1	\( 3^{4}\cdot 5^{6}\cdot 7^{4}\cdot 29^{5} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.77998046721343488.25	x^12 + 12x^10 - 4x^9 + 54x^8 - 36x^7 + 108x^6 - 162x^4 + 224x^3 - 108x^2 + 24x + 4	\( -\,2^{26}\cdot 3^{19} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.77998046721343488.26	x^12 - 15x^8 - 36x^7 - 6x^6 + 18x^4 - 12x^3 + 36x^2 + 6	\( -\,2^{26}\cdot 3^{19} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.98716277881700352.15	x^12 - 24x^9 - 27x^8 - 36x^7 + 228x^6 + 216x^5 + 531x^4 - 408x^3 + 648x^2 + 288x + 2352	\( 2^{20}\cdot 3^{23} \)	$D_6:D_6$ (as 12T81)	$[2]$
12.0.98716277881700352.16	x^12 - 18x^10 - 12x^9 + 162x^8 + 216x^7 - 576x^6 - 1296x^5 + 108x^4 + 2400x^3 + 2592x^2 + 1152x + 192	\( 2^{20}\cdot 3^{23} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.138663194171277312.2	x^12 - 2x^6 + 3	\( 2^{30}\cdot 3^{17} \)	$D_6:D_6$ (as 12T81)	$[3]$
12.0.138663194171277312.3	x^12 + 2x^6 + 3	\( 2^{30}\cdot 3^{17} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.138663194171277312.42	x^12 - 18x^6 + 243	\( 2^{30}\cdot 3^{17} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.138663194171277312.43	x^12 + 18x^6 + 243	\( 2^{30}\cdot 3^{17} \)	$D_6:D_6$ (as 12T81)	Trivial
12.2.164341563462254592.27	x^12 - 18x^8 - 72x^6 - 108x^4 - 72x^2 - 18	\( -\,2^{35}\cdot 3^{14} \)	$D_6:D_6$ (as 12T81)	$[3]$
12.2.164341563462254592.42	x^12 - 18x^8 + 72x^6 - 108x^4 + 72x^2 - 18	\( -\,2^{35}\cdot 3^{14} \)	$D_6:D_6$ (as 12T81)	Trivial
12.0.164341563462254592.47	x^12 + 8x^10 + 22x^8 + 60x^4 - 96x^2 + 72	\( 2^{35}\cdot 3^{14} \)	$D_6:D_6$ (as 12T81)	$[2]$