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 58)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.699484667904.1	x^12 - 6x^11 + 11x^10 - 18x^8 + 6x^7 + 13x^6 + 6x^5 - 18x^4 + 11x^2 - 6x + 1	\( 2^{16}\cdot 3^{6}\cdot 11^{4} \)	$S_3^2$ (as 12T16)	Trivial
12.0.937024000000.1	x^12 - 4x^11 + 8x^10 - 12x^9 + 15x^8 - 18x^7 + 24x^6 - 26x^5 + 21x^4 - 18x^3 + 18x^2 - 12x + 4	\( 2^{12}\cdot 5^{6}\cdot 11^{4} \)	$S_3^2$ (as 12T16)	Trivial
12.0.1911029760000.1	x^12 - 6x^11 + 17x^10 - 30x^9 + 42x^8 - 54x^7 + 69x^6 - 78x^5 + 68x^4 - 42x^3 + 19x^2 - 6x + 1	\( 2^{22}\cdot 3^{6}\cdot 5^{4} \)	$S_3^2$ (as 12T16)	Trivial
12.0.4694952902656.12	x^12 - 4x^11 + 6x^10 - 14x^8 + 16x^7 + 10x^6 - 32x^5 + 9x^4 + 20x^3 - 12x^2 + 8	\( 2^{24}\cdot 23^{4} \)	$S_3^2$ (as 12T16)	Trivial
12.0.6718464000000.1	x^12 - 4x^9 - 8x^8 + 4x^7 + 8x^6 + 16x^5 + 28x^4 + 16x^3 + 8x^2 + 8x + 4	\( 2^{16}\cdot 3^{8}\cdot 5^{6} \)	$S_3^2$ (as 12T16)	Trivial
12.0.9003384318096.1	x^12 - 3x^11 + 12x^10 - 31x^9 + 69x^8 - 108x^7 + 143x^6 - 129x^5 + 78x^4 - 11x^3 - 3x^2 - 6x + 4	\( 2^{4}\cdot 3^{14}\cdot 7^{6} \)	$S_3^2$ (as 12T16)	Trivial
12.0.11866206109696.7	x^12 - 4x^11 + 8x^10 - 8x^9 + 11x^8 - 16x^7 + 34x^6 - 60x^5 + 78x^4 - 72x^3 + 56x^2 - 32x + 8	\( 2^{24}\cdot 29^{4} \)	$S_3^2$ (as 12T16)	Trivial
12.0.13722579360000.2	x^12 - 3x^11 + 3x^10 - x^8 + 3x^7 - 6x^6 + 3x^5 + x^4 + 6x^3 - 3x^2 - 9x + 9	\( 2^{8}\cdot 3^{6}\cdot 5^{4}\cdot 7^{6} \)	$S_3^2$ (as 12T16)	Trivial
12.0.19131876000000.2	x^12 - 6x^11 + 27x^10 - 80x^9 + 189x^8 - 342x^7 + 507x^6 - 594x^5 + 540x^4 - 362x^3 + 156x^2 - 36x + 4	\( 2^{8}\cdot 3^{14}\cdot 5^{6} \)	$S_3^2$ (as 12T16)	Trivial
12.0.19275612160000.1	x^12 - 6x^11 + 15x^10 - 20x^9 + 7x^8 + 26x^7 - 45x^6 + 26x^5 + 7x^4 - 20x^3 + 15x^2 - 6x + 1	\( 2^{18}\cdot 5^{4}\cdot 7^{6} \)	$S_3^2$ (as 12T16)	Trivial
12.0.20061226008576.1	x^12 - 6x^11 + 21x^10 - 50x^9 + 72x^8 - 54x^7 + 33x^6 - 54x^5 + 72x^4 - 50x^3 + 21x^2 - 6x + 1	\( 2^{22}\cdot 3^{14} \)	$S_3^2$ (as 12T16)	Trivial
12.0.20061226008576.3	x^12 - 6x^11 + 13x^10 - 10x^9 - 8x^8 + 26x^7 - 35x^6 + 38x^5 - 2x^4 - 42x^3 + 43x^2 - 18x + 3	\( 2^{22}\cdot 3^{14} \)	$S_3^2$ (as 12T16)	Trivial
12.0.25389989167104.6	x^12 + 8x^6 + 4	\( 2^{16}\cdot 3^{18} \)	$S_3^2$ (as 12T16)	Trivial
12.0.46708681640625.2	x^12 - 3x^11 + 3x^10 - 18x^7 + 99x^6 - 234x^5 + 315x^4 - 270x^3 + 153x^2 - 54x + 9	\( 3^{14}\cdot 5^{10} \)	$S_3^2$ (as 12T16)	Trivial
12.0.72964670628096.1	x^12 - x^11 - x^10 + 12x^9 - 5x^8 - 5x^7 + 52x^6 - 35x^5 + 37x^4 + 24x^3 + 23x^2 + 5x + 1	\( 2^{8}\cdot 3^{10}\cdot 13^{6} \)	$S_3^2$ (as 12T16)	$[2]$
12.0.101559956668416.8	x^12 - 4x^9 + 52x^6 + 24x^3 + 3	\( 2^{18}\cdot 3^{18} \)	$S_3^2$ (as 12T16)	Trivial
12.0.128536820158464.5	x^12 - 6x^9 + 18x^6 - 18x^3 + 9	\( 2^{12}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.135573141513744.1	x^12 + 19x^6 + 16	\( 2^{4}\cdot 3^{14}\cdot 11^{6} \)	$S_3^2$ (as 12T16)	Trivial
12.0.197324726861824.3	x^12 - 4x^10 - 4x^9 + 30x^8 + 12x^7 + 24x^6 + 16x^5 + 36x^4 - 16x^3 + 28x^2 - 8x + 4	\( 2^{22}\cdot 19^{6} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.294122500000000.1	x^12 - 3x^11 + 9x^10 - 20x^9 + 45x^8 - 63x^7 + 84x^6 - 87x^5 + 95x^4 - 40x^3 + 29x^2 - 7x + 1	\( 2^{8}\cdot 5^{10}\cdot 7^{6} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.302534120546064.1	x^12 - 6x^11 + 17x^10 - 30x^9 + 33x^8 - 18x^7 + 3x^6 - 6x^5 + 11x^4 - 6x^3 + 7x^2 - 6x + 4	\( 2^{4}\cdot 3^{6}\cdot 11^{10} \)	$S_3^2$ (as 12T16)	Trivial
12.0.490329056390625.1	x^12 + 9x^6 + 9	\( 3^{22}\cdot 5^{6} \)	$S_3^2$ (as 12T16)	Trivial
12.0.592143556000000.1	x^12 - 5x^11 + 13x^10 - 28x^9 + 63x^8 - 73x^7 - 18x^6 + 133x^5 - 33x^4 - 38x^3 + 37x^2 + 11x + 1	\( 2^{8}\cdot 5^{6}\cdot 23^{6} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.684178814003344.1	x^12 - 2x^11 + 9x^10 - 4x^9 + 21x^8 + 4x^7 + 39x^6 + 10x^5 + 45x^4 + 72x^3 + 31x^2 + 6x + 4	\( 2^{4}\cdot 11^{6}\cdot 17^{6} \)	$S_3^2$ (as 12T16)	Trivial
12.0.708051067974441.1	x^12 - 4x^9 + 31x^6 - 54x^3 + 27	\( 3^{14}\cdot 23^{6} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.722204136308736.19	x^12 - 12x^9 + 18x^8 - 36x^7 + 72x^6 - 108x^5 + 249x^4 - 492x^3 + 648x^2 - 504x + 196	\( 2^{24}\cdot 3^{16} \)	$S_3^2$ (as 12T16)	Trivial
12.0.1094032426497921.1	x^12 - 2x^9 + 109x^6 - 108x^3 + 27	\( 3^{6}\cdot 107^{6} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.1624959306694656.21	x^12 + 40x^6 + 16	\( 2^{22}\cdot 3^{18} \)	$S_3^2$ (as 12T16)	Trivial
12.0.1624959306694656.35	x^12 - 6x^11 + 21x^10 - 42x^9 + 54x^8 - 54x^7 + 85x^6 - 174x^5 + 132x^4 + 42x^3 + 27x^2 - 198x + 121	\( 2^{22}\cdot 3^{18} \)	$S_3^2$ (as 12T16)	Trivial
12.0.1699835058651136.5	x^12 - 4x^11 + 7x^10 + 6x^9 - 50x^8 + 88x^7 - 9x^6 - 242x^5 + 518x^4 - 580x^3 + 391x^2 - 150x + 25	\( 2^{16}\cdot 11^{10} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.1776132919332864.1	x^12 - 4x^11 + 2x^10 + 12x^9 - 4x^8 - 34x^7 + 15x^6 + 44x^5 + 34x^4 - 14x^3 + 15x^2 - 4x + 1	\( 2^{12}\cdot 3^{6}\cdot 29^{6} \)	$S_3^2$ (as 12T16)	$[6]$
12.0.2056589122535424.16	x^12 + 24x^6 + 36	\( 2^{16}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.2056589122535424.22	x^12 - 12x^9 + 72x^6 - 144x^3 + 144	\( 2^{16}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.3550014724000000.1	x^12 - 4x^11 + 11x^10 - 28x^9 + 96x^8 - 246x^7 + 359x^6 - 306x^5 + 174x^4 - 82x^3 + 33x^2 - 8x + 1	\( 2^{8}\cdot 5^{6}\cdot 31^{6} \)	$S_3^2$ (as 12T16)	$[6]$
12.0.4244902593608889.2	x^12 - 12x^9 + 83x^6 - 282x^3 + 343	\( 3^{14}\cdot 31^{6} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.6499837226778624.20	x^12 - 12x^10 + 54x^8 - 88x^6 - 39x^4 + 180x^2 + 4	\( 2^{24}\cdot 3^{18} \)	$S_3^2$ (as 12T16)	$[2]$
12.0.6499837226778624.35	x^12 - 8x^9 + 36x^8 - 36x^7 + 30x^6 - 36x^5 + 81x^4 - 20x^3 - 18x^2 + 36x + 22	\( 2^{24}\cdot 3^{18} \)	$S_3^2$ (as 12T16)	$[2]$
12.0.8226356490141696.13	x^12 + 18x^6 + 9	\( 2^{18}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.8226356490141696.18	x^12 + 12x^6 - 36x^3 + 27	\( 2^{18}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.8226356490141696.37	x^12 - 12x^9 + 84x^6 - 216x^3 + 243	\( 2^{18}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.11057373810786304.1	x^12 - 10x^10 - 8x^9 + 63x^8 + 48x^7 - 60x^6 + 44x^5 + 231x^4 - 68x^3 + 58x^2 - 16x + 4	\( 2^{18}\cdot 59^{6} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.11957422500000000.1	x^12 + 3x^10 - 20x^9 + 60x^8 - 120x^7 + 275x^6 - 780x^5 + 1620x^4 - 2020x^3 + 1503x^2 - 660x + 139	\( 2^{8}\cdot 3^{14}\cdot 5^{10} \)	$S_3^2$ (as 12T16)	$[3]$
12.12.49632710656000000.1	x^12 - 4x^11 - 16x^10 + 92x^9 - 15x^8 - 536x^7 + 878x^6 + 52x^5 - 1109x^4 + 720x^3 + 38x^2 - 104x + 4	\( 2^{18}\cdot 5^{6}\cdot 59^{4} \)	$S_3^2$ (as 12T16)	Trivial (GRH)
12.0.131621703842267136.43	x^12 + 36x^6 + 36	\( 2^{22}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.131621703842267136.44	x^12 + 60x^6 + 36	\( 2^{22}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.131621703842267136.65	x^12 - 12x^9 + 336x^6 - 360x^3 + 108	\( 2^{22}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.131621703842267136.76	x^12 - 6x^11 + 21x^10 - 26x^9 - 18x^8 + 90x^7 + 57x^6 - 522x^5 + 882x^4 - 542x^3 + 489x^2 - 1050x + 625	\( 2^{22}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	$[3]$
12.0.131621703842267136.88	x^12 + 72x^6 + 144	\( 2^{22}\cdot 3^{22} \)	$S_3^2$ (as 12T16)	Trivial
12.0.169682989931106304.1	x^12 - 6x^11 + 21x^10 - 50x^9 + 67x^8 - 34x^7 + 3x^6 - 34x^5 + 67x^4 - 50x^3 + 21x^2 - 6x + 1	\( 2^{12}\cdot 23^{10} \)	$S_3^2$ (as 12T16)	$[3]$
12.12.268738560000000000.1	x^12 - 6x^11 + x^10 + 50x^9 - 80x^8 - 46x^7 + 161x^6 - 46x^5 - 80x^4 + 50x^3 + x^2 - 6x + 1	\( 2^{22}\cdot 3^{8}\cdot 5^{10} \)	$S_3^2$ (as 12T16)	Trivial (GRH)