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 80)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.12657677564169.1	x^12 - x^10 - 4x^9 - 2x^8 + 3x^7 + 3x^6 + 4x^5 + 6x^4 - x^3 - 2x^2 + x + 1	\( 3^{10}\cdot 11^{8} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.15850845241344.1	x^12 - 4x^11 + 10x^10 - 12x^9 + 2x^8 + 20x^7 - 32x^6 + 16x^5 + 16x^4 - 24x^3 + 10x^2 + 1	\( 2^{28}\cdot 3^{10} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.39077188880625.1	x^12 + 3x^10 - 3x^9 + 3x^8 + 18x^7 - 52x^6 + 30x^5 + 51x^4 - 87x^3 + 51x^2 - 12x + 1	\( 3^{12}\cdot 5^{4}\cdot 7^{6} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.62882616180736.5	x^12 - 8x^9 - x^8 + 32x^6 + 7x^4 - 32x^3 + 32x^2 - 24x + 9	\( 2^{32}\cdot 11^{4} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.89679990882304.3	x^12 - 12x^10 + 49x^8 - 76x^6 + 28x^4 + 24x^2 + 4	\( 2^{30}\cdot 17^{4} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.142657607172096.1	x^12 - 2x^11 - x^10 - 6x^9 - 8x^8 + 26x^7 + 61x^6 + 26x^5 - 8x^4 - 6x^3 - x^2 - 2x + 1	\( 2^{28}\cdot 3^{12} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.207778300343289.1	x^12 + 6x^10 - 2x^9 + 27x^8 - 9x^7 + 49x^6 - 27x^5 + 66x^4 - 21x^3 + 36x^2 + 9x + 9	\( 3^{16}\cdot 13^{6} \)	$S_3\wr C_2$ (as 12T34)	$[2]$
12.0.228509902503936.2	x^12 - 2x^9 - 9x^8 + 6x^7 + 2x^6 - 18x^5 + 93x^4 - 112x^3 + 72x^2 - 24x + 4	\( 2^{16}\cdot 3^{20} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.228509902503936.3	x^12 + 12x^10 + 54x^8 + 116x^6 + 129x^4 + 72x^2 + 4	\( 2^{16}\cdot 3^{20} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.358719963529216.3	x^12 - 4x^11 + 4x^10 + 8x^9 - 24x^8 + 8x^7 + 80x^6 - 112x^5 + 33x^4 - 4x^3 + 36x^2 - 32x + 8	\( 2^{32}\cdot 17^{4} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.4.570630428688384.1	x^12 + 6x^10 - 8x^9 - 3x^8 - 16x^6 - 3x^4 + 8x^3 + 6x^2 + 1	\( 2^{30}\cdot 3^{12} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.4.570630428688384.2	x^12 - 6x^8 - 16x^6 + 57x^4 - 48x^2 + 16	\( 2^{30}\cdot 3^{12} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.570630428688384.13	x^12 - 4x^9 + 12x^7 + 12x^6 + 36x^5 + 81x^4 + 92x^3 + 36x^2 + 8	\( 2^{30}\cdot 3^{12} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.570630428688384.17	x^12 - 12x^10 + 54x^8 - 108x^6 + 81x^4 + 16	\( 2^{30}\cdot 3^{12} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.991623123042304.6	x^12 + 10x^10 + 29x^8 + 16x^6 - 16x^4 + 24x^2 + 4	\( 2^{30}\cdot 31^{4} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.1025271882697689.2	x^12 - 6x^11 + 15x^10 - 20x^9 - 6x^8 + 78x^7 - 116x^6 + 57x^5 + 75x^4 - 147x^3 + 123x^2 - 54x + 12	\( 3^{14}\cdot 11^{8} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.1283918464548864.8	x^12 - 6x^11 + 21x^10 - 50x^9 + 78x^8 - 78x^7 + 37x^6 + 18x^5 - 12x^4 - 30x^3 + 39x^2 - 18x + 3	\( 2^{28}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.4.1828652958613504.2	x^12 - 6x^10 - 4x^9 + 10x^8 - 48x^6 + 99x^4 - 112x^3 + 54x^2 - 12x + 1	\( 2^{18}\cdot 17^{8} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.2282521714753536.19	x^12 - 4x^11 + 8x^10 - 20x^9 + 45x^8 - 56x^7 + 64x^6 - 64x^5 - 24x^4 + 32x^3 + 32x^2 + 16x + 4	\( 2^{32}\cdot 3^{12} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.2282521714753536.30	x^12 + 8x^6 - 72x^5 + 177x^4 - 248x^3 + 216x^2 - 96x + 32	\( 2^{32}\cdot 3^{12} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.2282521714753536.36	x^12 - 12x^10 + 54x^8 - 116x^6 + 129x^4 - 72x^2 + 144	\( 2^{32}\cdot 3^{12} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.3656158440062976.16	x^12 + 12x^10 + 54x^8 + 164x^6 + 417x^4 + 504x^2 + 16	\( 2^{20}\cdot 3^{20} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.3656158440062976.22	x^12 - 4x^9 + 18x^8 + 12x^7 + 8x^6 - 36x^5 - 15x^4 + 76x^3 + 72x^2 + 96x + 64	\( 2^{20}\cdot 3^{20} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.5135673858195456.11	x^12 - 4x^11 + 8x^10 - 16x^9 + 39x^8 - 100x^7 + 200x^6 - 288x^5 + 308x^4 - 224x^3 + 100x^2 - 24x + 6	\( 2^{30}\cdot 3^{14} \)	$S_3\wr C_2$ (as 12T34)	$[2]$
12.4.6189907940737024.8	x^12 - 14x^10 - 12x^9 + 40x^8 + 48x^7 - 28x^6 - 72x^5 - 35x^4 + 10x^2 + 4x + 2	\( 2^{30}\cdot 7^{8} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.4.7314611834454016.2	x^12 - 6x^10 + 5x^8 - 6x^6 + 24x^4 - 66x^2 + 64	\( 2^{20}\cdot 17^{8} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.4.29258447337816064.2	x^12 - 2x^11 - x^10 - 4x^9 - 45x^8 + 2x^7 + 71x^6 - 48x^5 - 28x^4 + 64x^3 - 26x^2 - 4x + 2	\( 2^{22}\cdot 17^{8} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.29258447337816064.4	x^12 - 6x^11 + 23x^10 - 48x^9 + 67x^8 - 42x^7 + 43x^6 - 136x^5 + 204x^4 - 68x^3 - 102x^2 + 68x + 34	\( 2^{22}\cdot 17^{8} \)	$S_3\wr C_2$ (as 12T34)	$[2]$
12.0.46221064723759104.17	x^12 - 12x^10 - 4x^9 + 72x^8 + 60x^7 - 96x^6 - 180x^5 - 15x^4 + 92x^3 + 108x^2 + 48x + 8	\( 2^{30}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T34)	$[2]$
12.0.46221064723759104.25	x^12 + 6x^10 - 12x^9 + 12x^8 - 48x^7 + 76x^6 - 120x^5 + 213x^4 - 288x^3 + 270x^2 - 108x + 22	\( 2^{30}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T34)	$[6]$
12.0.46221064723759104.27	x^12 - 4x^9 + 36x^8 + 60x^7 + 28x^6 + 36x^5 + 177x^4 + 156x^3 + 36x^2 + 24	\( 2^{30}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T34)	$[2]$
12.0.46221064723759104.42	x^12 - 12x^10 + 54x^8 - 140x^6 + 273x^4 - 288x^2 + 400	\( 2^{30}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.103997395628457984.32	x^12 + 12x^10 + 54x^8 + 148x^6 + 321x^4 + 360x^2 + 16	\( 2^{28}\cdot 3^{18} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.184884258895036416.44	x^12 - 12x^10 - 8x^9 + 72x^8 + 120x^7 - 60x^6 - 360x^5 - 303x^4 + 88x^3 + 432x^2 + 384x + 128	\( 2^{32}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T34)	$[6]$
12.0.184884258895036416.49	x^12 - 18x^8 - 72x^7 + 432x^5 + 1161x^4 + 1944x^3 + 2592x^2 + 2592x + 1296	\( 2^{32}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.184884258895036416.52	x^12 - 16x^9 + 18x^8 + 48x^7 + 128x^6 - 144x^5 - 735x^4 - 656x^3 + 1152x^2 + 3264x + 4624	\( 2^{32}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T34)	$[3]$
12.0.184884258895036416.57	x^12 + 12x^10 + 90x^8 + 316x^6 + 873x^4 + 648x^2 + 144	\( 2^{32}\cdot 3^{16} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.4.303305489096114176.6	x^12 - 12x^10 + 39x^8 - 104x^6 + 135x^4 + 4x^2 + 1	\( 2^{30}\cdot 7^{10} \)	$S_3\wr C_2$ (as 12T34)	$[3]$
12.0.328460078808039424.13	x^12 + 4x^10 - 16x^9 + 38x^8 - 28x^7 + 158x^6 - 264x^5 + 332x^4 - 416x^3 + 1688x^2 - 2432x + 2032	\( 2^{22}\cdot 23^{8} \)	$S_3\wr C_2$ (as 12T34)	$[6]$
12.0.415989582513831936.37	x^12 + 12x^10 + 54x^8 + 124x^6 + 177x^4 + 144x^2 + 16	\( 2^{30}\cdot 3^{18} \)	$S_3\wr C_2$ (as 12T34)	$[6]$
12.0.415989582513831936.109	x^12 + 12x^10 + 54x^8 + 156x^6 + 369x^4 + 432x^2 + 144	\( 2^{30}\cdot 3^{18} \)	$S_3\wr C_2$ (as 12T34)	$[2]$
12.4.528480705039302656.7	x^12 + 10x^10 + 53x^8 + 12x^6 - 36x^4 - 24x^2 + 16	\( 2^{18}\cdot 17^{10} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.4.635809301889286144.1	x^12 + 8x^10 - 40x^9 - 61x^8 + 104x^7 - 100x^6 + 296x^5 + 1236x^4 - 712x^3 - 1220x^2 + 1704x - 398	\( 2^{32}\cdot 23^{6} \)	$S_3\wr C_2$ (as 12T34)	Trivial (GRH)
12.4.635809301889286144.3	x^12 - 20x^10 - 8x^9 + 129x^8 + 56x^7 - 316x^6 - 152x^5 + 364x^4 + 96x^3 - 120x^2 - 48x + 4	\( 2^{32}\cdot 23^{6} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.920664383502155776.25	x^12 - 14x^10 - 20x^9 + 98x^8 + 392x^7 + 320x^6 - 1184x^5 - 2959x^4 - 480x^3 + 6082x^2 + 8036x + 3362	\( 2^{32}\cdot 11^{8} \)	$S_3\wr C_2$ (as 12T34)	$[3]$
12.0.935976560656121856.99	x^12 - 12x^10 + 90x^8 - 300x^6 + 585x^4 - 216x^2 + 144	\( 2^{28}\cdot 3^{20} \)	$S_3\wr C_2$ (as 12T34)	$[3]$
12.0.935976560656121856.100	x^12 + 12x^10 - 32x^9 + 90x^8 - 336x^7 + 1096x^6 - 2592x^5 + 6372x^4 - 10848x^3 + 15552x^2 - 13824x + 9216	\( 2^{28}\cdot 3^{20} \)	$S_3\wr C_2$ (as 12T34)	$[3]$
12.0.935976560656121856.116	x^12 - 6x^10 - 8x^9 + 9x^8 + 60x^7 - 122x^6 - 324x^5 + 513x^4 + 876x^3 + 972x^2 + 432x + 144	\( 2^{28}\cdot 3^{20} \)	$S_3\wr C_2$ (as 12T34)	$[3]$
12.4.1872540629620228096.2	x^12 - 10x^10 - 8x^9 + 18x^8 + 112x^7 + 44x^6 - 128x^5 - 415x^4 - 224x^3 + 326x^2 + 632x + 8	\( 2^{28}\cdot 17^{8} \)	$S_3\wr C_2$ (as 12T34)	Trivial
12.0.2113922820157210624.4	x^12 + 20x^10 + 161x^8 + 368x^6 + 308x^4 + 82x^2 + 4	\( 2^{20}\cdot 17^{10} \)	$S_3\wr C_2$ (as 12T34)	$[2]$