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 162)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.42194001221.1	x^12 - 3x^11 + 7x^10 - 12x^9 + 17x^8 - 21x^7 + 24x^6 - 24x^5 + 22x^4 - 17x^3 + 10x^2 - 4x + 1	\( 41\cdot 1029121981 \)	$S_{12}$ (as 12T301)	Trivial
12.0.42925852301.1	x^12 - x^11 - 2x^10 + 3x^9 + x^8 - x^7 - x^6 - 2x^5 + 3x^4 + 2x^3 - 2x^2 - x + 1	\( 79\cdot 543365219 \)	$S_{12}$ (as 12T301)	Trivial
12.0.66699927001.1	x^12 - x^9 + x^7 - x^4 - x^3 + x + 1	\( 47\cdot 1117\cdot 1270499 \)	$S_{12}$ (as 12T301)	Trivial
12.0.72509192309.1	x^12 - x^10 - x^9 + x^7 + x^6 + x^5 - 2x^3 - x^2 + x + 1	\( 72509192309 \)	$S_{12}$ (as 12T301)	Trivial
12.2.293890894259.1	x^12 - x^9 - x^4 + x + 1	\( -\,103\cdot 2853309653 \)	$S_{12}$ (as 12T301)	Trivial
12.2.362031460339.1	x^12 - x^7 + x^6 + 2x^5 - 2x^4 + x^3 - x^2 - x + 1	\( -\,362031460339 \)	$S_{12}$ (as 12T301)	Trivial
12.4.764131428301.1	x^12 - 2x^10 - x^9 + 4x^8 + 2x^7 - 3x^5 - 5x^4 + 3x^3 + 4x^2 - x - 1	\( 764131428301 \)	$S_{12}$ (as 12T301)	Trivial
12.4.802389895609.1	x^12 - 2x^11 - 2x^10 + 4x^9 + x^8 - x^7 - 2x^6 - x^5 + 2x^4 + x^3 - x^2 - 2x + 1	\( 107^{2}\cdot 70083841 \)	$S_{12}$ (as 12T301)	Trivial
12.6.5192327768191.1	x^12 - 5x^10 + 9x^8 - 2x^7 - 9x^6 + 6x^5 + 8x^4 - 4x^3 - 5x^2 + x + 1	\( -\,5192327768191 \)	$S_{12}$ (as 12T301)	Trivial
12.6.5528913603539.1	x^12 - 3x^11 + 2x^10 + 7x^9 - 13x^8 + 3x^7 + 13x^6 - 14x^5 + 7x^3 - 4x^2 - x + 1	\( -\,197\cdot 2251\cdot 12468037 \)	$S_{12}$ (as 12T301)	Trivial
12.0.8630788777645.1	x^12 - x + 1	\( 5\cdot 89\cdot 19395030961 \)	$S_{12}$ (as 12T301)	Trivial
12.2.9201412118867.1	x^12 - x - 1	\( -\,1237\cdot 7438489991 \)	$S_{12}$ (as 12T301)	Trivial
12.8.18137291911168.1	x^12 - 4x^10 - 2x^9 + 9x^8 + 2x^7 - 15x^6 + 8x^5 + 14x^4 - 10x^3 - 7x^2 + 2x + 1	\( 2^{12}\cdot 151\cdot 2237\cdot 13109 \)	$S_{12}$ (as 12T301)	Trivial
12.8.18277154559581.1	x^12 - 2x^11 - 3x^10 + 6x^9 - 3x^7 + 3x^6 - x^5 + 4x^4 - 4x^3 - 3x^2 + 4x - 1	\( 18277154559581 \)	$S_{12}$ (as 12T301)	Trivial
12.0.180572493057277.1	x^12 - x + 7	\( 85333\cdot 2116092169 \)	$S_{12}$ (as 12T301)	Trivial
12.2.411948938473472.1	x^12 - 4x - 4	\( -\,2^{12}\cdot 103\cdot 191\cdot 317\cdot 16127 \)	$S_{12}$ (as 12T301)	Trivial
12.2.1168638779604992.1	x^12 - 4x - 1	\( -\,2^{14}\cdot 37\cdot 4357\cdot 442457 \)	$S_{12}$ (as 12T301)	Trivial
12.2.1177552703270912.1	x^12 - 2x - 1	\( -\,2^{12}\cdot 287488452947 \)	$S_{12}$ (as 12T301)	Trivial
12.2.1523471121907712.1	x^12 - 8x + 4	\( -\,2^{18}\cdot 181\cdot 4673\cdot 6871 \)	$S_{12}$ (as 12T301)	Trivial
12.2.2598699674894336.1	x^12 - 4x - 2	\( -\,2^{24}\cdot 13\cdot 11914967 \)	$S_{12}$ (as 12T301)	Trivial
12.0.3396406826684416.1	x^12 - 4x^9 + 6x^6 - 4x^3 + 2x + 1	\( 2^{12}\cdot 167\cdot 3169\cdot 1566827 \)	$S_{12}$ (as 12T301)	Trivial
12.2.5733680032329728.1	x^12 - 4x^9 + 6x^6 - 4x^3 - 2x + 1	\( -\,2^{12}\cdot 19\cdot 1933\cdot 38114309 \)	$S_{12}$ (as 12T301)	Trivial
12.10.7770704775363639.1	x^12 - 2x^11 - 10x^10 + 20x^9 + 35x^8 - 71x^7 - 49x^6 + 105x^5 + 22x^4 - 57x^3 - 2x^2 + 8x - 1	\( -\,3^{2}\cdot 401\cdot 2153146238671 \)	$S_{12}$ (as 12T301)	Trivial
12.0.7961450256191488.1	x^12 - 4x + 4	\( 2^{12}\cdot 7\cdot 1987\cdot 139745017 \)	$S_{12}$ (as 12T301)	Trivial
12.10.11517353618919691.1	x^12 - 3x^11 - 9x^10 + 28x^9 + 33x^8 - 97x^7 - 65x^6 + 149x^5 + 72x^4 - 91x^3 - 37x^2 + 11x + 3	\( -\,2539073\cdot 4536046667 \)	$S_{12}$ (as 12T301)	Trivial
12.0.17091537115205632.1	x^12 - 2x + 2	\( 2^{12}\cdot 59\cdot 263\cdot 4987\cdot 53923 \)	$S_{12}$ (as 12T301)	Trivial
12.0.18259888406357677.1	x^12 - x + 2	\( 89\cdot 1429\cdot 17509\cdot 8200013 \)	$S_{12}$ (as 12T301)	Trivial
12.2.19428810320850944.1	x^12 - 2x - 2	\( -\,2^{12}\cdot 13\cdot 364873991903 \)	$S_{12}$ (as 12T301)	Trivial
12.12.42775710278251337.1	x^12 - x^11 - 14x^10 + 18x^9 + 59x^8 - 93x^7 - 66x^6 + 149x^5 - 20x^4 - 55x^3 + 18x^2 + 5x - 2	\( 229\cdot 186793494664853 \)	$S_{12}$ (as 12T301)	Trivial
12.2.74792742614662208.1	x^12 - 8x - 1	\( -\,2^{6}\cdot 1168636603354097 \)	$S_{12}$ (as 12T301)	Trivial
12.2.74935400187822080.1	x^12 - 8x - 4	\( -\,2^{18}\cdot 5\cdot 257\cdot 3413\cdot 65179 \)	$S_{12}$ (as 12T301)	Trivial
12.12.123976424294163733.1	x^12 - 3x^11 - 9x^10 + 33x^9 + 18x^8 - 122x^7 + 32x^6 + 164x^5 - 109x^4 - 41x^3 + 40x^2 - 4x - 1	\( 337\cdot 367882564671109 \)	$S_{12}$ (as 12T301)	Trivial
12.2.151617403440732195.1	x^12 - 3x + 1	\( -\,3^{12}\cdot 5\cdot 19\cdot 3003104141 \)	$S_{12}$ (as 12T301)	Trivial (GRH)
12.2.151635235641628707.1	x^12 - 3x - 1	\( -\,3^{13}\cdot 37\cdot 2570526557 \)	$S_{12}$ (as 12T301)	Trivial (GRH)
12.2.169886493259208739.1	x^12 - 3x - 2	\( -\,3^{12}\cdot 13\cdot 23509\cdot 1045987 \)	$S_{12}$ (as 12T301)	Trivial
12.0.374860495827888093.1	x^12 + 6x^10 + 15x^8 + 20x^6 + 15x^4 + 6x^2 - 3x + 1	\( 3^{12}\cdot 705366156973 \)	$S_{12}$ (as 12T301)	$[2]$
12.2.453024419859845651.1	x^12 - x - 5	\( -\,347\cdot 377687\cdot 3456687359 \)	$S_{12}$ (as 12T301)	Trivial
12.2.678113134910248995.1	x^12 - 6x^10 + 15x^8 - 20x^6 + 15x^4 - 6x^2 - 3x + 1	\( -\,3^{12}\cdot 5\cdot 14411\cdot 17708549 \)	$S_{12}$ (as 12T301)	Trivial
12.0.760106315407770477.1	x^12 - 3x + 4	\( 3^{12}\cdot 104369\cdot 13704013 \)	$S_{12}$ (as 12T301)	$[2]$
12.0.1427834126566025181.1	x^12 - 3x + 3	\( 3^{12}\cdot 29\cdot 1093\cdot 84762653 \)	$S_{12}$ (as 12T301)	$[2]$
12.0.1578291809504382976.1	x^12 - 2x + 3	\( 2^{12}\cdot 15534847\cdot 24803923 \)	$S_{12}$ (as 12T301)	Trivial (GRH)
12.0.1579460160795535021.1	x^12 - x + 3	\( 1579460160795535021 \)	$S_{12}$ (as 12T301)	Trivial (GRH)
12.2.1579460731418876243.1	x^12 - x - 3	\( -\,7\cdot 59\cdot 181\cdot 7433\cdot 2842602107 \)	$S_{12}$ (as 12T301)	Trivial
12.2.1731086765648386083.1	x^12 - 3x - 3	\( -\,3^{12}\cdot 7\cdot 47\cdot 157\cdot 63062071 \)	$S_{12}$ (as 12T301)	Trivial
12.0.4303041290059988992.1	x^12 - 4x + 7	\( 2^{14}\cdot 19\cdot 241\cdot 57356802247 \)	$S_{12}$ (as 12T301)	Trivial (GRH)
12.0.4674312312664536064.1	x^12 - 4x + 8	\( 2^{10}\cdot 61\cdot 585337\cdot 127844473 \)	$S_{12}$ (as 12T301)	Trivial
12.2.4674896630965947392.1	x^12 - 4x - 8	\( -\,2^{10}\cdot 29\cdot 157425129006127 \)	$S_{12}$ (as 12T301)	Trivial
12.2.4768475351443570688.1	x^12 - 4x + 2	\( -\,2^{24}\cdot 3371\cdot 84314233 \)	$S_{12}$ (as 12T301)	Trivial
12.2.4786349914701123584.1	x^12 - 8x + 3	\( -\,2^{12}\cdot 41\cdot 28501035601069 \)	$S_{12}$ (as 12T301)	Trivial (GRH)
12.2.4786726609061150720.1	x^12 - 4x + 1	\( -\,2^{25}\cdot 5\cdot 28531113917 \)	$S_{12}$ (as 12T301)	Trivial (GRH)