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 all 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.25149318588731261951875.1	x^18 - 7x^17 + 20x^16 - 23x^15 - 7x^14 + 25x^13 + 98x^12 - 384x^11 + 633x^10 - 636x^9 + 343x^8 + 113x^7 - 528x^6 + 630x^5 - 461x^4 + 223x^3 - 74x^2 + 16x - 1	\( -\,5^{4}\cdot 23^{6}\cdot 43^{7} \)	18T782	Trivial (GRH)
18.6.73108484269567621953125.1	x^18 - 3x^17 - x^16 + 16x^15 - 41x^14 + 36x^13 + 28x^12 - 134x^11 + 182x^10 - 46x^9 - 96x^8 + 84x^7 + 148x^6 - 420x^5 + 341x^4 - 140x^3 - 116x^2 + 53x + 19	\( 5^{7}\cdot 23^{6}\cdot 43^{6} \)	18T782	Trivial (GRH)
18.4.82920283397994741760000.3	x^18 - x^16 + 5x^14 - 23x^12 + 2x^10 - 25x^8 + 20x^6 - 13x^4 + 8x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 23^{6}\cdot 43^{4} \)	18T782	Trivial (GRH)
18.0.82920283397994741760000.5	x^18 + 6x^16 + 13x^14 + 37x^12 + 55x^10 + 79x^8 + 73x^6 + 50x^4 + 20x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 23^{6}\cdot 43^{4} \)	18T782	Trivial (GRH)
18.0.82920283397994741760000.6	x^18 + 10x^16 + 47x^14 + 133x^12 + 240x^10 + 271x^8 + 178x^6 + 62x^4 + 12x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 23^{6}\cdot 43^{4} \)	18T782	Trivial (GRH)
18.6.229758542086710080000000.2	x^18 - 9x^17 + 43x^16 - 140x^15 + 335x^14 - 609x^13 + 841x^12 - 847x^11 + 528x^10 - 461x^8 + 639x^7 - 547x^6 + 349x^5 - 175x^4 + 67x^3 - 13x^2 - 2x + 1	\( 2^{12}\cdot 5^{7}\cdot 23^{4}\cdot 37^{6} \)	18T782	Trivial (GRH)
18.4.3987700862576146359609375.1	x^18 - 9x^17 + 36x^16 - 84x^15 + 111x^14 - 21x^13 - 212x^12 + 375x^11 - 187x^10 - 286x^9 + 399x^8 + 345x^7 - 1167x^6 + 1080x^5 - 201x^4 - 440x^3 + 126x^2 + 134x + 1	\( -\,3^{11}\cdot 5^{7}\cdot 257^{6} \)	18T782	$[2]$
18.4.7528727907097315901440000.1	x^18 - 5x^14 + 3x^12 - 5x^10 - 10x^8 + 20x^6 - 5x^4 - 5x^2 + 1	\( -\,2^{24}\cdot 5^{4}\cdot 23^{4}\cdot 37^{6} \)	18T782	Trivial (GRH)
18.2.10365035424749342720000000.1	x^18 + 9x^16 + 27x^14 + 14x^12 - 62x^10 - 210x^8 - 350x^6 + 35x^4 - 450x^2 - 125	\( 2^{18}\cdot 5^{7}\cdot 23^{6}\cdot 43^{4} \)	18T782	Trivial (GRH)
18.6.10365035424749342720000000.1	x^18 - 15x^14 - 20x^12 + 62x^10 + 105x^8 - 85x^6 - 60x^4 + 250x^2 - 125	\( 2^{18}\cdot 5^{7}\cdot 23^{6}\cdot 43^{4} \)	18T782	Trivial (GRH)
18.2.10365035424749342720000000.2	x^18 + 5x^16 + x^14 - 42x^12 - 113x^10 - 120x^8 + 40x^4 - 150x^2 - 125	\( 2^{18}\cdot 5^{7}\cdot 23^{6}\cdot 43^{4} \)	18T782	Trivial (GRH)
18.6.11963102587728439078828125.1	x^18 - x^17 + 5x^16 + x^15 - 2x^14 + 25x^13 - 21x^12 + 50x^11 + 55x^10 + 193x^9 + 414x^8 + 268x^7 + 448x^6 + 58x^5 - 55x^4 - 85x^3 + 8x^2 + 8x - 1	\( 3^{12}\cdot 5^{7}\cdot 257^{6} \)	18T782	Trivial (GRH)
18.10.14704546693549445120000000.1	x^18 - 13x^16 - 8x^15 + 65x^14 + 108x^13 - 68x^12 - 332x^11 - 248x^10 + 184x^9 + 419x^8 + 166x^7 - 151x^6 - 152x^5 - x^4 + 50x^3 + 4x^2 - 8x + 1	\( 2^{18}\cdot 5^{7}\cdot 23^{4}\cdot 37^{6} \)	18T782	Trivial (GRH)
18.0.188218197677432897536000000.1	x^18 + 19x^16 + 131x^14 + 388x^12 + 390x^10 - 269x^8 - 477x^6 + 723x^4 + 1440x^2 + 625	\( -\,2^{24}\cdot 5^{6}\cdot 23^{4}\cdot 37^{6} \)	18T782	$[2]$ (GRH)
18.0.188218197677432897536000000.2	x^18 + 13x^16 + 61x^14 + 194x^12 + 544x^10 + 943x^8 + 1011x^6 + 713x^4 + 270x^2 + 25	\( -\,2^{24}\cdot 5^{6}\cdot 23^{4}\cdot 37^{6} \)	18T782	$[2]$ (GRH)
18.10.941090988387164487680000000.1	x^18 - 9x^16 + 23x^14 - 6x^12 + 6x^10 - 195x^8 + 395x^6 - 425x^4 + 400x^2 - 125	\( 2^{24}\cdot 5^{7}\cdot 23^{4}\cdot 37^{6} \)	18T782	Trivial (GRH)
18.8.14721945919978712958250621632.2	x^18 - 3x^17 - 15x^16 + 32x^15 + 117x^14 - 147x^13 - 504x^12 + 675x^11 + 1119x^10 - 3362x^9 - 927x^8 + 10140x^7 - 1716x^6 - 15909x^5 + 5283x^4 + 11057x^3 - 4905x^2 - 1995x + 967	\( -\,2^{6}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.12.235551134719659407332009946112.2	x^18 - 6x^16 - 57x^14 + 56x^12 + 426x^10 - 309x^8 - 773x^6 + 900x^4 - 297x^2 + 27	\( -\,2^{10}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.8.235551134719659407332009946112.2	x^18 - 3x^17 - 15x^16 + 54x^15 + 72x^14 - 405x^13 + 45x^12 + 1137x^11 - 768x^10 - 1078x^9 + 1239x^8 + 93x^7 - 531x^6 - 1278x^5 - 162x^4 + 3924x^3 + 1218x^2 - 2658x - 1286	\( -\,2^{10}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.12.942204538878637629328039784448.2	x^18 - 6x^16 - 57x^14 + 230x^12 + 390x^10 - 2271x^8 + 2374x^6 - 225x^4 - 360x^2 + 48	\( -\,2^{12}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.10.942204538878637629328039784448.5	x^18 + 15x^16 + 24x^14 - 143x^12 - 57x^10 + 363x^8 - 167x^6 - 36x^4 + 27x^2 - 3	\( 2^{12}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.10.942204538878637629328039784448.6	x^18 - 3x^17 - 21x^16 + 76x^15 + 96x^14 - 717x^13 + 560x^12 + 2847x^11 - 5757x^10 - 1706x^9 + 19188x^8 - 14043x^7 - 26356x^6 + 35136x^5 + 10224x^4 - 30440x^3 + 6852x^2 + 5184x - 1679	\( 2^{12}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.4.3768818155514550517312159137792.2	x^18 - 111x^14 - 577x^12 - 501x^10 + 1851x^8 + 3685x^6 + 2340x^4 + 576x^2 + 48	\( -\,2^{14}\cdot 3^{23}\cdot 367^{6} \)	18T782	$[2]$ (GRH)
18.6.3768818155514550517312159137792.2	x^18 + 6x^16 - 78x^14 - 144x^12 + 999x^10 + 783x^8 - 1998x^6 - 1998x^4 - 432x^2 - 27	\( 2^{14}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.4.5025090874019400689749545517056.1	x^18 + 27x^16 + 186x^14 - 277x^12 - 5199x^10 - 6606x^8 + 700x^6 + 1215x^4 + 216x^2 + 9	\( -\,2^{16}\cdot 3^{22}\cdot 367^{6} \)	18T782	$[10]$ (GRH)
18.0.8864796219037016739196554182656.1	x^18 + 42x^16 + 676x^14 + 5547x^12 + 25443x^10 + 66275x^8 + 93787x^6 + 62298x^4 + 12272x^2 + 676	\( -\,2^{18}\cdot 13^{2}\cdot 193^{4}\cdot 229^{6} \)	18T782	$[2, 94]$ (GRH)
18.6.15075272622058202069248636551168.2	x^18 + 27x^16 + 264x^14 + 1144x^12 + 1992x^10 + 264x^8 - 1937x^6 - 423x^4 + 612x^2 - 48	\( 2^{16}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.14.15075272622058202069248636551168.3	x^18 - 21x^16 + 141x^14 - 215x^12 - 1056x^10 + 3342x^8 + 397x^6 - 8568x^4 + 6264x^2 - 108	\( 2^{16}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.14.15075272622058202069248636551168.4	x^18 - 189x^14 + 841x^12 + 2457x^10 - 15687x^8 + 24421x^6 - 15588x^4 + 4320x^2 - 432	\( 2^{16}\cdot 3^{23}\cdot 367^{6} \)	18T782	Trivial (GRH)
18.18.1206993703226402676089520612229833232.1	x^18 - 7x^17 - 86x^16 + 667x^15 + 2417x^14 - 23129x^13 - 22797x^12 + 367676x^11 - 35719x^10 - 2789975x^9 + 1325038x^8 + 10107152x^7 - 5424234x^6 - 15658948x^5 + 10207056x^4 + 8619424x^3 - 7408928x^2 + 209280x + 544256	\( 2^{4}\cdot 193^{7}\cdot 229^{8} \)	18T782	Trivial (GRH)
18.0.106457240281657124613827288017419894784.1	x^18 - 9x^17 + 183x^16 - 1197x^15 + 12952x^14 - 66141x^13 + 492684x^12 - 2013565x^11 + 11334053x^10 - 35236854x^9 + 157899241x^8 - 312205750x^7 + 1218166350x^6 - 884685172x^5 + 4598843440x^4 + 907163984x^3 + 8815673936x^2 - 7949622416x + 5480201264	\( -\,2^{18}\cdot 13^{2}\cdot 193^{4}\cdot 229^{9} \)	18T782	$[2, 2, 277500]$ (GRH)
18.18.14494774105115134246729616047541332754922448.1	x^18 - 7x^17 - 477x^16 + 2580x^15 + 96946x^14 - 368364x^13 - 10774715x^12 + 24785442x^11 + 700028791x^10 - 696537758x^9 - 26370561888x^8 - 2128102298x^7 + 531816604330x^6 + 488362579857x^5 - 4540455488533x^4 - 6842969625882x^3 + 4393485098751x^2 + 6578218070638x - 1347265689967	\( 2^{4}\cdot 193^{7}\cdot 229^{11} \)	18T782	$[4]$ (GRH)