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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.6.1075933959508438187960608169.1	x^18 - 9x^17 + 42x^16 - 132x^15 + 296x^14 - 476x^13 + 518x^12 - 274x^11 - 201x^10 + 609x^9 - 652x^8 + 334x^7 + 42x^6 - 210x^5 + 164x^4 - 62x^3 + 7x^2 + 3x - 1	\( 7^{16}\cdot 13^{9}\cdot 43\cdot 71 \)	18T586	$[2]$ (GRH)
18.16.7106493786222379509303476224.1	x^18 - 20x^16 + 156x^14 - 602x^12 + 1204x^10 - 1197x^8 + 504x^6 - 24x^4 - 24x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.8.7106493786222379509303476224.1	x^18 - 6x^16 - 12x^14 + 98x^12 + 35x^10 - 434x^8 - 168x^6 + 508x^4 + 270x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.16.7106493786222379509303476224.2	x^18 - 17x^16 + 109x^14 - 329x^12 + 462x^10 - 217x^8 - 84x^6 + 93x^4 - 20x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.8.7106493786222379509303476224.2	x^18 - 10x^16 + 4x^14 + 105x^12 - 98x^10 - 189x^8 - 7x^6 + 51x^4 + 15x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.12.7106493786222379509303476224.3	x^18 - 13x^16 + 37x^14 + 70x^12 - 273x^10 - 63x^8 + 455x^6 - 66x^4 - 10x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.4.7106493786222379509303476224.3	x^18 + 11x^16 + 11x^14 - 175x^12 - 637x^10 - 826x^8 - 413x^6 - 40x^4 + 8x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.8.7106493786222379509303476224.3	x^18 - 5x^16 - 20x^14 + 63x^12 + 203x^10 - 91x^8 - 637x^6 - 559x^4 - 145x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.12.7106493786222379509303476224.4	x^18 - 5x^16 - 34x^14 + 238x^12 - 343x^10 - 77x^8 + 469x^6 - 300x^4 + 51x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.4.7106493786222379509303476224.4	x^18 + 16x^16 + 92x^14 + 210x^12 + 63x^10 - 364x^8 - 245x^6 + 155x^4 + 58x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.8.7106493786222379509303476224.4	x^18 + 8x^16 - 5x^14 - 98x^12 - 42x^10 + 280x^8 + 168x^6 - 59x^4 - 31x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.12.15039354951005461512587733491.1	x^18 - 9x^17 + 33x^16 - 60x^15 + 32x^14 + 112x^13 - 294x^12 + 230x^11 + 177x^10 - 467x^9 + 249x^8 + 150x^7 - 238x^6 + 56x^5 + 58x^4 - 32x^3 - 4x^2 + 6x + 1	\( -\,7^{17}\cdot 13^{8}\cdot 41\cdot 1933 \)	18T586	Trivial (GRH)
18.2.49745456503556656565124333568.1	x^18 + 14x^16 + 63x^14 + 84x^12 - 133x^10 - 518x^8 - 595x^6 - 315x^4 - 77x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	$[3]$ (GRH)
18.10.49745456503556656565124333568.2	x^18 - 28x^14 + 28x^12 + 119x^10 - 98x^8 - 161x^6 + 63x^4 + 42x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.2.49745456503556656565124333568.2	x^18 + 21x^16 + 182x^14 + 840x^12 + 2219x^10 + 3339x^8 + 2639x^6 + 840x^4 - 7x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	$[5]$ (GRH)
18.10.49745456503556656565124333568.3	x^18 - 42x^14 - 42x^12 + 294x^10 + 182x^8 - 588x^6 - 28x^4 + 63x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.14.49745456503556656565124333568.3	x^18 - 21x^16 + 175x^14 - 742x^12 + 1701x^10 - 2030x^8 + 1008x^6 + 70x^4 - 154x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.6.49745456503556656565124333568.3	x^18 + 7x^16 - 35x^14 - 231x^12 + 315x^10 + 1463x^8 + 441x^6 - 812x^4 - 399x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.10.49745456503556656565124333568.4	x^18 - 7x^16 - 28x^14 + 175x^12 + 252x^10 - 1036x^8 - 609x^6 + 812x^4 - 112x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.14.49745456503556656565124333568.4	x^18 - 7x^16 - 21x^14 + 231x^12 - 525x^10 + 252x^8 + 539x^6 - 714x^4 + 252x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.6.49745456503556656565124333568.4	x^18 + 14x^16 + 56x^14 - 28x^12 - 574x^10 - 630x^8 + 1050x^6 + 1162x^4 + 259x^2 - 7	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.10.49745456503556656565124333568.5	x^18 - 7x^16 - 28x^14 + 224x^12 + 98x^10 - 1421x^8 + 147x^6 + 1715x^4 - 343x^2 - 343	\( 2^{18}\cdot 7^{17}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.12.92384419220890933620945190912.1	x^18 - x^16 - 82x^14 + 525x^12 - 1267x^10 + 1211x^8 - 175x^6 - 221x^4 + 39x^2 + 13	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.4.92384419220890933620945190912.1	x^18 + 24x^16 + 193x^14 + 525x^12 - 287x^10 - 2667x^8 - 1904x^6 - 247x^4 + 78x^2 + 13	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	$[3]$ (GRH)
18.8.92384419220890933620945190912.1	x^18 + 12x^16 + 15x^14 - 238x^12 - 707x^10 + 826x^6 + 104x^4 - 117x^2 + 13	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.4.92384419220890933620945190912.2	x^18 + 19x^16 + 78x^14 - 294x^12 - 2065x^10 - 2730x^8 + 154x^6 + 1924x^4 + 793x^2 + 13	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.8.92384419220890933620945190912.2	x^18 - 2x^16 - 69x^14 - 77x^12 + 574x^10 + 371x^8 - 938x^6 - 78x^4 + 156x^2 + 13	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.10.92384419220890933620945190912.1	x^18 - 56x^14 + 91x^12 + 805x^10 - 2254x^8 - 539x^6 + 5096x^4 - 2548x^2 - 637	\( 2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.14.92384419220890933620945190912.1	x^18 - 12x^16 + 43x^14 - 7x^12 - 252x^10 + 490x^8 - 301x^6 - 13x^4 + 65x^2 - 13	\( 2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.6.92384419220890933620945190912.1	x^18 - 6x^16 - 89x^14 + 63x^12 + 2492x^10 + 8197x^8 + 10619x^6 + 5408x^4 + 585x^2 - 13	\( 2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.10.92384419220890933620945190912.2	x^18 + 8x^16 - 26x^14 - 70x^12 + 154x^10 + 133x^8 - 266x^6 - 52x^4 + 130x^2 - 13	\( 2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.14.92384419220890933620945190912.2	x^18 - 24x^16 + 214x^14 - 882x^12 + 1645x^10 - 952x^8 - 539x^6 + 611x^4 - 104x^2 - 13	\( 2^{18}\cdot 7^{16}\cdot 13^{9} \)	18T586	Trivial (GRH)
18.0.216895506996594951140594638751.1	x^18 - 9x^17 + 60x^16 - 276x^15 + 1040x^14 - 3164x^13 + 8190x^12 - 17914x^11 + 33819x^10 - 54695x^9 + 76338x^8 - 90906x^7 + 92078x^6 - 77770x^5 + 53800x^4 - 29270x^3 + 11843x^2 - 3165x + 433	\( -\,7^{16}\cdot 13^{8}\cdot 8000831 \)	18T586	$[165]$ (GRH)
18.12.2460473406698990007514321649664.1	x^18 - 3x^16 - 87x^14 + 210x^12 + 1722x^10 - 3654x^8 + 1715x^6 - 159x^4 - 27x^2 + 1	\( -\,2^{18}\cdot 3^{24}\cdot 7^{16} \)	18T586	Trivial (GRH)
18.12.2460473406698990007514321649664.2	x^18 - 3x^16 - 108x^14 + 833x^12 - 1953x^10 + 1050x^8 + 651x^6 - 264x^4 + 15x^2 + 1	\( -\,2^{18}\cdot 3^{24}\cdot 7^{16} \)	18T586	Trivial (GRH)
18.6.17223313846892930052600251547648.1	x^18 + 21x^16 + 42x^14 - 700x^12 + 252x^10 + 2877x^8 - 2044x^6 - 1197x^4 - 168x^2 - 7	\( 2^{18}\cdot 3^{24}\cdot 7^{17} \)	18T586	Trivial (GRH)
18.6.17223313846892930052600251547648.2	x^18 + 21x^16 + 84x^14 - 581x^12 - 3927x^10 - 3318x^8 + 8533x^6 + 1533x^4 - 42x^2 - 7	\( 2^{18}\cdot 3^{24}\cdot 7^{17} \)	18T586	Trivial (GRH)
18.0.869245000449362794439473301291008.1	x^18 + 66x^16 + 1747x^14 + 23660x^12 + 173859x^10 + 685517x^8 + 1396052x^6 + 1433185x^4 + 689767x^2 + 122317	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9}\cdot 97^{2} \)	18T586	$[2, 4, 1584]$ (GRH)
18.18.869245000449362794439473301291008.1	x^18 - 82x^16 + 2563x^14 - 38815x^12 + 306005x^10 - 1286299x^8 + 2798880x^6 - 2856321x^4 + 1114724x^2 - 122317	\( 2^{18}\cdot 7^{16}\cdot 13^{9}\cdot 97^{2} \)	18T586	Trivial (GRH)
18.18.869245000449362794439473301291008.2	x^18 - 66x^16 + 1747x^14 - 23660x^12 + 173859x^10 - 685517x^8 + 1396052x^6 - 1433185x^4 + 689767x^2 - 122317	\( 2^{18}\cdot 7^{16}\cdot 13^{9}\cdot 97^{2} \)	18T586	Trivial (GRH)