Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.167297208611536987435565056.1	x^21 - 7x^20 + 23x^19 - 46x^18 + 59x^17 - 38x^16 - 51x^15 + 276x^14 - 725x^13 + 1392x^12 - 2056x^11 + 2397x^10 - 2311x^9 + 1987x^8 - 1615x^7 + 1208x^6 - 783x^5 + 436x^4 - 201x^3 + 66x^2 - 12x + 1	\( -\,2^{18}\cdot 17^{6}\cdot 31^{9} \)	21T57	Trivial (GRH)
21.3.336444035684435024524918784.1	x^21 - 5x^20 + 11x^19 - 5x^18 - 29x^17 + 64x^16 - 22x^15 - 117x^14 + 218x^13 - 124x^12 - 76x^11 + 132x^10 - 38x^9 + 31x^8 - 168x^7 + 204x^6 - 47x^5 - 120x^4 + 134x^3 - 63x^2 + 13x - 1	\( -\,2^{14}\cdot 11^{13}\cdot 29^{6} \)	21T57	Trivial (GRH)
21.9.1772300592033793551446534901465088.1	x^21 - 2x^20 - 10x^19 + 18x^18 + 68x^17 - 28x^16 - 376x^15 - 352x^14 + 648x^13 + 856x^12 - 848x^11 - 912x^10 + 1240x^9 + 432x^8 - 1144x^7 + 120x^6 + 448x^5 - 144x^3 - 64x^2 + 32x + 16	\( 2^{20}\cdot 7^{6}\cdot 37^{7}\cdot 73^{6} \)	21T57	Trivial (GRH)
21.9.5581771880796940582540826805350057.1	x^21 - 2x^20 - 29x^19 + 68x^18 + 307x^17 - 748x^16 - 1496x^15 + 3371x^14 + 3691x^13 - 7180x^12 - 6204x^11 + 7336x^10 + 7843x^9 - 91x^8 - 4359x^7 - 3432x^6 + 52x^5 + 951x^4 + 433x^3 + 29x^2 - 27x - 5	\( 11^{13}\cdot 29^{6}\cdot 43^{7} \)	21T57	Trivial (GRH)
21.7.6400890533463290121080023755169887.1	x^21 - 3x^20 - 17x^19 + 29x^18 + 208x^17 - 102x^16 - 1409x^15 - x^14 + 3951x^13 + 2695x^12 - 3516x^11 - 6803x^10 - 5950x^9 - 1331x^8 + 8064x^7 + 12913x^6 + 7673x^5 + 1263x^4 - 612x^3 - 375x^2 - 90x - 9	\( -\,3^{21}\cdot 29^{9}\cdot 59^{6} \)	21T57	Trivial (GRH)
21.7.2439749867262143600576492887163977728.1	x^21 - 6x^20 + 36x^19 - 114x^18 + 327x^17 - 693x^16 + 1251x^15 - 2007x^14 + 2295x^13 - 2524x^12 + 1179x^11 + 198x^10 - 1188x^9 + 3231x^8 - 2097x^7 + 618x^6 + 438x^5 - 1026x^4 + 44x^3 - 6x^2 + 45x + 9	\( -\,2^{14}\cdot 3^{33}\cdot 547^{6} \)	21T57	Trivial (GRH)
21.21.212470339051203253792638525635605096824832.1	x^21 - 2x^20 - 60x^19 + 88x^18 + 1406x^17 - 1488x^16 - 16808x^15 + 12300x^14 + 112044x^13 - 52936x^12 - 427504x^11 + 114160x^10 + 930280x^9 - 75840x^8 - 1117904x^7 - 130544x^6 + 685440x^5 + 222592x^4 - 153568x^3 - 89600x^2 - 11520x + 64	\( 2^{20}\cdot 7^{6}\cdot 37^{7}\cdot 1621^{6} \)	21T57	Trivial (GRH)
21.21.246696137770519024549261686620317576855552.1	x^21 - 7x^20 - 30x^19 + 276x^18 + 229x^17 - 4177x^16 + 958x^15 + 31524x^14 - 22008x^13 - 128130x^12 + 119206x^11 + 284832x^10 - 294144x^9 - 344214x^8 + 353470x^7 + 228416x^6 - 201861x^5 - 81891x^4 + 44564x^3 + 13672x^2 - 457x - 221	\( 2^{20}\cdot 37^{7}\cdot 11633^{6} \)	21T57	Trivial (GRH)