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 13 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.20.7198079267989980836471065337135104.1	x^22 - 24x^20 + 220x^18 - 980x^16 + 2267x^14 - 2696x^12 + 1324x^10 + 265x^8 - 563x^6 + 215x^4 - 29x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.20.15891297445653813609959315666834999.1	x^22 - 11x^21 + 41x^20 - 25x^19 - 223x^18 + 525x^17 + 92x^16 - 1654x^15 + 1480x^14 + 1772x^13 - 3759x^12 + 506x^11 + 3901x^10 - 2800x^9 - 1867x^8 + 2565x^7 + 335x^6 - 1066x^5 - 4x^4 + 202x^3 + 3x^2 - 14x - 1	\( -\,79\cdot 1451^{2}\cdot 18521\cdot 71823490019^{2} \)	22T53	Trivial (GRH)
22.20.41132601907967489839076730415672831.1	x^22 - 11x^21 + 39x^20 - 5x^19 - 285x^18 + 513x^17 + 519x^16 - 2214x^15 + 571x^14 + 4063x^13 - 3308x^12 - 3539x^11 + 4878x^10 + 1039x^9 - 3472x^8 + 490x^7 + 1272x^6 - 427x^5 - 239x^4 + 95x^3 + 25x^2 - 5x - 1	\( -\,151\cdot 2053^{2}\cdot 33769\cdot 43747835269^{2} \)	22T53	Trivial (GRH)
22.20.165555823163769559238834502754107392.1	x^22 - 23x^20 + 207x^18 - 897x^16 + 1679x^14 + 483x^12 - 7636x^10 + 13041x^8 - 9660x^6 + 3312x^4 - 483x^2 + 23	\( -\,2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.20.56501459388151144478039723653407440896.1	x^22 - 25x^20 + 250x^18 - 1243x^16 + 2879x^14 - 334x^12 - 14126x^10 + 33691x^8 - 35857x^6 + 18585x^4 - 4105x^2 + 289	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.20.56501459388151144478039723653407440896.2	x^22 - 28x^20 + 296x^18 - 1503x^16 + 3716x^14 - 3348x^12 - 2647x^10 + 7446x^8 - 5457x^6 + 1686x^4 - 192x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.20.282486367499249645189922024341045561876.1	x^22 - 3x^21 - 17x^20 + 53x^19 + 120x^18 - 388x^17 - 461x^16 + 1529x^15 + 1071x^14 - 3536x^13 - 1601x^12 + 4931x^11 + 1610x^10 - 4134x^9 - 1099x^8 + 2031x^7 + 485x^6 - 555x^5 - 128x^4 + 76x^3 + 18x^2 - 4x - 1	\( -\,2^{2}\cdot 5647\cdot 36767\cdot 31618751\cdot 10757635112949841811531 \)	22T59	Trivial (GRH)
22.20.245193039241591144351217789804876939315088.1	x^22 - x^21 - 22x^20 + 21x^19 + 204x^18 - 185x^17 - 1038x^16 + 888x^15 + 3162x^14 - 2526x^13 - 5908x^12 + 4344x^11 + 6683x^10 - 4429x^9 - 4388x^8 + 2536x^7 + 1577x^6 - 744x^5 - 294x^4 + 95x^3 + 28x^2 - 4x - 1	\( -\,2^{4}\cdot 3^{4}\cdot 19^{2}\cdot 31\cdot 65380800771598157\cdot 258573494153022619 \)	22T59	Trivial (GRH)
22.20.1580153645858805893796455628954412194463744.1	x^22 - 55x^20 + 1199x^18 - 13299x^16 + 81114x^14 - 279642x^12 + 532422x^10 - 491194x^8 + 80201x^6 + 190157x^4 - 119053x^2 + 18225	\( -\,2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.20.6320614583435223575185822515817648777854976.1	x^22 - 55x^20 + 1177x^18 - 12639x^16 + 73898x^14 - 237402x^12 + 390258x^10 - 246906x^8 - 33011x^6 + 40249x^4 - 451x^2 + 1	\( -\,2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.20.15646172003756569249283257910156250000000000.1	x^22 - 61x^20 + 1150x^18 - 7485x^16 - 13755x^14 + 419313x^12 - 2209803x^10 + 5513775x^8 - 7283940x^6 + 4978855x^4 - 1483189x^2 + 85264	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.20.4129233136056857981979443884256982828952059904.1	x^22 - 68x^20 + 1749x^18 - 21878x^16 + 146579x^14 - 538577x^12 + 1028049x^10 - 796919x^8 - 100770x^6 + 299644x^4 - 34200x^2 + 729	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.20.4129233136056857981979443884256982828952059904.2	x^22 - 48x^20 + 773x^18 - 5165x^16 + 14676x^14 - 11976x^12 - 15879x^10 + 31691x^8 - 16674x^6 + 3536x^4 - 313x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)