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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.577860666762298833296687104.1	x^22 - 2x^20 - 2x^19 + 5x^18 + 6x^17 - 5x^16 - 12x^15 + 2x^14 + 18x^13 + 4x^12 - 18x^11 - 11x^10 + 14x^9 + 14x^8 - 8x^7 - 11x^6 + 2x^5 + 8x^4 - 4x^2 + 1	\( -\,2^{30}\cdot 73^{2}\cdot 577\cdot 53149\cdot 3293113 \)	22T57	Trivial (GRH)
22.0.1441291887151686135870128128.1	x^22 - 2x^20 - 2x^19 + 5x^18 + 6x^17 - 5x^16 - 12x^15 + 2x^14 + 18x^13 + 4x^12 - 18x^11 - 11x^10 + 14x^9 + 15x^8 - 8x^7 - 12x^6 + 2x^5 + 8x^4 - 4x^2 + 1	\( -\,2^{22}\cdot 10177\cdot 33765428299628041 \)	22T57	Trivial (GRH)
22.2.126778690041778214971308507136.1	x^22 - 4x^21 + 14x^20 - 38x^19 + 89x^18 - 184x^17 + 341x^16 - 572x^15 + 876x^14 - 1228x^13 + 1579x^12 - 1862x^11 + 2008x^10 - 1978x^9 + 1765x^8 - 1416x^7 + 1009x^6 - 628x^5 + 333x^4 - 144x^3 + 47x^2 - 10x + 1	\( 2^{33}\cdot 11^{2}\cdot 121975057867858073 \)	22T57	Trivial (GRH)
22.6.1572374828482515451166834294784.1	x^22 - 4x^21 + 8x^20 - 8x^19 - 2x^18 + 20x^17 - 32x^16 + 22x^15 + 9x^14 - 38x^13 + 40x^12 - 12x^11 - 20x^10 + 30x^9 - 15x^8 - 6x^7 + 12x^6 - 8x^5 - x^4 + 4x^3 - 2x^2 + 1	\( 2^{33}\cdot 3^{2}\cdot 47\cdot 311\cdot 1391443157437409 \)	22T57	Trivial (GRH)
22.4.12168778905430087144801751269376.1	x^22 - 2x^21 - x^20 + 10x^19 - 11x^18 - 10x^17 + 34x^16 - 18x^15 - 34x^14 + 50x^13 + x^12 - 52x^11 + 28x^10 + 28x^9 - 36x^8 - 2x^7 + 23x^6 - 8x^5 - 6x^4 + 6x^3 - x^2 - 2x + 1	\( -\,2^{33}\cdot 1416632312516459164303 \)	22T57	Trivial (GRH)
22.4.31964561289410824381582196867072.1	x^22 - 2x^21 + 3x^20 - 2x^19 - 3x^18 + 6x^17 - 10x^16 + 6x^15 + 2x^14 - 6x^13 + 13x^12 - 4x^11 + 4x^9 - 8x^8 - 2x^7 - x^6 - 4x^5 + 2x^4 + 2x^3 + x^2 + 2x - 1	\( -\,2^{33}\cdot 235475711\cdot 15802753811681 \)	22T57	Trivial (GRH)
22.2.58315043828929313782568927100928.1	x^22 - 8x^21 + 32x^20 - 90x^19 + 202x^18 - 378x^17 + 607x^16 - 856x^15 + 1073x^14 - 1210x^13 + 1241x^12 - 1164x^11 + 1007x^10 - 806x^9 + 595x^8 - 406x^7 + 253x^6 - 144x^5 + 73x^4 - 34x^3 + 14x^2 - 4x + 1	\( 2^{33}\cdot 223\cdot 94616983\cdot 321748692401 \)	22T57	Trivial (GRH)
22.6.2235701649852680852322529969176576.1	x^22 - 2x^21 - x^20 + 8x^19 - 9x^18 - 2x^17 + 15x^16 - 16x^15 + 8x^14 + 2x^13 - 14x^12 + 22x^11 - 13x^10 - 6x^9 + 13x^8 - 10x^7 + 4x^6 - 5x^4 + 6x^3 - x^2 - 2x + 1	\( 2^{33}\cdot 3^{2}\cdot 11^{2}\cdot 241\cdot 991697156691810497 \)	22T57	Trivial (GRH)
22.6.5846186244289687455223944279228416.1	x^22 + 2x^20 - 4x^19 - 3x^18 - 6x^17 + 12x^15 + 10x^14 + 12x^13 - 9x^12 - 16x^11 - 16x^10 - 8x^9 + 11x^8 + 10x^7 + 9x^6 + 2x^5 - 5x^4 - 2x^3 - 2x^2 + 1	\( 2^{33}\cdot 7\cdot 39297136127\cdot 2474137595057 \)	22T57	Trivial (GRH)
22.6.6719996816960288878148142661369856.1	x^22 - 2x^21 - x^20 + 10x^19 - 11x^18 - 8x^17 + 30x^16 - 20x^15 - 16x^14 + 34x^13 - 18x^12 - 4x^11 + 13x^10 - 16x^9 + 13x^8 - 12x^6 + 8x^5 - 2x^4 + x^2 - 2x + 1	\( 2^{33}\cdot 2399\cdot 3769\cdot 593353\cdot 145817511551 \)	22T57	Trivial (GRH)
22.12.548480837855418232714401433337724928.1	x^22 - 2x^21 - 15x^20 + 28x^19 + 98x^18 - 162x^17 - 370x^16 + 496x^15 + 903x^14 - 844x^13 - 1496x^12 + 726x^11 + 1679x^10 - 122x^9 - 1197x^8 - 302x^7 + 462x^6 + 244x^5 - 62x^4 - 68x^3 - 5x^2 + 6x + 1	\( -\,2^{33}\cdot 7\cdot 113\cdot 66841\cdot 1207680851138975089 \)	22T57	Trivial (GRH)
22.12.954120607243639301569748987902164992.1	x^22 - 2x^21 - 21x^20 + 32x^19 + 193x^18 - 192x^17 - 983x^16 + 496x^15 + 2915x^14 - 344x^13 - 4994x^12 - 730x^11 + 4913x^10 + 1626x^9 - 2700x^8 - 1304x^7 + 754x^6 + 502x^5 - 75x^4 - 90x^3 - 5x^2 + 6x + 1	\( -\,2^{33}\cdot 71979199\cdot 1543143840124960849 \)	22T57	Trivial (GRH)
22.18.2855192247049898659094689096800227295232.1	x^22 - 22x^20 + 207x^18 - 2x^17 - 1092x^16 + 28x^15 + 3559x^14 - 156x^13 - 7445x^12 + 450x^11 + 10059x^10 - 736x^9 - 8611x^8 + 714x^7 + 4442x^6 - 426x^5 - 1238x^4 + 152x^3 + 140x^2 - 24x - 1	\( 2^{33}\cdot 79\cdot 3767\cdot 449833\cdot 2443537\cdot 1016137678657 \)	22T57	Trivial (GRH)
22.16.4849461357032540054012505516531188236288.1	x^22 - 4x^21 - 14x^20 + 64x^19 + 85x^18 - 434x^17 - 310x^16 + 1626x^15 + 804x^14 - 3674x^13 - 1589x^12 + 5118x^11 + 2305x^10 - 4288x^9 - 2238x^8 + 1974x^7 + 1299x^6 - 372x^5 - 387x^4 - 22x^3 + 42x^2 + 12x + 1	\( -\,2^{33}\cdot 31\cdot 2287\cdot 372719\cdot 21364574876217246673 \)	22T57	Trivial (GRH)
22.14.11415669953671419566832206870342147244032.1	x^22 - 6x^21 - 5x^20 + 90x^19 - 75x^18 - 502x^17 + 754x^16 + 1304x^15 - 2700x^14 - 1626x^13 + 4915x^12 + 730x^11 - 4996x^10 + 344x^9 + 2915x^8 - 496x^7 - 983x^6 + 192x^5 + 193x^4 - 32x^3 - 21x^2 + 2x + 1	\( 2^{33}\cdot 7\cdot 5926651993\cdot 32033476985376969871 \)	22T57	Trivial (GRH)
22.16.47139885424515679279908496898278071205888.1	x^22 - 4x^21 - 16x^20 + 70x^19 + 116x^18 - 516x^17 - 533x^16 + 2066x^15 + 1752x^14 - 4808x^13 - 4036x^12 + 6422x^11 + 5961x^10 - 4476x^9 - 5101x^8 + 1158x^7 + 2240x^6 + 184x^5 - 405x^4 - 106x^3 + 19x^2 + 10x + 1	\( -\,2^{33}\cdot 7^{3}\cdot 31\cdot 89\cdot 1033\cdot 5613742962947696588359 \)	22T57	Trivial (GRH)
22.14.101482802839751113302452158783383633133568.1	x^22 - 2x^21 - 21x^20 + 32x^19 + 193x^18 - 192x^17 - 983x^16 + 496x^15 + 2915x^14 - 344x^13 - 4994x^12 - 730x^11 + 4915x^10 + 1626x^9 - 2700x^8 - 1304x^7 + 754x^6 + 502x^5 - 77x^4 - 90x^3 - 5x^2 + 6x + 1	\( 2^{33}\cdot 1721\cdot 9473\cdot 146628265753\cdot 4942156467121 \)	22T57	Trivial (GRH)
22.14.944768395651470345630534739134881931984896.1	x^22 - 6x^21 - 5x^20 + 90x^19 - 75x^18 - 502x^17 + 754x^16 + 1304x^15 - 2700x^14 - 1626x^13 + 4915x^12 + 730x^11 - 4994x^10 + 344x^9 + 2913x^8 - 496x^7 - 983x^6 + 192x^5 + 193x^4 - 32x^3 - 21x^2 + 2x + 1	\( 2^{33}\cdot 7^{2}\cdot 97\cdot 601\cdot 21863\cdot 17802497\cdot 98924197902511 \)	22T57	Trivial (GRH)