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 matches 1-50 of 62)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.49226653653406684545024.4	x^20 + 5x^18 + 14x^16 + 25x^14 + 34x^12 + 38x^10 + 38x^8 + 31x^6 + 18x^4 + 6x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{4}\cdot 7369^{2} \)	20T1040	Trivial (GRH)
20.0.49226653653406684545024.5	x^20 + 5x^18 + 14x^16 + 27x^14 + 41x^12 + 47x^10 + 43x^8 + 30x^6 + 15x^4 + 5x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{4}\cdot 7369^{2} \)	20T1040	Trivial (GRH)
20.4.109150463284655166015625.1	x^20 - 5x^19 + 6x^18 + 12x^17 - 31x^16 - x^15 + 58x^14 - 41x^13 - 50x^12 + 88x^11 + 26x^10 - 83x^9 - 17x^8 + 21x^7 + 9x^5 + x^4 - 7x^3 + 5x^2 + 6x + 1	\( 5^{10}\cdot 97^{2}\cdot 1039^{2}\cdot 1049^{2} \)	20T1040	Trivial (GRH)
20.0.802821734410240000000000.1	x^20 + 7x^18 + 24x^16 + 53x^14 + 81x^12 + 87x^10 + 67x^8 + 38x^6 + 15x^4 + 5x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 280001^{2} \)	20T1040	Trivial (GRH)
20.0.802821734410240000000000.2	x^20 + 7x^18 + 21x^16 + 36x^14 + 42x^12 + 43x^10 + 41x^8 + 28x^6 + 15x^4 + 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 280001^{2} \)	20T1040	Trivial (GRH)
20.0.12164157316311040000000000.1	x^20 + 4x^18 + 2x^16 - 7x^14 + x^12 + 27x^10 + 29x^8 + 4x^6 - 4x^4 + x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1040	Trivial (GRH)
20.0.12164157316311040000000000.2	x^20 - x^14 - 17x^12 - 3x^10 + 34x^8 + 41x^6 + 25x^4 + 8x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1040	Trivial (GRH)
20.4.12164157316311040000000000.3	x^20 + 8x^18 + 27x^16 + 52x^14 + 63x^12 + 49x^10 + 20x^8 - x^6 - 6x^4 - 3x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1040	Trivial (GRH)
20.4.12164157316311040000000000.4	x^20 - 3x^18 + 5x^16 - 4x^14 - 2x^12 + 8x^10 - 8x^8 + x^6 + 3x^4 - 3x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1040	Trivial (GRH)
20.4.34772137021532160000000000.1	x^20 - 10x^18 + 47x^16 - 137x^14 + 271x^12 - 371x^10 + 346x^8 - 214x^6 + 89x^4 - 30x^2 + 9	\( 2^{20}\cdot 3^{2}\cdot 5^{10}\cdot 29^{2}\cdot 59^{2}\cdot 359^{2} \)	20T1040	Trivial (GRH)
20.8.69576619586656130166015625.1	x^20 - 8x^19 + 25x^18 - 37x^17 + 7x^16 + 96x^15 - 244x^14 + 275x^13 + 111x^12 - 840x^11 + 930x^10 + 130x^9 - 981x^8 + 531x^7 + 195x^6 - 267x^5 + 128x^4 - 82x^3 + 34x^2 - 2x - 1	\( 5^{10}\cdot 97^{2}\cdot 27517559^{2} \)	20T1040	Trivial (GRH)
20.4.215613371594352640000000000.1	x^20 - 2x^16 + 4x^14 - 4x^12 - 6x^10 + 9x^8 - 3x^6 - 4x^4 + 5x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 4588681^{2} \)	20T1040	Trivial (GRH)
20.4.215613371594352640000000000.2	x^20 + 10x^18 + 41x^16 + 82x^14 + 62x^12 - 51x^10 - 135x^8 - 93x^6 - 21x^4 + 2x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 4588681^{2} \)	20T1040	Trivial (GRH)
20.8.276787479753533440000000000.1	x^20 - 3x^18 + x^16 - 2x^14 + 6x^12 + 5x^10 - 2x^8 - 3x^6 - 6x^4 + 3x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 31^{2}\cdot 167711^{2} \)	20T1040	Trivial (GRH)
20.4.822089456036085760000000000.2	x^20 + 2x^18 + 12x^16 + 32x^12 - 160x^10 - 640x^6 + 512x^4 - 512x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 280001^{2} \)	20T1040	Trivial (GRH)
20.8.1254027648371107840000000000.1	x^20 - x^18 - 3x^16 - 2x^14 + 10x^10 + 5x^8 - 7x^6 - 3x^4 + 1	\( 2^{20}\cdot 5^{10}\cdot 11066329^{2} \)	20T1040	Trivial (GRH)
20.8.1814252107220674560000000000.1	x^20 - 12x^18 + 63x^16 - 192x^14 + 380x^12 - 518x^10 + 503x^8 - 349x^6 + 164x^4 - 48x^2 + 9	\( 2^{20}\cdot 3^{2}\cdot 5^{10}\cdot 4436879^{2} \)	20T1040	Trivial (GRH)
20.0.3264751135420800640000000000.1	x^20 + 13x^18 + 73x^16 + 235x^14 + 484x^12 + 669x^10 + 629x^8 + 397x^6 + 157x^4 + 30x^2 + 1	\( 2^{16}\cdot 5^{10}\cdot 19^{2}\cdot 349^{2}\cdot 10771^{2} \)	20T1040	Trivial (GRH)
20.12.7753892385981245440000000000.1	x^20 - 8x^18 + 26x^16 - 40x^14 + 13x^12 + 50x^10 - 68x^8 + 20x^6 + 11x^4 - 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1040	Trivial (GRH)
20.8.7753892385981245440000000000.3	x^20 - 7x^18 + 8x^16 + 13x^14 - 46x^12 + 29x^10 + 51x^8 - 58x^6 + x^4 + 8x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1040	Trivial (GRH)
20.8.7753892385981245440000000000.4	x^20 + x^18 - 7x^16 - 6x^14 + 6x^12 + 4x^10 + 9x^8 - 9x^4 + x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1040	Trivial (GRH)
20.12.7809157899955077021572265625.1	x^20 - 2x^19 - 3x^18 + 2x^17 + 11x^16 + 24x^15 - 183x^14 + 461x^13 - 526x^12 - 67x^11 + 839x^10 - 758x^9 + 72x^8 + 238x^7 - 180x^6 + 56x^5 + 51x^4 - 33x^3 - 9x^2 + 4x + 1	\( 5^{10}\cdot 97^{2}\cdot 419^{2}\cdot 695771^{2} \)	20T1040	Trivial (GRH)
20.12.8239247507322480640000000000.1	x^20 - 11x^18 + 52x^16 - 143x^14 + 258x^12 - 303x^10 + 190x^8 - 18x^6 - 31x^4 + 5x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2} \)	20T1040	Trivial (GRH)
20.8.8239247507322480640000000000.1	x^20 - 2x^18 - 9x^16 + 20x^14 + 12x^12 - 50x^10 + 33x^8 - 9x^4 + 2x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2} \)	20T1040	Trivial (GRH)
20.4.12456097091902504960000000000.1	x^20 + 6x^18 + 20x^16 + 32x^14 - 32x^12 - 256x^10 - 512x^8 - 128x^6 + 768x^4 + 1536x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1040	Trivial (GRH)
20.8.12456097091902504960000000000.2	x^20 + 8x^14 - 272x^12 + 96x^10 + 2176x^8 - 5248x^6 + 6400x^4 - 4096x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2} \)	20T1040	Trivial (GRH)
20.8.37682138330093578240000000000.2	x^20 - 5x^18 - 11x^16 + 41x^14 + 76x^12 - 61x^10 - 182x^8 - 90x^6 - 13x^4 + 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 60662149^{2} \)	20T1040	Trivial (GRH)
20.0.115518346967817840640000000000.1	x^20 + 12x^18 + 63x^16 + 192x^14 + 377x^12 + 498x^10 + 448x^8 + 267x^6 + 94x^4 + 16x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{6}\cdot 199^{2}\cdot 401^{2} \)	20T1040	Trivial (GRH)
20.8.117192491010130099240000000000.1	x^20 - 19x^18 + 153x^16 - 682x^14 + 1839x^12 - 3065x^10 + 3064x^8 - 1640x^6 + 307x^4 + 42x^2 + 1	\( 2^{12}\cdot 5^{10}\cdot 1711669441^{2} \)	20T1040	Trivial (GRH)
20.12.145709806576045624081650390625.1	x^20 - 5x^19 - 3x^18 + 49x^17 - 50x^16 - 57x^15 - 21x^14 - 62x^13 + 1209x^12 - 1598x^11 + 195x^10 - 478x^9 + 596x^8 + 2874x^7 - 4084x^6 + 1013x^5 + 1030x^4 - 944x^3 + 457x^2 - 142x + 19	\( 5^{10}\cdot 419^{4}\cdot 695771^{2} \)	20T1040	Trivial (GRH)
20.8.195228947498876925539306640625.1	x^20 - 2x^19 - 2x^18 - 12x^17 + 40x^16 + 62x^15 - 127x^14 - 34x^13 - 339x^12 - 475x^11 + 848x^10 + 1598x^9 + 1691x^8 + 2491x^7 + 929x^6 - 2114x^5 - 2959x^4 - 1555x^3 - 278x^2 - 5x + 1	\( 5^{12}\cdot 97^{2}\cdot 419^{2}\cdot 695771^{2} \)	20T1040	Trivial (GRH)
20.8.220788092512617103360000000000.1	x^20 - 14x^18 + 68x^16 - 96x^14 - 240x^12 + 1088x^10 - 2752x^8 + 3968x^6 + 1024x^4 - 5120x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 4588681^{2} \)	20T1040	Trivial (GRH)
20.8.220788092512617103360000000000.2	x^20 - 20x^18 + 164x^16 - 656x^14 + 992x^12 + 1632x^10 - 8640x^8 + 11904x^6 - 5376x^4 - 1024x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 4588681^{2} \)	20T1040	Trivial (GRH)
20.8.398768247298782423040000000000.2	x^20 - 2x^18 - 15x^16 + 24x^14 + 25x^12 - 126x^10 + 87x^8 + 65x^6 - 43x^4 - 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 1630891^{2} \)	20T1040	Trivial (GRH)
20.16.870283298342363146240000000000.1	x^20 - 14x^18 + 78x^16 - 218x^14 + 310x^12 - 179x^10 - 34x^8 + 71x^6 - 11x^4 - 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T1040	Trivial (GRH)
20.8.870283298342363146240000000000.1	x^20 + 2x^18 - 12x^16 - 14x^14 + 37x^12 + 33x^10 - 32x^8 - 29x^6 + 5x^4 + 7x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T1040	Trivial (GRH)
20.8.870283298342363146240000000000.2	x^20 + 6x^18 + 6x^16 - 26x^14 - 54x^12 + 13x^10 + 88x^8 + 31x^6 - 33x^4 - 14x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T1040	Trivial (GRH)
20.12.982692381976802928640000000000.1	x^20 - x^18 - 20x^16 + 35x^14 + 67x^12 - 195x^10 + 131x^8 - x^6 - 21x^4 + 2x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{2}\cdot 28162171^{2} \)	20T1040	Trivial (GRH)
20.16.1275284484745083136000000000000.1	x^20 - 12x^18 + 53x^16 - 89x^14 - 48x^12 + 402x^10 - 588x^8 + 359x^6 - 79x^4 + x^2 + 1	\( 2^{20}\cdot 5^{12}\cdot 1039^{2}\cdot 67931^{2} \)	20T1040	Trivial (GRH)
20.8.1342861649047383255040000000000.1	x^20 - 2x^18 - 22x^16 + 12x^14 + 157x^12 + 82x^10 - 239x^8 - 172x^6 + 51x^4 + 30x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 5471^{2}\cdot 66191^{2} \)	20T1040	Trivial (GRH)
20.4.1533846811270295971840000000000.1	x^20 + 7x^18 - x^16 - 59x^14 - 7x^12 + 104x^10 - 40x^8 - 7x^6 + 31x^4 + 11x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 29^{2}\cdot 13345751^{2} \)	20T1040	Trivial (GRH)
20.0.3642745164401140602041259765625.1	x^20 + 9x^18 - 11x^17 + 80x^16 - 132x^15 + 370x^14 - 771x^13 + 1774x^12 - 3647x^11 + 6326x^10 - 11208x^9 + 16824x^8 - 22586x^7 + 31893x^6 - 30556x^5 + 31624x^4 - 27418x^3 + 13365x^2 - 7827x + 5659	\( 5^{12}\cdot 419^{4}\cdot 695771^{2} \)	20T1040	$[2, 20]$ (GRH)
20.12.7865791409133578659840000000000.1	x^20 - 30x^18 + 403x^16 - 3188x^14 + 16418x^12 - 57390x^10 + 137529x^8 - 222375x^6 + 231278x^4 - 139048x^2 + 36481	\( 2^{20}\cdot 5^{10}\cdot 191^{2}\cdot 4588681^{2} \)	20T1040	Trivial (GRH)
20.4.7939985803244795330560000000000.1	x^20 + 16x^18 + 104x^16 + 320x^14 + 208x^12 - 1600x^10 - 4352x^8 - 2560x^6 + 2816x^4 + 3584x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 27517559^{2} \)	20T1040	Trivial (GRH)
20.4.8436989447498220175360000000000.1	x^20 + 22x^18 + 208x^16 + 1144x^14 + 4128x^12 + 9696x^10 + 12160x^8 + 2304x^6 - 7936x^4 - 2560x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2} \)	20T1040	Trivial (GRH)
20.8.8436989447498220175360000000000.1	x^20 - 2x^18 - 8x^16 - 24x^14 - 16x^12 + 640x^10 + 256x^8 - 3200x^6 - 768x^4 + 4096x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 3169^{2}\cdot 8951^{2} \)	20T1040	Trivial (GRH)
20.4.20749381843718408693760000000000.1	x^20 + 12x^18 + 54x^16 + 100x^14 + 3x^12 - 268x^10 - 360x^8 - 94x^6 + 119x^4 + 75x^2 + 9	\( 2^{20}\cdot 3^{2}\cdot 5^{10}\cdot 41^{2}\cdot 1789^{2}\cdot 6469^{2} \)	20T1040	Trivial (GRH)
20.4.30001277698593305405440000000000.1	x^20 + x^18 - 9x^16 - 10x^14 + 19x^12 + 19x^10 - 14x^8 - 16x^6 + 3x^4 + 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 1711669441^{2} \)	20T1040	$[2]$ (GRH)
20.4.36542618506240341195973780832256.1	x^20 + 6x^18 + 8x^16 - 12x^14 - 27x^12 + 8x^10 + 32x^8 + 2x^6 - 14x^4 - 4x^2 + 1	\( 2^{40}\cdot 3^{10}\cdot 59^{2}\cdot 402107^{2} \)	20T1040	Trivial (GRH)
20.12.891170097502579861749760000000000.1	x^20 - 12x^18 + 24x^16 + 208x^14 - 864x^12 - 416x^10 + 5632x^8 - 3968x^6 - 8448x^4 + 7168x^2 + 1024	\( 2^{30}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \)	20T1040	Trivial (GRH)