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 60)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.709000307415298179856.1	x^20 - 5x^19 + 15x^18 - 37x^17 + 78x^16 - 139x^15 + 219x^14 - 307x^13 + 386x^12 - 442x^11 + 463x^10 - 442x^9 + 386x^8 - 307x^7 + 219x^6 - 139x^5 + 78x^4 - 37x^3 + 15x^2 - 5x + 1	\( 2^{4}\cdot 83^{4}\cdot 983^{4} \)	20T669	Trivial
20.0.960210593667613720576.1	x^20 + 2x^18 + x^14 + 7x^12 - 6x^10 + 7x^8 + x^6 + 2x^2 + 1	\( 2^{20}\cdot 5501^{4} \)	20T669	Trivial
20.0.1083064869622628748241.1	x^20 - 4x^19 + 10x^18 - 17x^17 + 26x^16 - 29x^15 + 24x^14 - 5x^13 - 7x^12 + 20x^11 - 14x^10 + 8x^9 + 12x^8 + x^7 - 6x^6 + 9x^5 + 9x^4 - 2x^3 - x^2 + x + 1	\( 37^{4}\cdot 4903^{4} \)	20T669	Trivial
20.0.4519908793361499099136.2	x^20 + 6x^18 + 18x^16 + 31x^14 + 37x^12 + 37x^10 + 25x^8 + 16x^6 + 13x^4 + 6x^2 + 1	\( 2^{12}\cdot 32411^{4} \)	20T669	Trivial
20.0.8085321984821794902016.1	x^20 + 2x^18 + x^14 - x^12 - 5x^10 - x^8 + x^6 + 2x^2 + 1	\( 2^{12}\cdot 37483^{4} \)	20T669	Trivial (GRH)
20.0.12010577056389693116416.1	x^20 - x^18 + x^16 + 4x^14 - 6x^12 + 11x^10 - 6x^8 + 4x^6 + x^4 - x^2 + 1	\( 2^{12}\cdot 41381^{4} \)	20T669	Trivial (GRH)
20.4.23382101649260778427129.1	x^20 - x^19 - 5x^18 + 6x^17 + 5x^16 - 7x^15 + 7x^14 - 14x^13 - 5x^12 + 14x^11 + 8x^10 + 14x^9 - 29x^8 - 18x^7 + 23x^6 + 5x^5 - x^4 + x^3 - 5x^2 - x + 1	\( 7^{8}\cdot 43^{2}\cdot 1217^{4} \)	20T669	Trivial (GRH)
20.0.28726125440461678263841.1	x^20 - 5x^19 + 15x^18 - 35x^17 + 68x^16 - 109x^15 + 150x^14 - 184x^13 + 207x^12 - 219x^11 + 223x^10 - 219x^9 + 207x^8 - 184x^7 + 150x^6 - 109x^5 + 68x^4 - 35x^3 + 15x^2 - 5x + 1	\( 17^{4}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.0.156746706211961203326976.2	x^20 + x^18 + 2x^16 + 2x^14 + 2x^12 + 3x^10 + 2x^8 + 2x^6 + 2x^4 + x^2 + 1	\( 2^{20}\cdot 13^{4}\cdot 19^{2}\cdot 347^{4} \)	20T669	Trivial (GRH)
20.0.305268944861499322564249.1	x^20 - 2x^19 - 8x^18 + 9x^17 + 43x^16 - 9x^15 - 143x^14 - 56x^13 + 302x^12 + 173x^11 - 294x^10 - 261x^9 + 53x^8 + 168x^7 + 118x^6 + 4x^5 - 54x^4 - 19x^3 + 11x^2 + 7x + 1	\( 83^{6}\cdot 983^{4} \)	20T669	Trivial (GRH)
20.0.320555445021992182349824.1	x^20 + x^18 + 2x^16 + 3x^14 + 3x^12 + 3x^10 + 3x^8 + 3x^6 + 2x^4 + x^2 + 1	\( 2^{20}\cdot 23^{2}\cdot 4903^{4} \)	20T669	Trivial (GRH)
20.4.444622235903180809437184.1	x^20 - 2x^19 + 14x^17 - 44x^16 + 76x^15 - 56x^14 + 18x^13 + 15x^12 + 68x^11 - 202x^10 + 250x^9 - 182x^8 + 8x^7 + 96x^6 - 122x^5 + 68x^4 - 24x^3 + 2x - 1	\( 2^{30}\cdot 13^{4}\cdot 347^{4} \)	20T669	Trivial (GRH)
20.8.444622235903180809437184.1	x^20 - 4x^18 - 10x^17 - 3x^16 + 8x^15 + 48x^14 + 38x^13 + 48x^12 + 26x^11 - 20x^10 + 20x^9 - 53x^8 - 64x^7 - 14x^6 + 14x^5 + 51x^4 + 4x^3 - 18x^2 + 1	\( 2^{30}\cdot 13^{4}\cdot 347^{4} \)	20T669	Trivial (GRH)
20.8.444622235903180809437184.2	x^20 - 2x^19 - 6x^18 + 10x^17 + x^16 - 12x^15 + 48x^14 - 4x^13 - 2x^12 + 8x^11 - 116x^10 + 8x^9 - 2x^8 - 4x^7 + 48x^6 - 12x^5 + x^4 + 10x^3 - 6x^2 - 2x + 1	\( 2^{30}\cdot 13^{4}\cdot 347^{4} \)	20T669	Trivial (GRH)
20.0.581602509282833286165009.1	x^20 - x^19 + 5x^17 - 2x^16 - 7x^15 + 13x^14 + x^13 - 8x^12 + 2x^11 + 9x^10 + 2x^9 - 8x^8 + x^7 + 13x^6 - 7x^5 - 2x^4 + 5x^3 - x + 1	\( 3^{4}\cdot 17^{6}\cdot 4153^{4} \)	20T669	Trivial (GRH)
20.4.670930019119154175410176.1	x^20 - x^18 - 3x^16 + 4x^14 + 3x^12 - 9x^10 - 2x^8 + 9x^6 + x^4 - 3x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 41^{2}\cdot 631^{4} \)	20T669	Trivial (GRH)
20.4.673757209047664342073344.1	x^20 + 3x^18 + 4x^16 - 2x^14 - 18x^12 - 29x^10 - 18x^8 - 2x^6 + 4x^4 + 3x^2 + 1	\( 2^{20}\cdot 53^{2}\cdot 3889^{4} \)	20T669	Trivial (GRH)
20.4.818158572767876702273536.1	x^20 - 7x^18 + 22x^16 - 41x^14 + 50x^12 - 37x^10 + 11x^8 + 6x^6 - 7x^4 + 1	\( 2^{20}\cdot 29^{2}\cdot 5519^{4} \)	20T669	Trivial (GRH)
20.0.829565981540845553188864.1	x^20 + 6x^18 + 18x^16 + 31x^14 + 23x^12 - 9x^10 - 26x^8 - 9x^6 + 5x^4 + 2x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 4903^{4} \)	20T669	Trivial (GRH)
20.4.829565981540845553188864.1	x^20 + x^18 - 11x^14 + 11x^12 - 12x^10 + 34x^8 - 37x^6 + 19x^4 - 6x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 4903^{4} \)	20T669	Trivial (GRH)
20.4.829565981540845553188864.2	x^20 - 3x^18 + 7x^16 - 18x^14 + 34x^12 - 47x^10 + 41x^8 - 26x^6 + 15x^4 - 4x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 4903^{4} \)	20T669	Trivial (GRH)
20.0.1860495326773308902342656.2	x^20 - x^18 + x^14 - x^12 + x^10 - x^8 + x^6 - x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T669	$[2]$ (GRH)
20.0.2320349626175642005405696.1	x^20 - x^12 + x^10 - x^8 + 1	\( 2^{20}\cdot 38569^{4} \)	20T669	$[2]$ (GRH)
20.4.4884303117783989161027984.1	x^20 - 5x^19 + 16x^18 - 42x^17 + 92x^16 - 178x^15 + 301x^14 - 450x^13 + 570x^12 - 661x^11 + 702x^10 - 632x^9 + 565x^8 - 462x^7 + 360x^6 - 261x^5 + 201x^4 + 10x^2 + 9x + 1	\( 2^{4}\cdot 83^{6}\cdot 983^{4} \)	20T669	Trivial (GRH)
20.4.7170151093155466780795369.1	x^20 - 4x^19 + 6x^18 - 8x^17 + 8x^16 + 3x^15 - 29x^14 + 40x^13 - 3x^12 - 31x^11 + 35x^10 - 31x^9 - 3x^8 + 40x^7 - 29x^6 + 3x^5 + 8x^4 - 8x^3 + 6x^2 - 4x + 1	\( 53^{6}\cdot 4241^{4} \)	20T669	Trivial (GRH)
20.4.16907520178290136214142976.3	x^20 - x^18 - 3x^16 - 17x^14 - 26x^12 - 36x^10 - 26x^8 - 17x^6 - 3x^4 - x^2 + 1	\( 2^{32}\cdot 89^{8} \)	20T669	Trivial (GRH)
20.4.18935287231287814496631729.1	x^20 + 2x^18 - 3x^16 - 21x^14 - 72x^12 - 183x^10 - 192x^8 + 51x^6 + 181x^4 + 66x^2 + 1	\( 3^{4}\cdot 17^{4}\cdot 97^{2}\cdot 4153^{4} \)	20T669	Trivial (GRH)
20.4.42818699878251316432179649.1	x^20 - 10x^19 + 44x^18 - 100x^17 + 77x^16 + 207x^15 - 725x^14 + 990x^13 - 493x^12 - 480x^11 + 1008x^10 - 774x^9 + 485x^8 - 702x^7 + 1009x^6 - 837x^5 + 371x^4 - 86x^3 + 26x^2 - 8x + 1	\( 83^{4}\cdot 983^{6} \)	20T669	Trivial (GRH)
20.0.46465044146768981515042816.1	x^20 + 2x^18 - 7x^16 + 5x^14 + 11x^12 - 20x^10 + 11x^8 + 5x^6 - 7x^4 + 2x^2 + 1	\( 2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T669	$[2]$ (GRH)
20.8.46465044146768981515042816.1	x^20 - 3x^18 - x^16 + 2x^14 + 5x^12 + 8x^10 + 5x^8 + 2x^6 - x^4 - 3x^2 + 1	\( 2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T669	Trivial (GRH)
20.0.46465044146768981515042816.2	x^20 + 3x^18 - x^16 - 2x^14 + 5x^12 - 8x^10 + 5x^8 - 2x^6 - x^4 + 3x^2 + 1	\( 2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T669	$[2]$ (GRH)
20.8.46465044146768981515042816.2	x^20 - 8x^18 + 24x^16 - 27x^14 - 10x^12 + 14x^10 + 84x^8 - 103x^6 + 17x^4 - 12x^2 + 4	\( 2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T669	Trivial (GRH)
20.8.46465044146768981515042816.3	x^20 - 2x^18 - 7x^16 - 5x^14 + 11x^12 + 20x^10 + 11x^8 - 5x^6 - 7x^4 - 2x^2 + 1	\( 2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T669	Trivial (GRH)
20.8.46465044146768981515042816.4	x^20 - 8x^18 + 12x^16 - 15x^14 + 32x^12 - 33x^10 + 30x^8 - 43x^6 + 41x^4 - 20x^2 + 4	\( 2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T669	Trivial (GRH)
20.8.52642662275826068288374921.1	x^20 - 10x^19 + 41x^18 - 84x^17 + 64x^16 + 100x^15 - 345x^14 + 461x^13 - 431x^12 + 701x^11 - 1487x^10 + 1995x^9 - 1210x^8 - 583x^7 + 1972x^6 - 2087x^5 + 1330x^4 - 551x^3 + 143x^2 - 20x + 1	\( 149^{6}\cdot 1481^{4} \)	20T669	Trivial (GRH)
20.4.104226732560060708467769344.1	x^20 - 2x^18 + 2x^16 - 2x^14 + x^12 - x^10 + x^8 - 2x^6 + 2x^4 - 2x^2 + 1	\( 2^{20}\cdot 17^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.0.104226732560060708467769344.2	x^20 + 10x^18 + 48x^16 + 138x^14 + 255x^12 + 301x^10 + 211x^8 + 80x^6 + 14x^4 + 2x^2 + 1	\( 2^{20}\cdot 17^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.4.104226732560060708467769344.2	x^20 - 2x^18 + x^16 - x^14 + 2x^12 - 3x^10 + 2x^8 - x^6 + x^4 - 2x^2 + 1	\( 2^{20}\cdot 17^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.0.104226732560060708467769344.3	x^20 - 3x^18 + 8x^16 - 3x^14 + 40x^12 + 2x^10 + 30x^8 + 22x^6 + 9x^2 + 1	\( 2^{20}\cdot 17^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.12.160508627161048272206823424.1	x^20 - 2x^19 - 16x^18 + 42x^17 + 57x^16 - 216x^15 + 38x^14 + 88x^13 + 368x^12 - 270x^11 - 388x^10 + 28x^9 + 583x^8 - 94x^7 - 568x^6 + 416x^5 + 27x^4 - 152x^3 + 72x^2 - 14x + 1	\( 2^{30}\cdot 13^{4}\cdot 19^{2}\cdot 347^{4} \)	20T669	Trivial (GRH)
20.12.303303398211110919797211136.1	x^20 - 5x^18 + 6x^16 + 2x^14 - 9x^10 + 2x^6 + 6x^4 - 5x^2 + 1	\( 2^{20}\cdot 29^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.12.328077615685375622346297241.1	x^20 - 7x^19 + 12x^18 + 6x^17 - 32x^16 + 51x^15 - 12x^14 - 151x^13 + 57x^12 + 203x^11 - 53x^10 - 203x^9 + 57x^8 + 151x^7 - 12x^6 - 51x^5 - 32x^4 - 6x^3 + 12x^2 + 7x + 1	\( 7^{8}\cdot 53^{4}\cdot 139^{6} \)	20T669	Trivial (GRH)
20.12.369301640628035174640123904.1	x^20 - 6x^19 - 2x^18 + 62x^17 - 34x^16 - 272x^15 + 218x^14 + 626x^13 - 771x^12 - 286x^11 + 812x^10 - 262x^9 - 424x^8 + 446x^7 + 76x^6 - 306x^5 + 88x^4 + 72x^3 - 44x^2 + 4x + 1	\( 2^{30}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.4.369301640628035174640123904.1	x^20 - 6x^19 + 22x^18 - 66x^17 + 170x^16 - 364x^15 + 632x^14 - 888x^13 + 915x^12 - 156x^11 - 1944x^10 + 5142x^9 - 8741x^8 + 11514x^7 - 10502x^6 + 5324x^5 - 1637x^4 + 1426x^3 - 548x^2 - 170x + 25	\( 2^{30}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.12.423988229267185465614291561.1	x^20 - x^19 - 19x^18 + 9x^17 + 159x^16 + 7x^15 - 733x^14 - 382x^13 + 1886x^12 + 1875x^11 - 2270x^10 - 3913x^9 - 146x^8 + 3180x^7 + 2873x^6 + 300x^5 - 1549x^4 - 1071x^3 - 220x^2 - 4x + 1	\( 3^{10}\cdot 17^{6}\cdot 4153^{4} \)	20T669	Trivial (GRH)
20.12.493724556659941556721025024.1	x^20 - 12x^18 + 64x^16 - 195x^14 + 395x^12 - 605x^10 + 686x^8 - 496x^6 + 195x^4 - 33x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.4.499920644788987878141015625.1	x^20 - 5x^19 + 12x^18 - 32x^17 + 69x^16 - 78x^15 + 139x^14 - 240x^13 + 124x^12 - 290x^11 + 463x^10 - 204x^9 + 1209x^8 - 3208x^7 + 4811x^6 - 4727x^5 + 2852x^4 - 1210x^3 + 235x^2 - 29x - 1	\( 5^{8}\cdot 61^{6}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.4.666834700704333044833583104.1	x^20 + 8x^18 + 21x^16 + 6x^14 - 81x^12 - 171x^10 - 134x^8 - 36x^6 - 9x^4 - 7x^2 + 1	\( 2^{20}\cdot 43^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.4.842282596413217092613998736.1	x^20 - x^19 - x^18 + 11x^17 - 13x^16 + 36x^15 - 6x^14 + 63x^12 + 101x^11 + 83x^10 + 60x^9 + 328x^8 - 388x^7 + 1076x^6 + 114x^5 + 121x^4 - 84x^3 - 16x + 4	\( 2^{4}\cdot 149^{6}\cdot 1481^{4} \)	20T669	Trivial (GRH)
20.8.1147196059403710132070733249.1	x^20 - 2x^19 - 7x^18 + 15x^17 - 11x^16 + 8x^15 + 44x^14 - 165x^13 + 151x^12 + 206x^11 - 289x^10 - 60x^9 + 227x^8 - 677x^7 + 1108x^6 - 552x^5 - 319x^4 + 101x^3 + 53x^2 + 2x - 1	\( 3^{8}\cdot 97^{2}\cdot 65657^{4} \)	20T669	Trivial (GRH)