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 36 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.4108077596683185606441.1	x^20 - 8x^19 + 27x^18 - 49x^17 + 54x^16 - 53x^15 + 74x^14 - 78x^13 + 9x^12 + 59x^11 - 17x^10 - 68x^9 + 63x^8 + x^7 - 20x^6 + x^5 + 6x^4 - x^3 + x^2 - 2x + 1	\( 3^{10}\cdot 17^{4}\cdot 97^{6} \)	20T368	Trivial (GRH)
20.0.5156382820784106642241.1	x^20 - 5x^19 + 17x^18 - 41x^17 + 87x^16 - 150x^15 + 237x^14 - 318x^13 + 385x^12 - 418x^11 + 422x^10 - 377x^9 + 303x^8 - 205x^7 + 133x^6 - 82x^5 + 47x^4 - 19x^3 + 8x^2 - 3x + 1	\( 7^{10}\cdot 23^{2}\cdot 431^{4} \)	20T368	Trivial
20.0.44721246067437744140625.1	x^20 - 2x^19 + x^18 - 5x^17 + 14x^16 - 10x^15 + 3x^14 - 22x^13 + 44x^12 - 41x^11 + 36x^10 - 10x^9 + 36x^8 - 73x^7 + 45x^6 - 11x^5 + 34x^4 - 15x^3 + 9x^2 - 18x + 9	\( 3^{4}\cdot 5^{14}\cdot 67^{6} \)	20T368	Trivial (GRH)
20.0.44721246067437744140625.2	x^20 - x^19 + 8x^18 - 10x^17 + 21x^16 - 40x^15 + 34x^14 - 75x^13 + 87x^12 - 74x^11 + 143x^10 - 74x^9 + 87x^8 - 75x^7 + 34x^6 - 40x^5 + 21x^4 - 10x^3 + 8x^2 - x + 1	\( 3^{4}\cdot 5^{14}\cdot 67^{6} \)	20T368	Trivial (GRH)
20.0.60020399738333350163961.1	x^20 - 9x^19 + 34x^18 - 70x^17 + 84x^16 - 58x^15 + 39x^14 - 114x^13 + 339x^12 - 696x^11 + 1071x^10 - 1308x^9 + 1314x^8 - 1095x^7 + 759x^6 - 437x^5 + 207x^4 - 80x^3 + 25x^2 - 6x + 1	\( 3^{14}\cdot 17^{6}\cdot 151^{4} \)	20T368	Trivial (GRH)
20.0.156746706211961203326976.1	x^20 - 3x^18 + 4x^16 - 2x^14 + x^10 - 2x^6 + 4x^4 - 3x^2 + 1	\( 2^{20}\cdot 13^{4}\cdot 19^{2}\cdot 347^{4} \)	20T368	Trivial (GRH)
20.0.271341999200397872102841.1	x^20 - 2x^19 + 7x^18 - 8x^17 + 21x^16 - 22x^15 + 33x^14 - 29x^13 + 30x^12 - 13x^11 + 15x^10 + 13x^9 + 30x^8 + 29x^7 + 33x^6 + 22x^5 + 21x^4 + 8x^3 + 7x^2 + 2x + 1	\( 3^{14}\cdot 97^{2}\cdot 1567^{4} \)	20T368	Trivial (GRH)
20.4.344359285812922275390625.1	x^20 - 3x^19 + 12x^17 - 10x^16 - 35x^15 + 55x^14 + 39x^13 - 130x^12 + 10x^11 + 206x^10 - 130x^9 - 143x^8 + 201x^7 - 31x^6 - 78x^5 + 14x^4 + 9x^3 - 18x^2 - x + 1	\( 5^{10}\cdot 13^{4}\cdot 41^{4}\cdot 661^{2} \)	20T368	Trivial (GRH)
20.0.818158572767876702273536.1	x^20 - 3x^18 + 4x^16 + 2x^14 - 12x^12 + 17x^10 - 12x^8 + 2x^6 + 4x^4 - 3x^2 + 1	\( 2^{20}\cdot 29^{2}\cdot 5519^{4} \)	20T368	Trivial (GRH)
20.4.12465797319147795009765625.1	x^20 - 6x^19 + 9x^18 + 17x^17 - 55x^16 - 9x^15 + 117x^14 + 81x^13 - 395x^12 + 24x^11 + 648x^10 - 555x^9 - 138x^8 + 301x^7 + 99x^6 - 120x^5 + 207x^4 - 470x^3 + 547x^2 - 273x + 49	\( 5^{10}\cdot 13^{4}\cdot 41^{6}\cdot 97^{2} \)	20T368	Trivial (GRH)
20.4.18805933270743231481641721.1	x^20 - 3x^19 + 5x^18 - 17x^17 + 37x^16 + 9x^15 - 194x^14 + 401x^13 - 556x^12 + 1065x^11 - 2292x^10 + 3440x^9 - 3176x^8 + 1559x^7 - 12x^6 - 518x^5 + 348x^4 - 113x^3 + 12x^2 + 2x + 1	\( 13^{10}\cdot 97^{2}\cdot 347^{4} \)	20T368	Trivial (GRH)
20.0.75570724234611059753853009.1	x^20 - 5x^19 + 10x^18 - 15x^17 + 35x^16 - 86x^15 + 152x^14 - 197x^13 + 259x^12 - 400x^11 + 502x^10 - 481x^9 + 439x^8 - 370x^7 + 253x^6 - 151x^5 + 82x^4 - 39x^3 + 16x^2 - 5x + 1	\( 3^{10}\cdot 61^{6}\cdot 397^{4} \)	20T368	Trivial (GRH)
20.0.75570724234611059753853009.2	x^20 - 5x^19 + 18x^18 - 39x^17 + 73x^16 - 112x^15 + 174x^14 - 242x^13 + 286x^12 - 320x^11 + 317x^10 - 336x^9 + 268x^8 - 183x^7 + 164x^6 - 83x^5 + 52x^4 - 16x^3 + 9x^2 - 2x + 1	\( 3^{10}\cdot 61^{6}\cdot 397^{4} \)	20T368	Trivial (GRH)
20.8.78123008526754449462890625.1	x^20 - 5x^18 + 20x^16 - 25x^14 + 25x^12 - 301x^10 + 505x^8 - 165x^6 + 60x^4 - 45x^2 + 9	\( 3^{6}\cdot 5^{14}\cdot 23^{4}\cdot 89^{4} \)	20T368	Trivial (GRH)
20.0.104226732560060708467769344.1	x^20 - 2x^16 + 2x^14 - 3x^12 + 5x^10 - 3x^8 + 2x^6 - 2x^4 + 1	\( 2^{20}\cdot 17^{2}\cdot 61^{4}\cdot 397^{4} \)	20T368	$[3]$ (GRH)
20.0.191089745854193889068530761.1	x^20 - 5x^19 + 17x^18 - 38x^17 + 72x^16 - 123x^15 + 186x^14 - 257x^13 + 310x^12 - 319x^11 + 273x^10 - 295x^9 + 216x^8 - 111x^7 + 124x^6 - 15x^5 + 72x^4 + 30x^3 + 25x^2 + 5x + 1	\( 3^{10}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T368	Trivial (GRH)
20.0.382286008207589204343914496.1	x^20 - 2x^19 - 2x^18 - 14x^17 + 32x^16 - 70x^14 - 86x^13 + 629x^12 + 970x^11 + 1196x^10 + 316x^9 - 509x^8 - 678x^7 - 510x^6 + 4x^5 + 123x^4 + 94x^3 + 38x^2 - 12x + 1	\( 2^{30}\cdot 3^{10}\cdot 1567^{4} \)	20T368	$[2]$ (GRH)
20.0.455293169564857148863676416.1	x^20 + 13x^16 + 8x^14 + 2x^12 - 16x^10 + 2x^8 + 8x^6 + 13x^4 + 1	\( 2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T368	Trivial (GRH)
20.8.455293169564857148863676416.1	x^20 - 4x^18 + 15x^16 - 54x^14 + 31x^12 - 238x^10 - 8x^8 + 82x^6 + 21x^4 - 14x^2 + 1	\( 2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T368	Trivial (GRH)
20.8.486911802025734669619140625.1	x^20 - 4x^19 - 7x^18 + 40x^17 + 2x^16 - 165x^15 + 106x^14 + 411x^13 - 291x^12 - 554x^11 + 441x^10 + 590x^9 - 271x^8 - 449x^7 + 42x^6 + 198x^5 + 16x^4 - 40x^3 - 10x^2 + 4x + 1	\( 5^{10}\cdot 13^{4}\cdot 347^{6} \)	20T368	Trivial (GRH)
20.8.1953075213168861236572265625.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 226x^16 + 380x^15 + 194x^14 - 1072x^13 + 575x^12 + 814x^11 - 555x^10 - 674x^9 + 379x^8 + 412x^7 - 171x^6 - 95x^5 - 78x^4 + 127x^3 - 47x^2 + 9x - 1	\( 3^{6}\cdot 5^{16}\cdot 23^{4}\cdot 89^{4} \)	20T368	Trivial (GRH)
20.4.3178202722755606120397450849.1	x^20 - 3x^19 + 7x^18 - 31x^17 + 84x^16 - 207x^15 + 390x^14 - 865x^13 + 1764x^12 - 2715x^11 + 3797x^10 - 5272x^9 + 7488x^8 - 8788x^7 + 8066x^6 - 4996x^5 + 1968x^4 - 279x^3 + 17x^2 - 8x + 1	\( 13^{12}\cdot 97^{2}\cdot 347^{4} \)	20T368	Trivial (GRH)
20.12.6281540192907626635312758784.1	x^20 - 8x^18 + 13x^16 - 32x^14 + 50x^12 + 44x^10 - 34x^8 - 200x^6 + 197x^4 - 28x^2 + 1	\( 2^{44}\cdot 7^{2}\cdot 31^{4}\cdot 53^{4} \)	20T368	Trivial (GRH)
20.12.12498016119724696953525390625.1	x^20 - 5x^19 - 4x^18 + 43x^17 - 19x^16 - 112x^15 + 210x^14 + 98x^13 - 774x^12 - 328x^11 + 921x^10 + 630x^9 - 344x^8 - 543x^7 - 98x^6 + 227x^5 + 96x^4 - 42x^3 - 19x^2 + 2x + 1	\( 5^{10}\cdot 61^{6}\cdot 397^{4} \)	20T368	Trivial (GRH)
20.4.12498016119724696953525390625.1	x^20 - 5x^19 + 20x^18 - 45x^17 + 55x^16 - 46x^15 - 72x^14 + 7x^13 - 113x^12 + 50x^11 - 124x^10 - 119x^9 + 55x^8 + 82x^7 + 99x^6 - 49x^5 - 76x^4 - 33x^3 + 2x^2 + 5x + 1	\( 5^{10}\cdot 61^{6}\cdot 397^{4} \)	20T368	$[2]$ (GRH)
20.12.12498016119724696953525390625.2	x^20 - 5x^19 - 4x^18 + 56x^17 - 108x^16 + 79x^15 + 141x^14 - 690x^13 + 943x^12 + 343x^11 - 2573x^10 + 1979x^9 + 2124x^8 - 3128x^7 - 293x^6 + 1575x^5 - 248x^4 - 227x^3 + 19x^2 + 16x + 1	\( 5^{10}\cdot 61^{6}\cdot 397^{4} \)	20T368	Trivial (GRH)
20.12.18928478473103616375574757376.1	x^20 - 17x^18 + 121x^16 - 469x^14 + 1079x^12 - 1508x^10 + 1268x^8 - 638x^6 + 201x^4 - 26x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 23^{2}\cdot 4903^{4} \)	20T368	Trivial (GRH)
20.4.31602750247376961471572265625.1	x^20 + 6x^18 - 8x^17 - 3x^16 + 7x^15 + 224x^14 - 458x^13 + 659x^12 - 401x^11 - 27x^10 + 155x^9 - 19x^8 - 284x^7 + 166x^6 + 67x^5 - 87x^4 - 84x^3 - 34x^2 - 2x + 1	\( 5^{10}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T368	Trivial (GRH)
20.0.69504083479956608292792303616.1	x^20 - 2x^18 + 11x^16 - 5x^14 + 31x^12 + 29x^10 + 124x^8 - 80x^6 + 704x^4 - 512x^2 + 1024	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 439^{2} \)	20T368	$[3]$ (GRH)
20.16.97738885512935359526308151296.1	x^20 - 8x^19 + 18x^18 + 12x^17 - 150x^16 + 422x^15 - 434x^14 - 960x^13 + 3223x^12 - 1716x^11 - 4955x^10 + 6682x^9 + 2165x^8 - 6870x^7 + 322x^6 + 3148x^5 - 310x^4 - 640x^3 + 19x^2 + 34x - 1	\( 2^{40}\cdot 31^{4}\cdot 557^{4} \)	20T368	Trivial (GRH)
20.0.102239305125160963202612199424.1	x^20 + 5x^18 + 22x^16 + 67x^14 + 178x^12 + 385x^10 + 712x^8 + 1072x^6 + 1408x^4 + 1280x^2 + 1024	\( 2^{20}\cdot 47^{2}\cdot 81509^{4} \)	20T368	$[4]$ (GRH)
20.20.1033176787766327594146728515625.1	x^20 - 31x^18 + 383x^16 - 2494x^14 + 9467x^12 - 21771x^10 + 30363x^8 - 24809x^6 + 10867x^4 - 2026x^2 + 49	\( 3^{6}\cdot 5^{16}\cdot 23^{6}\cdot 89^{4} \)	20T368	Trivial (GRH)
20.0.1950870747766649155582852857856.1	x^20 + 12x^18 + 67x^16 + 182x^14 + 295x^12 + 110x^10 + 12x^8 - 334x^6 + 493x^4 - 320x^2 + 81	\( 2^{40}\cdot 36497^{4} \)	20T368	$[12]$ (GRH)
20.0.2433062929616749991460283088896.1	x^20 - x^16 - 50x^14 + 235x^12 - 264x^10 + 607x^8 - 764x^6 + 282x^4 + 456x^2 + 121	\( 2^{40}\cdot 38569^{4} \)	20T368	$[12]$ (GRH)
20.16.8455924749076998400000000000000.1	x^20 - 13x^18 + 50x^16 - 50x^14 - 92x^12 + 213x^10 - 92x^8 - 50x^6 + 50x^4 - 13x^2 + 1	\( 2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T368	Trivial (GRH)
20.20.4814952815150509881600000000000000.1	x^20 - 44x^18 + 727x^16 - 5938x^14 + 26610x^12 - 68394x^10 + 102563x^8 - 88319x^6 + 40956x^4 - 8740x^2 + 529	\( 2^{20}\cdot 3^{4}\cdot 5^{14}\cdot 23^{6}\cdot 89^{4} \)	20T368	Trivial (GRH)