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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.13497977700448485769216.1	x^20 - 5x^19 + 17x^18 - 39x^17 + 80x^16 - 135x^15 + 217x^14 - 297x^13 + 392x^12 - 439x^11 + 477x^10 - 439x^9 + 392x^8 - 297x^7 + 217x^6 - 135x^5 + 80x^4 - 39x^3 + 17x^2 - 5x + 1	\( 2^{32}\cdot 61^{7} \)	20T671	Trivial
20.4.337385929308761961864713.1	x^20 + 3x^18 - 2x^17 + x^16 - 2x^15 - 13x^14 + 48x^13 - 2x^12 + 125x^11 - 18x^10 + 17x^9 - 141x^8 - 168x^7 - 166x^6 - 128x^5 - 52x^4 - 15x^3 + 3x^2 + 5x + 1	\( 2297^{7} \)	20T671	Trivial (GRH)
20.0.2099318241033027057614848.2	x^20 - 4x^19 + 8x^18 - 16x^17 + 33x^16 - 26x^15 + 52x^14 - 90x^13 + 74x^12 - 22x^11 + 144x^10 - 26x^9 + 78x^8 - 74x^7 - 8x^6 - 54x^5 + 17x^4 - 2x^3 + 12x^2 + 2x + 1	\( 2^{24}\cdot 277^{7} \)	20T671	Trivial (GRH)
20.4.3455482291314812356919296.1	x^20 - 8x^19 + 27x^18 - 48x^17 + 47x^16 - 44x^15 + 118x^14 - 296x^13 + 495x^12 - 580x^11 + 447x^10 - 152x^9 - 99x^8 + 180x^7 - 128x^6 + 64x^5 - 27x^4 + 3x^2 + 1	\( 2^{40}\cdot 61^{7} \)	20T671	Trivial (GRH)
20.4.12819390169663673256612900114045184.1	x^20 - x^19 + 12x^18 - 75x^17 + 265x^16 - 1058x^15 + 2205x^14 - 3436x^13 + 4274x^12 + 5840x^11 - 18867x^10 + 25478x^9 - 28749x^8 - 86545x^7 + 160862x^6 + 216686x^5 - 320346x^4 - 111111x^3 + 232630x^2 - 252825x + 91349	\( 2^{8}\cdot 33769^{7} \)	20T671	Trivial (GRH)
20.12.45702574402961582626142131083938873.1	x^20 - 8x^19 + 17x^18 + 45x^17 - 365x^16 + 1422x^15 - 4484x^14 + 4961x^13 + 10706x^12 - 9731x^11 - 41922x^10 - 60932x^9 + 428148x^8 - 428679x^7 - 514417x^6 + 1389564x^5 - 509143x^4 - 1026653x^3 + 807854x^2 + 114306x - 163831	\( 89417^{7} \)	20T671	Trivial (GRH)
20.12.45702574402961582626142131083938873.2	x^20 - 5x^19 - 24x^18 + 152x^17 + 259x^16 - 1401x^15 - 4914x^14 + 10685x^13 + 41618x^12 - 59641x^11 - 133294x^10 + 161474x^9 + 138008x^8 - 199625x^7 - 23642x^6 + 80244x^5 - 4063x^4 - 11828x^3 - 381x^2 + 1187x - 53	\( 89417^{7} \)	20T671	Trivial (GRH)
20.4.1347783697341346832395134211051765625.1	x^20 - 6x^19 + 31x^18 - 185x^17 + 726x^16 - 2791x^15 + 6707x^14 - 9101x^13 - 11182x^12 + 98279x^11 - 252388x^10 + 455708x^9 - 273344x^8 + 402406x^7 + 356280x^6 - 640982x^5 - 5312340x^4 + 3375181x^3 + 5015565x^2 + 1328191x - 4698119	\( 5^{6}\cdot 36497^{7} \)	20T671	Trivial (GRH)
20.16.3281763883433900353692902429195567104.1	x^20 - 6x^19 + x^18 + 21x^17 - 102x^16 + 1334x^15 - 3485x^14 - 840x^13 + 7595x^12 - 40626x^11 + 228412x^10 - 279903x^9 - 634103x^8 + 1697024x^7 - 862745x^6 - 723776x^5 + 757692x^4 - 108596x^3 - 63711x^2 + 16233x - 109	\( 2^{16}\cdot 33769^{7} \)	20T671	Trivial (GRH)
20.8.3281763883433900353692902429195567104.1	x^20 - 2x^19 - 3x^17 - 147x^16 - 62x^15 + 126x^14 - 466x^13 + 3948x^12 + 19936x^11 + 30672x^10 + 8094x^9 - 34971x^8 - 84730x^7 - 141424x^6 - 72959x^5 + 151574x^4 + 211092x^3 + 27618x^2 - 48025x + 2659	\( 2^{16}\cdot 33769^{7} \)	20T671	Trivial (GRH)
20.8.3281763883433900353692902429195567104.2	x^20 - 6x^19 + 21x^18 + 19x^17 - 301x^16 + 906x^15 - 2119x^14 + 1854x^13 - 3574x^12 + 2224x^11 + 61739x^10 - 43833x^9 - 199776x^8 - 11474x^7 + 257934x^6 - 65100x^5 - 577890x^4 - 293970x^3 + 56238x^2 + 6201x + 127	\( 2^{16}\cdot 33769^{7} \)	20T671	Trivial (GRH)
20.16.52508222134942405659086438867129073664.1	x^20 - 51x^18 - 108x^17 + 396x^16 + 1606x^15 + 5062x^14 + 13078x^13 - 23179x^12 - 174206x^11 - 267790x^10 - 68436x^9 + 381849x^8 + 1503534x^7 + 3279178x^6 + 3448322x^5 + 1008374x^4 - 1198918x^3 - 1251823x^2 - 451984x - 58981	\( 2^{20}\cdot 33769^{7} \)	20T671	Trivial (GRH)
20.20.52508222134942405659086438867129073664.1	x^20 - 10x^19 - 4x^18 + 283x^17 - 369x^16 - 3085x^15 + 5534x^14 + 16920x^13 - 33433x^12 - 49731x^11 + 101616x^10 + 75504x^9 - 158461x^8 - 50137x^7 + 118058x^6 + 6419x^5 - 37569x^4 + 5598x^3 + 3920x^2 - 1316x + 113	\( 2^{20}\cdot 33769^{7} \)	20T671	Trivial (GRH)
20.0.840131554159078490545383021874065178624.1	x^20 - 8x^19 + 49x^18 - 154x^17 + 472x^16 - 1742x^15 + 10710x^14 - 58962x^13 + 245772x^12 - 779470x^11 + 1916506x^10 - 3774324x^9 + 7846830x^8 - 13098808x^7 + 20131243x^6 + 4732336x^5 + 18103847x^4 + 727124x^3 + 4672912x^2 - 318602x + 899981	\( 2^{24}\cdot 33769^{7} \)	20T671	$[6, 4350]$ (GRH)
20.0.13442104866545255848726128349985042857984.1	x^20 + 77x^18 + 2406x^16 + 40674x^14 + 413385x^12 + 2625554x^10 + 10384201x^8 + 24381218x^6 + 30054410x^4 + 13946597x^2 + 33769	\( 2^{28}\cdot 33769^{7} \)	20T671	$[2, 46106]$ (GRH)
20.20.13442104866545255848726128349985042857984.1	x^20 - 95x^18 + 3274x^16 - 51403x^14 + 408466x^12 - 1756047x^10 + 4367477x^8 - 6483648x^6 + 5673192x^4 - 2701520x^2 + 540304	\( 2^{28}\cdot 33769^{7} \)	20T671	Trivial (GRH)