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 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.3455482291314812356919296.2	x^20 - 3x^19 + 6x^17 - 5x^16 + 8x^15 - 76x^13 + 78x^12 + 174x^11 - 200x^10 - 116x^9 + 202x^8 - 80x^7 - 128x^6 + 72x^5 + 12x^4 - 12x^3 + 8x^2 - 8x - 4	\( 2^{40}\cdot 61^{7} \)	20T966	Trivial (GRH)
20.2.7373869322657929465211312.1	x^20 - 7x^19 + 18x^18 - 20x^17 - 3x^16 + 49x^15 - 79x^14 + 79x^13 - 43x^12 - 17x^11 + 48x^10 - 17x^9 - 43x^8 + 79x^7 - 79x^6 + 49x^5 - 3x^4 - 20x^3 + 18x^2 - 7x + 1	\( -\,2^{4}\cdot 19^{8}\cdot 83^{7} \)	20T966	Trivial
20.2.12233251970273405676027904.1	x^20 - 5x^18 - 4x^17 + 13x^16 + 4x^15 + 6x^14 - 18x^13 + 7x^12 - 18x^11 - 43x^10 + 26x^9 + 33x^8 + 50x^7 - 14x^6 - 16x^5 + 3x^4 - 56x^3 - 21x^2 + 10x - 1	\( -\,2^{24}\cdot 13^{8}\cdot 19^{7} \)	20T966	Trivial
20.4.55287716661036997710708736.1	x^20 - 3x^19 - 3x^18 + 19x^17 - 15x^16 - 12x^15 + 12x^14 - 4x^13 + 22x^12 + 6x^11 - 42x^10 - 6x^9 + 22x^8 + 4x^7 + 12x^6 + 12x^5 - 15x^4 - 19x^3 - 3x^2 + 3x + 1	\( 2^{44}\cdot 61^{7} \)	20T966	Trivial (GRH)
20.0.55287716661036997710708736.2	x^20 + 5x^18 + 23x^16 + 42x^14 + 13x^12 - 81x^10 - 91x^8 + 94x^6 + 71x^4 - 35x^2 + 61	\( 2^{44}\cdot 61^{7} \)	20T966	Trivial (GRH)
20.0.55287716661036997710708736.3	x^20 + 10x^18 + 35x^16 + 44x^14 + 13x^12 + 122x^10 + 505x^8 + 808x^6 + 723x^4 + 350x^2 + 61	\( 2^{44}\cdot 61^{7} \)	20T966	Trivial (GRH)
20.6.141123228345293902340861952.1	x^20 - 13x^18 + 68x^16 - 181x^14 + 247x^12 - 126x^10 - 70x^8 + 114x^6 - 51x^4 + 15x^2 - 3	\( -\,2^{12}\cdot 3^{7}\cdot 251^{8} \)	20T966	Trivial (GRH)
20.6.195732031524374490816446464.1	x^20 - 13x^18 + 67x^16 - 190x^14 + 329x^12 - 355x^10 + 193x^8 + 38x^6 - 133x^4 + 95x^2 - 19	\( -\,2^{28}\cdot 13^{8}\cdot 19^{7} \)	20T966	Trivial (GRH)
20.4.558095166421902810436075520000000.4	x^20 + x^18 - 41x^16 - 230x^14 - 555x^12 - 613x^10 + 29x^8 + 950x^6 + 1175x^4 + 625x^2 + 125	\( 2^{44}\cdot 5^{7}\cdot 67^{8} \)	20T966	Trivial (GRH)
20.0.4573892877654497650654332738659328.1	x^20 - 3x^19 + x^18 - 3x^17 + 42x^16 - 66x^15 + 88x^14 + 357x^13 - 1520x^12 + 752x^11 + 1668x^10 - 2353x^9 + 3135x^8 - 159x^7 - 1887x^6 - 5971x^5 - 6198x^4 + 2612x^3 + 12420x^2 + 13608x + 8667	\( 2^{10}\cdot 3^{24}\cdot 7^{7}\cdot 79^{7} \)	20T966	$[2]$ (GRH)
20.4.4573892877654497650654332738659328.1	x^20 + 6x^18 - 12x^16 - 181x^14 + 240x^12 + 2499x^10 - 5681x^8 - 52038x^6 + 15813x^4 + 57267x^2 + 44793	\( 2^{10}\cdot 3^{24}\cdot 7^{7}\cdot 79^{7} \)	20T966	Trivial (GRH)
20.0.4573892877654497650654332738659328.2	x^20 - 8x^18 - 12x^16 + 300x^14 + 1881x^12 + 2001x^10 - 2353x^8 - 14728x^6 + 24570x^4 + 81648x^2 + 44793	\( 2^{10}\cdot 3^{24}\cdot 7^{7}\cdot 79^{7} \)	20T966	$[2]$ (GRH)
20.4.4573892877654497650654332738659328.2	x^20 - 2x^19 - 16x^18 + 26x^17 + 118x^16 - 93x^15 - 394x^14 - 88x^13 - 404x^12 - 159x^11 + 5182x^10 + 6445x^9 - 6774x^8 - 12551x^7 + 3187x^6 + 13207x^5 + 2588x^4 - 8346x^3 - 8001x^2 - 3222x - 657	\( 2^{10}\cdot 3^{24}\cdot 7^{7}\cdot 79^{7} \)	20T966	Trivial (GRH)
20.0.5001984585680627954608248429847552.2	x^20 - 4x^19 + 8x^18 - 26x^17 + 128x^16 - 285x^15 + 24x^14 + 1604x^13 - 5273x^12 + 14359x^11 - 44804x^10 + 119159x^9 - 182765x^8 - 83940x^7 + 1254961x^6 - 3416862x^5 + 5372078x^4 - 5435872x^3 + 3552917x^2 - 1412213x + 271445	\( 2^{10}\cdot 61^{7}\cdot 397^{7} \)	20T966	$[2]$ (GRH)
20.4.5001984585680627954608248429847552.2	x^20 - 8x^19 + 12x^18 + 91x^17 - 399x^16 + 160x^15 + 1983x^14 - 2137x^13 - 10263x^12 + 22539x^11 + 15224x^10 - 70271x^9 - 38287x^8 + 252651x^7 - 146823x^6 - 126788x^5 - 117789x^4 + 270872x^3 + 32559x^2 - 10657x + 2785	\( 2^{10}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.4.5001984585680627954608248429847552.3	x^20 + 11x^18 - 114x^16 - 1059x^14 + 3404x^12 + 23898x^10 - 43685x^8 - 136223x^6 + 12145x^4 + 121085x^2 + 24217	\( 2^{10}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.4.5001984585680627954608248429847552.4	x^20 - 2x^19 - 4x^18 + 14x^17 + 60x^16 - 64x^15 + 259x^14 - 1788x^13 - 3379x^12 - 10540x^11 - 6298x^10 + 18228x^9 + 97178x^8 + 226752x^7 + 323120x^6 + 497726x^5 + 203646x^4 - 444270x^3 + 244453x^2 - 59912x + 2495	\( 2^{10}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.8.5001984585680627954608248429847552.10	x^20 - 9x^19 + 21x^18 - 13x^17 + 65x^16 + 142x^15 - 2365x^14 + 6769x^13 - 9974x^12 + 15945x^11 - 17027x^10 - 35897x^9 + 135513x^8 - 86153x^7 - 230658x^6 + 216722x^5 + 245643x^4 - 111548x^3 - 144515x^2 - 25950x + 4625	\( 2^{10}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.8.5001984585680627954608248429847552.11	x^20 - 5x^19 - 5x^18 + 95x^17 - 438x^16 + 1580x^15 - 4706x^14 + 11669x^13 - 23898x^12 + 37466x^11 - 36688x^10 - 822x^9 + 74202x^8 - 130424x^7 + 102259x^6 + 1459x^5 - 85166x^4 + 77059x^3 - 23761x^2 + 615x - 367	\( 2^{10}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.8.5001984585680627954608248429847552.12	x^20 - 3x^19 - 15x^18 + 55x^17 - 54x^16 + 55x^15 + 359x^14 - 490x^13 - 1140x^12 - 8644x^11 + 28564x^10 + 10333x^9 - 152068x^8 + 285138x^7 - 58962x^6 - 670645x^5 + 1017354x^4 - 383753x^3 - 171196x^2 + 97711x + 7585	\( 2^{10}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.8.5001984585680627954608248429847552.13	x^20 - 8x^19 + 40x^18 - 80x^17 - 105x^16 + 627x^15 - 1925x^14 - 444x^13 + 7292x^12 - 6262x^11 + 983x^10 + 27046x^9 + 5062x^8 + 27492x^7 + 29580x^6 - 17672x^5 + 3728x^4 - 13472x^3 - 12784x^2 + 8480x - 800	\( 2^{10}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.12.205110242714618772105806401824722944.1	x^20 - 6x^19 - 20x^18 + 172x^17 + 81x^16 - 1904x^15 + 421x^14 + 11618x^13 - 3206x^12 - 55960x^11 + 34756x^10 + 207572x^9 - 367880x^8 - 179256x^7 + 1187502x^6 - 1009852x^5 - 494372x^4 + 990274x^3 - 239735x^2 - 99768x + 22651	\( 2^{12}\cdot 33769^{7} \)	20T966	Trivial (GRH)
20.12.1347783697341346832395134211051765625.1	x^20 - 5x^19 + 10x^18 + 19x^17 - 358x^16 + 1421x^15 - 1915x^14 - 11527x^13 + 56996x^12 - 56386x^11 - 232215x^10 + 817458x^9 - 282186x^8 - 2631475x^7 + 4064657x^6 + 2545449x^5 - 11247840x^4 - 1023297x^3 + 10748090x^2 + 1917583x - 782737	\( 5^{6}\cdot 36497^{7} \)	20T966	Trivial (GRH)
20.8.1347783697341346832395134211051765625.1	x^20 - 4x^19 + 2x^18 - 34x^17 - 136x^16 + 1358x^15 - 1619x^14 - 1448x^13 + 10328x^12 - 22702x^11 + 31397x^10 - 6974x^9 - 102895x^8 + 143016x^7 - 43776x^6 - 104414x^5 + 79479x^4 + 109440x^3 - 57785x^2 + 19802x - 723	\( 5^{6}\cdot 36497^{7} \)	20T966	Trivial (GRH)
20.12.3281763883433900353692902429195567104.1	x^20 - 2x^19 + 15x^18 - 24x^17 - 87x^16 + 706x^15 - 3607x^14 + 3752x^13 + 14398x^12 - 81692x^11 + 144876x^10 + 120056x^9 - 762268x^8 + 824752x^7 + 312200x^6 - 1143296x^5 + 704608x^4 - 122592x^3 - 8128x^2 + 1216x + 64	\( 2^{16}\cdot 33769^{7} \)	20T966	Trivial (GRH)
20.4.3281763883433900353692902429195567104.1	x^20 - x^19 - 28x^18 + 35x^17 + 84x^16 + 351x^15 - 3662x^14 + 7975x^13 + 145x^12 - 57716x^11 + 212402x^10 - 414046x^9 + 440077x^8 - 298497x^7 + 756959x^6 - 2216604x^5 + 3131232x^4 - 2071744x^3 + 404056x^2 + 312636x - 260564	\( 2^{16}\cdot 33769^{7} \)	20T966	Trivial (GRH)
20.8.3281763883433900353692902429195567104.3	x^20 - 3x^19 - 24x^18 + 129x^17 - 88x^16 - 1270x^15 + 4848x^14 - 1769x^13 - 21558x^12 + 42266x^11 - 27403x^10 - 22839x^9 + 40386x^8 - 285943x^7 + 893823x^6 + 1123264x^5 - 704049x^4 - 6317628x^3 - 6291263x^2 + 10656088x + 11791993	\( 2^{16}\cdot 33769^{7} \)	20T966	Trivial (GRH)
20.12.5122032215736963025518846392163893248.2	x^20 - 20x^18 + 66x^16 + 951x^14 - 6654x^12 - 3505x^10 + 128873x^8 - 366888x^6 + 394433x^4 - 169519x^2 + 24217	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.12.5122032215736963025518846392163893248.3	x^20 - 4x^19 - 52x^18 + 296x^17 + 264x^16 - 3994x^15 + 3310x^14 + 24886x^13 - 55387x^12 - 58176x^11 + 267367x^10 + 38654x^9 - 491367x^8 - 151574x^7 + 246914x^6 + 113338x^5 - 23758x^4 - 17534x^3 + 174x^2 + 700x - 23	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.4.5122032215736963025518846392163893248.3	x^20 + 14x^18 - 6x^17 - 127x^16 + 222x^15 - 3175x^14 + 5576x^13 - 25498x^12 + 37338x^11 - 75591x^10 + 100264x^9 + 221224x^8 + 51548x^7 + 2428039x^6 + 86060x^5 + 9325209x^4 + 2063292x^3 + 22584596x^2 + 4068144x + 28702565	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T966	$[2]$ (GRH)
20.12.5122032215736963025518846392163893248.4	x^20 - 47x^18 + 1007x^16 - 12703x^14 + 101776x^12 - 527901x^10 + 1759517x^8 - 3654580x^6 + 4430859x^4 - 2736521x^2 + 605425	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.8.5122032215736963025518846392163893248.4	x^20 - 4x^19 - 43x^18 + 176x^17 + 629x^16 - 2078x^15 - 6811x^14 + 4530x^13 + 80518x^12 + 99056x^11 - 955313x^10 - 93758x^9 + 5218113x^8 - 3583648x^7 - 16534276x^6 + 32821138x^5 + 3807111x^4 - 83978742x^3 + 70926733x^2 + 61492888x - 80809721	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T966	Trivial (GRH)
20.0.5122032215736963025518846392163893248.8	x^20 + 8x^18 - 79x^16 - 223x^14 + 5585x^12 + 5732x^10 - 174976x^8 - 283819x^6 + 1770700x^4 + 4213758x^2 + 605425	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T966	$[2]$ (GRH)
20.16.46799436188632660609169542229953405952.1	x^20 - 2x^19 - 45x^18 + 178x^17 + 480x^16 - 4124x^15 + 5143x^14 + 25884x^13 - 99649x^12 + 83910x^11 + 211013x^10 - 615300x^9 + 652635x^8 - 232056x^7 - 265359x^6 + 486840x^5 - 375112x^4 + 161448x^3 - 39081x^2 + 4882x - 239	\( 2^{10}\cdot 89417^{7} \)	20T966	Trivial (GRH)
20.16.46799436188632660609169542229953405952.2	x^20 - x^19 - 37x^18 + 29x^17 + 506x^16 - 316x^15 - 3150x^14 + 1669x^13 + 8233x^12 - 4292x^11 - 589x^10 + 1831x^9 - 40673x^8 + 21110x^7 + 98350x^6 - 45691x^5 - 121443x^4 + 16210x^3 + 68874x^2 + 17367x - 2107	\( 2^{10}\cdot 89417^{7} \)	20T966	Trivial (GRH)
20.0.55205220243101566254904697284680320000.1	x^20 + 75x^18 + 2202x^16 + 32636x^14 + 263150x^12 + 1158186x^10 + 2660692x^8 + 2931649x^6 + 1587038x^4 + 401467x^2 + 36497	\( 2^{10}\cdot 5^{4}\cdot 36497^{7} \)	20T966	$[11164]$ (GRH)
20.16.55205220243101566254904697284680320000.1	x^20 - 2x^19 - 34x^18 - 28x^17 + 205x^16 + 2482x^15 + 6497x^14 - 28804x^13 - 110775x^12 + 13578x^11 + 427036x^10 + 763576x^9 + 907759x^8 + 461840x^7 - 973705x^6 - 2172678x^5 - 1924973x^4 - 927948x^3 - 254057x^2 - 37120x - 2249	\( 2^{10}\cdot 5^{4}\cdot 36497^{7} \)	20T966	Trivial (GRH)
20.16.55205220243101566254904697284680320000.2	x^20 - 2x^19 - 58x^18 - 29x^17 + 601x^16 - 348x^15 - 3815x^14 + 4392x^13 + 9768x^12 - 7124x^11 + 4105x^10 - 60836x^9 - 11960x^8 + 223601x^7 - 101287x^6 - 209801x^5 + 152847x^4 + 35810x^3 - 34168x^2 - 2199x + 503	\( 2^{10}\cdot 5^{4}\cdot 36497^{7} \)	20T966	Trivial (GRH)
20.0.2261205821157440153800896400780505907200.1	x^20 - 4x^19 + 56x^18 - 194x^17 + 1339x^16 - 3824x^15 + 17079x^14 - 38016x^13 + 120099x^12 - 189042x^11 + 436689x^10 - 375706x^9 + 708930x^8 + 3896x^7 + 691548x^6 + 234744x^5 + 1300160x^4 + 110736x^3 - 119280x^2 - 7136x + 4512	\( 2^{20}\cdot 5^{2}\cdot 36497^{7} \)	20T966	$[2, 5582]$ (GRH)
20.8.2261205821157440153800896400780505907200.1	x^20 - 4x^19 + 25x^18 + 188x^17 + 156x^16 - 1704x^15 - 20149x^14 - 30268x^13 + 95467x^12 + 345188x^11 + 581369x^10 - 217930x^9 - 2249500x^8 - 4825764x^7 - 6476292x^6 - 2063656x^5 + 6393928x^4 + 14828288x^3 + 9192176x^2 - 8052032x - 7328928	\( 2^{20}\cdot 5^{2}\cdot 36497^{7} \)	20T966	Trivial (GRH)
20.12.47922622657159844463789611243472287694848.1	x^20 - 3x^18 - 811x^16 + 4168x^14 + 120289x^12 - 378233x^10 - 3439542x^8 + 1520089x^6 + 12876048x^4 - 11266542x^2 + 89417	\( 2^{20}\cdot 89417^{7} \)	20T966	Trivial (GRH)
20.4.47922622657159844463789611243472287694848.1	x^20 + 36x^18 + 172x^16 - 3516x^14 - 35697x^12 - 19335x^10 + 1042219x^8 + 5186186x^6 + 9835870x^4 + 6616858x^2 + 89417	\( 2^{20}\cdot 89417^{7} \)	20T966	$[2]$ (GRH)
20.12.47922622657159844463789611243472287694848.2	x^20 - 36x^18 - 257x^16 + 11237x^14 + 75205x^12 - 705264x^10 - 6301627x^8 - 7063943x^6 + 19403489x^4 - 7779279x^2 + 89417	\( 2^{20}\cdot 89417^{7} \)	20T966	Trivial (GRH)
20.4.47922622657159844463789611243472287694848.2	x^20 + 33x^18 + 229x^16 - 2873x^14 - 44867x^12 - 106304x^10 + 1300229x^8 + 9746453x^6 + 25305011x^4 + 23427254x^2 + 89417	\( 2^{20}\cdot 89417^{7} \)	20T966	$[2]$ (GRH)
20.20.56530145528936003845022410019512647680000.1	x^20 - 98x^18 + 3452x^16 - 55109x^14 + 455903x^12 - 2054778x^10 + 4982610x^8 - 5951154x^6 + 2834940x^4 - 547455x^2 + 36497	\( 2^{20}\cdot 5^{4}\cdot 36497^{7} \)	20T966	Trivial (GRH)
20.20.56530145528936003845022410019512647680000.2	x^20 - 75x^18 + 2202x^16 - 32636x^14 + 263150x^12 - 1158186x^10 + 2660692x^8 - 2931649x^6 + 1587038x^4 - 401467x^2 + 36497	\( 2^{20}\cdot 5^{4}\cdot 36497^{7} \)	20T966	Trivial (GRH)