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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.232015274172464742006784.1	x^20 + 9x^18 + 41x^16 + 120x^14 + 244x^12 + 348x^10 + 340x^8 + 216x^6 + 84x^4 + 20x^2 + 4	\( 2^{38}\cdot 11^{2}\cdot 17^{8} \)	20T561	Trivial (GRH)
20.0.490875290811165073997824.3	x^20 + x^18 - 3x^16 + 12x^14 + 2x^12 + 38x^10 + 2x^8 + 12x^6 - 3x^4 + x^2 + 1	\( 2^{46}\cdot 17^{8} \)	20T561	Trivial (GRH)
20.4.928061096689858968027136.1	x^20 - 2x^18 - 5x^16 + 12x^14 + 29x^12 - 14x^10 - 31x^8 + 20x^6 + 15x^4 - 10x^2 + 1	\( 2^{40}\cdot 11^{2}\cdot 17^{8} \)	20T561	Trivial (GRH)
20.4.1963501163244660295991296.1	x^20 + x^18 - 7x^16 - 4x^14 + 6x^12 - 26x^10 + 6x^8 - 4x^6 - 7x^4 + x^2 + 1	\( 2^{48}\cdot 17^{8} \)	20T561	Trivial (GRH)
20.0.13378570905081069605274292224.1	x^20 - 10x^19 + 45x^18 - 110x^17 + 146x^16 - 78x^15 + 27x^14 - 300x^13 + 1009x^12 - 1634x^11 + 1576x^10 - 692x^9 + 124x^8 - 600x^7 + 1992x^6 - 2136x^5 + 1184x^4 + 16x^3 + 16	\( 2^{12}\cdot 3^{2}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.8.21822182114965484993955979209.1	x^20 - 17x^18 - 15x^17 + 98x^16 + 176x^15 - 217x^14 - 766x^13 - 89x^12 + 1651x^11 + 1366x^10 - 1769x^9 - 2834x^8 + 611x^7 + 2816x^6 + 465x^5 - 1498x^4 - 447x^3 + 457x^2 + 105x - 69	\( 3^{10}\cdot 883^{8} \)	20T561	Trivial (GRH)
20.8.21822182114965484993955979209.2	x^20 - 11x^18 - 11x^16 + 177x^14 + 353x^12 + 305x^10 + 353x^8 + 177x^6 - 11x^4 - 11x^2 + 1	\( 3^{10}\cdot 883^{8} \)	20T561	Trivial (GRH)
20.0.21822182114965484993955979209.4	x^20 + 18x^18 + 145x^16 + 702x^14 + 2334x^12 + 5694x^10 + 10087x^8 + 11883x^6 + 8014x^4 + 2328x^2 + 9	\( 3^{10}\cdot 883^{8} \)	20T561	$[4]$ (GRH)
20.0.36004287916157947645483014400.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 645x^16 - 1692x^15 + 3930x^14 - 8100x^13 + 14934x^12 - 24604x^11 + 36442x^10 - 48280x^9 + 57008x^8 - 59126x^7 + 53249x^6 - 40754x^5 + 26016x^4 - 13336x^3 + 5256x^2 - 1424x + 212	\( 2^{8}\cdot 5^{2}\cdot 17^{8}\cdot 73^{8} \)	20T561	Trivial (GRH)
20.4.36471111833111739050142726400.1	x^20 - 3x^18 - 17x^16 + 2x^14 + 5x^12 - 25x^10 + 5x^8 + 2x^6 - 17x^4 - 3x^2 + 1	\( 2^{8}\cdot 5^{2}\cdot 11^{8}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.4.67729015206972914876701104384.1	x^20 - 6x^19 + 21x^18 - 63x^17 + 169x^16 - 416x^15 + 844x^14 - 1309x^13 + 1591x^12 - 1528x^11 + 990x^10 - 8x^9 - 239x^8 - 566x^7 + 519x^6 + 343x^5 + 497x^4 - 2148x^3 + 606x^2 + 1269x - 603	\( 2^{8}\cdot 3^{6}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.4.67729015206972914876701104384.2	x^20 - 6x^18 + 22x^16 - 6x^15 - 65x^14 - 66x^13 - 69x^12 - 110x^11 - 131x^10 - 110x^9 - 69x^8 - 66x^7 - 65x^6 - 6x^5 + 22x^4 - 6x^2 + 1	\( 2^{8}\cdot 3^{6}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.0.429600776840936568436030050304.1	x^20 - 10x^19 + 49x^18 - 156x^17 + 346x^16 - 524x^15 + 408x^14 + 398x^13 - 1876x^12 + 3014x^11 - 1248x^10 - 5888x^9 + 16570x^8 - 24156x^7 + 24605x^6 - 19546x^5 + 13529x^4 - 8244x^3 + 6426x^2 - 3698x + 1621	\( 2^{12}\cdot 17^{2}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.4.1226888202065878901646801316096.1	x^20 + 17x^18 + 95x^16 + 170x^14 - 91x^12 - 413x^10 - 91x^8 + 170x^6 + 95x^4 + 17x^2 + 1	\( 2^{8}\cdot 11^{8}\cdot 29^{2}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.0.1384004827497111507492367073536.1	x^20 - 10x^19 + 39x^18 - 66x^17 + 38x^16 - 100x^15 + 472x^14 - 330x^13 - 1198x^12 + 1182x^11 + 2306x^10 - 1812x^9 - 2630x^8 - 3872x^7 + 10487x^6 + 2358x^5 - 8571x^4 - 1910x^3 + 2458x^2 + 1158x + 157	\( 2^{8}\cdot 17^{8}\cdot 31^{2}\cdot 73^{8} \)	20T561	$[5]$ (GRH)
20.8.1493856740684256831493846073344.1	x^20 - x^19 - 6x^18 + 17x^17 + 4x^16 - 114x^15 - 26x^14 + 500x^13 + 1503x^12 - 1060x^11 - 9162x^10 + 1128x^9 + 24663x^8 - 5046x^7 - 31096x^6 + 14496x^5 + 9360x^4 - 5907x^3 + 3264x^2 - 3745x + 1225	\( 2^{18}\cdot 11^{8}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.8.1493856740684256831493846073344.2	x^20 - 9x^19 + 29x^18 - 5x^17 - 119x^16 + 118x^15 + 12x^14 + 104x^13 + 144x^12 - 586x^11 - 166x^10 + 586x^9 + 144x^8 - 104x^7 + 12x^6 - 118x^5 - 119x^4 + 5x^3 + 29x^2 + 9x + 1	\( 2^{18}\cdot 11^{8}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.4.1522184067422557252866763915264.1	x^20 + 10x^18 + 6x^16 - 264x^14 - 1039x^12 - 1012x^10 + 609x^8 + 564x^6 + 454x^4 + 94x^2 + 9	\( 2^{22}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.0.1926514210331674023159498080256.1	x^20 + 5x^18 - 12x^16 + 30x^14 + 603x^12 + 2134x^10 + 4723x^8 + 6798x^6 + 5148x^4 + 1593x^2 + 81	\( 2^{16}\cdot 3^{4}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.0.1926514210331674023159498080256.2	x^20 + 14x^18 + 64x^16 + 93x^14 - 45x^12 - 173x^10 - 45x^8 + 93x^6 + 64x^4 + 14x^2 + 1	\( 2^{16}\cdot 3^{4}\cdot 881^{8} \)	20T561	$[3]$ (GRH)
20.0.3283695903258231417561212391424.1	x^20 - 10x^19 + 59x^18 - 246x^17 + 762x^16 - 1812x^15 + 3354x^14 - 4824x^13 + 6822x^12 - 13372x^11 + 38992x^10 - 100784x^9 + 212681x^8 - 349790x^7 + 462031x^6 - 482390x^5 + 399126x^4 - 252060x^3 + 116828x^2 - 35368x + 5352	\( 2^{12}\cdot 47^{2}\cdot 881^{8} \)	20T561	$[9]$ (GRH)
20.4.6088736269690229011467055661056.1	x^20 - 5x^18 + 46x^16 - 41x^14 + 420x^12 - 785x^10 - 394x^8 - 2165x^6 + 1349x^4 - 264x^2 + 16	\( 2^{24}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.4.6088736269690229011467055661056.2	x^20 - 7x^18 + 38x^16 - 233x^14 + 707x^12 - 1298x^10 + 5464x^8 - 12592x^6 + 5328x^4 - 5184x^2 + 11664	\( 2^{24}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.4.6659353092972573996508538343424.1	x^20 + 5x^18 - 19x^16 - 79x^14 - 167x^12 - 1152x^10 - 616x^8 + 6328x^6 + 2528x^4 - 10368x^2 + 400	\( 2^{12}\cdot 17^{10}\cdot 73^{8} \)	20T561	Trivial (GRH)
20.8.7759664031689416767375792783616.1	x^20 - 5x^19 - 6x^18 + 76x^17 - 139x^16 - 44x^15 + 500x^14 - 799x^13 + 665x^12 - 216x^11 + 78x^10 - 216x^9 + 665x^8 - 799x^7 + 500x^6 - 44x^5 - 139x^4 + 76x^3 - 6x^2 - 5x + 1	\( 2^{8}\cdot 17^{4}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.0.9891814612054618806013214744409.1	x^20 - 10x^19 + 43x^18 - 102x^17 + 191x^16 - 508x^15 + 1404x^14 - 2570x^13 + 3299x^12 - 4636x^11 + 8490x^10 - 13339x^9 + 12442x^8 - 1952x^7 - 8883x^6 + 9671x^5 - 1445x^4 - 4950x^3 + 5546x^2 - 2692x + 581	\( 3^{20}\cdot 11^{8}\cdot 13^{2}\cdot 23^{8} \)	20T561	Trivial (GRH)
20.12.17338627892985066208435482722304.1	x^20 - x^19 - 9x^18 - 22x^17 + 58x^16 + 426x^15 - 709x^14 - 1909x^13 + 3232x^12 + 3995x^11 - 6276x^10 - 4627x^9 + 4806x^8 + 2121x^7 + 111x^6 + 2238x^5 - 456x^4 - 2620x^3 - 1388x^2 - 252x - 12	\( 2^{16}\cdot 3^{6}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.4.17338627892985066208435482722304.1	x^20 + 14x^18 + 27x^16 - 225x^14 - 266x^12 + 1488x^10 - 474x^8 - 2182x^6 + 2236x^4 - 771x^2 + 81	\( 2^{16}\cdot 3^{6}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.8.17338627892985066208435482722304.1	x^20 - 5x^19 + 2x^18 + 35x^17 - 93x^16 + 45x^15 + 306x^14 - 959x^13 + 805x^12 + 1704x^11 - 4688x^10 + 2586x^9 + 3642x^8 - 5740x^7 + 2324x^6 + 796x^5 - 1200x^4 + 936x^3 - 44x^2 - 228x + 36	\( 2^{16}\cdot 3^{6}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.20.19630211233054062426348821057536.1	x^20 - 2x^19 - 32x^18 + 64x^17 + 413x^16 - 826x^15 - 2777x^14 + 5546x^13 + 10546x^12 - 20970x^11 - 23116x^10 + 45532x^9 + 28870x^8 - 55732x^7 - 19678x^6 + 36176x^5 + 6510x^4 - 10466x^3 - 737x^2 + 678x + 1	\( 2^{12}\cdot 11^{8}\cdot 29^{2}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.0.22502679947598717278426884000000.1	x^20 - 8x^19 + 40x^18 - 148x^17 + 453x^16 - 1158x^15 + 2542x^14 - 4954x^13 + 9028x^12 - 15318x^11 + 23914x^10 - 33626x^9 + 43131x^8 - 48412x^7 + 45784x^6 - 34488x^5 + 21703x^4 - 10888x^3 + 4356x^2 - 1328x + 464	\( 2^{8}\cdot 5^{6}\cdot 17^{8}\cdot 73^{8} \)	20T561	$[2]$ (GRH)
20.12.22502679947598717278426884000000.1	x^20 - x^19 - 25x^18 + 44x^17 + 147x^16 - 458x^15 + 216x^14 + 859x^13 - 2167x^12 + 3066x^11 - 3369x^10 + 3066x^9 - 2167x^8 + 859x^7 + 216x^6 - 458x^5 + 147x^4 + 44x^3 - 25x^2 - x + 1	\( 2^{8}\cdot 5^{6}\cdot 17^{8}\cdot 73^{8} \)	20T561	Trivial (GRH)
20.4.22502679947598717278426884000000.1	x^20 - x^19 + x^18 - 28x^17 - 38x^16 - 66x^15 - 25x^14 + 685x^13 - 766x^12 + 6607x^11 - 15460x^10 + 33695x^9 - 69366x^8 + 81537x^7 - 99741x^6 + 67248x^5 - 20632x^4 - 3312x^3 + 11672x^2 + 900x - 916	\( 2^{8}\cdot 5^{6}\cdot 17^{8}\cdot 73^{8} \)	20T561	$[2]$ (GRH)
20.12.22502679947598717278426884000000.2	x^20 - 9x^19 + 19x^18 + 59x^17 - 322x^16 + 378x^15 + 551x^14 - 2035x^13 + 2092x^12 + 152x^11 - 2349x^10 + 2227x^9 - 2224x^8 + 1382x^7 + 1393x^6 - 41x^5 + 199x^4 - 591x^3 + 130x^2 + 14x - 2	\( 2^{8}\cdot 5^{6}\cdot 17^{8}\cdot 73^{8} \)	20T561	Trivial (GRH)
20.12.30824227365306784370551969284096.1	x^20 - 6x^18 - 42x^16 + 217x^14 + 427x^12 - 3335x^10 + 5477x^8 - 3907x^6 + 1330x^4 - 200x^2 + 9	\( 2^{20}\cdot 3^{4}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.12.89026331508491569254118932699681.1	x^20 - 3x^19 - 29x^18 + 56x^17 + 290x^16 - 454x^15 - 1205x^14 + 1663x^13 + 2187x^12 - 2443x^11 - 1940x^10 + 744x^9 + 1619x^8 + 764x^7 - 1410x^6 - 613x^5 + 824x^4 + 373x^3 - 58x^2 - 24x + 1	\( 3^{22}\cdot 11^{8}\cdot 13^{2}\cdot 23^{8} \)	20T561	Trivial (GRH)
20.12.95606831403792437215606148694016.1	x^20 + 8x^18 - 37x^16 - 303x^14 + 260x^12 + 2035x^10 - 1966x^8 - 1267x^6 + 851x^4 - 113x^2 + 1	\( 2^{24}\cdot 11^{8}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.16.95606831403792437215606148694016.1	x^20 - 23x^18 + 94x^16 - 92x^14 - 155x^12 + 352x^10 - 155x^8 - 92x^6 + 94x^4 - 23x^2 + 1	\( 2^{24}\cdot 11^{8}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.4.95606831403792437215606148694016.1	x^20 + 7x^18 - 33x^16 - 369x^14 - 573x^12 + 2394x^10 + 8748x^8 + 8776x^6 + 1872x^4 + 148x^2 + 4	\( 2^{24}\cdot 11^{8}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.4.109977798871279761519623692877824.1	x^20 + 6x^18 - 9x^14 - 5x^12 - 3x^10 - 5x^8 - 9x^6 + 6x^2 + 1	\( 2^{20}\cdot 17^{2}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.16.382427325615169748862424594776064.1	x^20 - 23x^18 + 154x^16 - 202x^14 - 731x^12 + 1798x^10 - 731x^8 - 202x^6 + 154x^4 - 23x^2 + 1	\( 2^{26}\cdot 11^{8}\cdot 113^{8} \)	20T561	Trivial (GRH)
20.0.493187637844908549928831508545536.1	x^20 + 37x^18 + 507x^16 + 3454x^14 + 12941x^12 + 27683x^10 + 33949x^8 + 23478x^6 + 8667x^4 + 1485x^2 + 81	\( 2^{24}\cdot 3^{4}\cdot 881^{8} \)	20T561	$[14]$ (GRH)
20.20.4438688740604176949359483576909824.1	x^20 - 46x^18 + 811x^16 - 7048x^14 + 33155x^12 - 87190x^10 + 126613x^8 - 94628x^6 + 30124x^4 - 1824x^2 + 16	\( 2^{24}\cdot 3^{6}\cdot 881^{8} \)	20T561	Trivial (GRH)
20.0.36063779114647973956917740340219904.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 495x^16 - 1308x^15 + 3000x^14 - 5454x^13 + 7990x^12 - 10474x^11 + 11952x^10 - 8880x^9 + 843x^8 + 5784x^7 - 4499x^6 - 2106x^5 + 25895x^4 - 44530x^3 - 17248x^2 + 38672x + 79760	\( 2^{12}\cdot 11^{10}\cdot 113^{10} \)	20T561	$[3, 144]$ (GRH)