Global number field search results

Further refine search

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 145)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.1430869177844446526464.1	x^20 - 5x^19 + 11x^18 - 11x^17 - x^16 + 16x^15 - 20x^14 + 11x^13 + 5x^12 - 20x^11 + 27x^10 - 2x^9 - 22x^8 + 40x^7 - 9x^6 - 5x^5 + 17x^4 - 7x^3 + 5x^2 - 3x + 1	\( 2^{10}\cdot 31^{3}\cdot 2617^{4} \)	20T1015	Trivial
20.0.2904089910121808158573.1	x^20 - 3x^19 + 3x^18 - 3x^17 + 8x^16 - 13x^15 + 16x^14 - 18x^13 + 22x^12 - 30x^11 + 32x^10 - 25x^9 + 18x^8 - 17x^7 + 25x^6 - 31x^5 + 29x^4 - 21x^3 + 11x^2 - 4x + 1	\( 67\cdot 83^{2}\cdot 631\cdot 1777^{4} \)	20T1015	Trivial
20.2.2948433986992424882176.1	x^20 + 3x^18 + 4x^16 + x^14 - 3x^12 - 6x^10 - 9x^8 - 13x^6 - 12x^4 - 6x^2 - 1	\( -\,2^{12}\cdot 41^{2}\cdot 4549^{4} \)	20T1015	Trivial
20.0.4371478816323106637197.1	x^20 - 6x^19 + 17x^18 - 27x^17 + 25x^16 - 17x^15 + 29x^14 - 63x^13 + 80x^12 - 61x^11 + 45x^10 - 59x^9 + 68x^8 - 47x^7 + 33x^6 - 39x^5 + 32x^4 - 9x^3 - x^2 - x + 1	\( 19^{4}\cdot 31\cdot 113^{2}\cdot 151^{4}\cdot 163 \)	20T1015	Trivial
20.0.7199975815923652533248.1	x^20 - 2x^19 + 2x^18 + 5x^17 - 6x^16 + 29x^14 - 29x^13 + 14x^12 + 44x^11 - 47x^10 + 59x^9 - 5x^8 - 6x^7 + 50x^6 - 15x^5 + 25x^4 - x^3 + 5x^2 + x + 1	\( 2^{10}\cdot 23^{3}\cdot 4903^{4} \)	20T1015	Trivial
20.2.7555362091668088760576.1	x^20 - 5x^19 + 8x^18 + x^17 - 19x^16 + 14x^15 + 41x^14 - 98x^13 + 67x^12 + 34x^11 - 74x^10 - 22x^9 + 160x^8 - 198x^7 + 131x^6 - 45x^5 + 5x^4 - x^3 + x^2 - x - 1	\( -\,2^{8}\cdot 41^{3}\cdot 4549^{4} \)	20T1015	Trivial
20.2.44283824745892362441775.1	x^20 - 3x^19 + 2x^18 - 2x^17 + 9x^16 - 4x^15 - 7x^14 - 8x^13 + 12x^12 + 9x^11 + 2x^10 - 6x^9 - 17x^8 - 8x^7 + 13x^6 + 20x^5 + x^4 - 10x^3 - 4x^2 + 1	\( -\,5^{2}\cdot 37^{2}\cdot 2239\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.2.57560993687222192692051.1	x^20 - 5x^19 + 16x^18 - 32x^17 + 47x^16 - 40x^15 + 10x^14 + 52x^13 - 98x^12 + 140x^11 - 116x^10 + 88x^9 - 17x^8 - 13x^7 + 40x^6 - 19x^5 + 6x^4 + 8x^3 - 3x^2 + x + 1	\( -\,107^{2}\cdot 5419\cdot 5519^{4} \)	20T1015	Trivial
20.0.62267826829026858176237.1	x^20 - 5x^19 + 16x^18 - 29x^17 + 36x^16 - 38x^15 + 40x^14 - 48x^13 + 56x^12 - 56x^11 + 52x^10 - 38x^9 + 29x^8 - 32x^7 + 35x^6 - 31x^5 + 19x^4 - 8x^3 + x + 1	\( 59\cdot 317^{2}\cdot 1567\cdot 1609^{4} \)	20T1015	Trivial (GRH)
20.2.101783918515684285613056.1	x^20 + 3x^18 + 6x^16 + x^14 - 18x^12 - 24x^10 + 32x^8 + 4x^6 - 14x^4 + 5x^2 - 1	\( -\,2^{10}\cdot 17^{2}\cdot 61^{4}\cdot 397^{4} \)	20T1015	Trivial (GRH)
20.2.226770366080175808449271.1	x^20 - 2x^19 + 6x^18 - 12x^17 + 16x^16 - 14x^15 + 4x^14 + 20x^13 - 41x^12 + 32x^11 + 17x^10 - 58x^9 + 32x^8 + 20x^7 - 22x^6 - 14x^5 + 22x^4 + 2x^3 - 15x^2 + 8x - 1	\( -\,37^{3}\cdot 61\cdot 127\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.4.362393727775925633046301.1	x^20 - 2x^19 + x^18 + 6x^17 - 11x^16 + 8x^15 - 8x^14 + 13x^13 - 5x^12 - 14x^11 + 61x^10 - 127x^9 + 84x^8 + 97x^7 - 201x^6 + 104x^5 + 38x^4 - 75x^3 + 40x^2 - 10x + 1	\( 7^{2}\cdot 79\cdot 139\cdot 317^{2}\cdot 1609^{4} \)	20T1015	Trivial (GRH)
20.0.471985256475970094291797.1	x^20 - x^19 + 6x^17 + 6x^16 - 10x^15 + 6x^14 + 35x^13 + 7x^12 - 43x^11 + 21x^10 + 81x^9 - 11x^8 - 85x^7 - 16x^6 + 46x^5 + 20x^4 - 11x^3 - 7x^2 + x + 1	\( 11^{2}\cdot 17^{4}\cdot 157\cdot 4153^{4} \)	20T1015	Trivial
20.2.567100624951232630982503.1	x^20 - 7x^19 + 21x^18 - 32x^17 + 20x^16 + 5x^15 + 19x^14 - 139x^13 + 290x^12 - 332x^11 + 214x^10 - 41x^9 - 66x^8 + 109x^7 - 116x^6 + 70x^5 - 7x^4 - 21x^3 + 16x^2 - 6x + 1	\( -\,13^{4}\cdot 199^{2}\cdot 347^{4}\cdot 34583 \)	20T1015	Trivial (GRH)
20.4.888626986003080704163721.1	x^20 - x^19 - 5x^18 + 4x^17 + 6x^16 - 15x^15 + 4x^14 + 23x^13 - 35x^12 - x^11 + 54x^10 - 42x^9 - 27x^8 + 52x^7 - 4x^6 - 28x^5 + 9x^4 + 10x^3 - 5x^2 - 2x + 1	\( 7^{4}\cdot 43^{2}\cdot 1217^{4}\cdot 91249 \)	20T1015	Trivial (GRH)
20.0.1534847018498855146544128.1	x^20 - 8x^19 + 41x^18 - 158x^17 + 488x^16 - 1257x^15 + 2766x^14 - 5250x^13 + 8676x^12 - 12524x^11 + 15790x^10 - 17345x^9 + 16545x^8 - 13566x^7 + 9511x^6 - 5636x^5 + 2826x^4 - 1169x^3 + 396x^2 - 101x + 17	\( 2^{10}\cdot 23^{2}\cdot 4903^{5} \)	20T1015	Trivial (GRH)
20.6.1691110832936975699766791.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 612x^16 - 1428x^15 + 2740x^14 - 4390x^13 + 5906x^12 - 6654x^11 + 6177x^10 - 4535x^9 + 2336x^8 - 410x^7 - 677x^6 + 896x^5 - 623x^4 + 283x^3 - 83x^2 + 14x - 1	\( -\,137^{2}\cdot 5639\cdot 11243^{4} \)	20T1015	Trivial (GRH)
20.4.1910581632286882552001669.1	x^20 - 10x^19 + 38x^18 - 57x^17 - 21x^16 + 168x^15 - 120x^14 - 162x^13 + 207x^12 + 110x^11 - 210x^10 - 45x^9 + 150x^8 - 24x^7 - 42x^6 + 24x^5 - 6x^4 - 6x^3 + 2x^2 + 3x + 1	\( 7^{4}\cdot 37\cdot 101^{2}\cdot 107\cdot 431^{4}\cdot 571 \)	20T1015	Trivial (GRH)
20.4.1963665390321744883022657.1	x^20 - x^19 - 10x^18 + 6x^17 + 49x^16 - 16x^15 - 139x^14 + 18x^13 + 246x^12 - 4x^11 - 271x^10 + 9x^9 + 178x^8 - 55x^7 - 77x^6 + 77x^5 + 42x^4 - 33x^3 - 20x^2 + 1	\( 673^{2}\cdot 4673\cdot 5519^{4} \)	20T1015	Trivial (GRH)
20.4.3653341998272480107199281.1	x^20 - 4x^19 + 13x^18 - 26x^17 + 47x^16 - 56x^15 + 45x^14 + x^13 - 70x^12 + 144x^11 - 181x^10 + 139x^9 - 107x^8 + 64x^7 - 11x^6 + 36x^5 - 39x^4 - 14x^3 + 28x^2 - 10x + 1	\( 13^{2}\cdot 9769\cdot 38569^{4} \)	20T1015	Trivial (GRH)
20.4.4190415957918622090223749.1	x^20 - 10x^19 + 36x^18 - 39x^17 - 80x^16 + 232x^15 - 45x^14 - 379x^13 + 238x^12 + 353x^11 - 255x^10 - 260x^9 + 109x^8 + 177x^7 + 6x^6 - 76x^5 - 32x^4 + 6x^3 + 13x^2 + 5x + 1	\( 17^{6}\cdot 439^{4}\cdot 4674181 \)	20T1015	Trivial (GRH)
20.6.4830858228494718956812959.1	x^20 - 3x^19 + 2x^18 + 7x^17 - 8x^16 - 11x^15 + 7x^14 + 48x^13 - 44x^12 - 80x^11 + 125x^10 + 54x^9 - 191x^8 + 36x^7 + 170x^6 - 140x^5 - 8x^4 + 66x^3 - 39x^2 + 10x - 1	\( -\,3^{3}\cdot 43\cdot 163^{2}\cdot 271\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.8.6130984268238865203986432.1	x^20 - 4x^19 + 3x^18 + 16x^17 - 33x^16 + 16x^15 - 6x^14 - 28x^13 + 93x^12 - 128x^11 + 157x^10 - 128x^9 + 93x^8 - 28x^7 - 6x^6 + 16x^5 - 33x^4 + 16x^3 + 3x^2 - 4x + 1	\( 2^{20}\cdot 17\cdot 61^{4}\cdot 397^{4} \)	20T1015	Trivial (GRH)
20.6.6736516842429754982164739.1	x^20 - x^19 - 3x^18 - 5x^17 - 2x^16 + 10x^15 + 18x^14 + 18x^13 + 2x^12 - 19x^11 - 27x^10 - 19x^9 + 2x^8 + 18x^7 + 18x^6 + 10x^5 - 2x^4 - 5x^3 - 3x^2 - x + 1	\( -\,11\cdot 17^{4}\cdot 157^{2}\cdot 4153^{4} \)	20T1015	Trivial (GRH)
20.6.7372775235505820194045952.1	x^20 - 2x^19 - 5x^18 + 8x^17 + 8x^16 - 8x^14 + 6x^13 - 39x^12 - 40x^11 - 75x^10 + 86x^9 + 147x^8 + 52x^7 + 346x^6 + 180x^5 - 89x^4 + 14x^3 + 26x^2 + 8x + 1	\( -\,2^{20}\cdot 23^{3}\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.4.8430318243745634506767641.1	x^20 - 2x^19 - 8x^18 + 8x^17 + 41x^16 + x^15 - 126x^14 - 52x^13 + 224x^12 + 90x^11 - 265x^10 - 66x^9 + 279x^8 - 75x^7 - 123x^6 + 68x^5 + 10x^4 + 7x^3 - 13x^2 + x + 1	\( 23\cdot 37^{2}\cdot 4903^{4}\cdot 463303 \)	20T1015	Trivial (GRH)
20.10.8978120457836040599985152.1	x^20 - 12x^18 + 63x^16 - 194x^14 + 385x^12 - 493x^10 + 371x^8 - 100x^6 - 80x^4 + 83x^2 - 23	\( -\,2^{10}\cdot 23\cdot 641^{2}\cdot 5519^{4} \)	20T1015	Trivial (GRH)
20.6.11138046967442830397538304.1	x^20 + 2x^10 - 13x^8 + 19x^6 - 18x^4 + 9x^2 - 1	\( -\,2^{20}\cdot 107^{2}\cdot 5519^{4} \)	20T1015	Trivial (GRH)
20.0.13634782123289025019858657.1	x^20 + 8x^18 - x^17 + 32x^16 - 6x^15 + 83x^14 - 19x^13 + 148x^12 - 42x^11 + 182x^10 - 66x^9 + 149x^8 - 70x^7 + 83x^6 - 38x^5 + 39x^4 - 3x^3 + 14x^2 + 2x + 1	\( 673\cdot 4673^{2}\cdot 5519^{4} \)	20T1015	Trivial (GRH)
20.4.14701068513065801441443661.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 570x^16 - 1296x^15 + 2430x^14 - 3816x^13 + 5037x^12 - 5548x^11 + 4954x^10 - 3315x^9 + 1182x^8 + 654x^7 - 1625x^6 + 1665x^5 - 1149x^4 + 563x^3 - 183x^2 + 33x - 1	\( 13^{4}\cdot 167^{2}\cdot 347^{4}\cdot 1272989 \)	20T1015	Trivial (GRH)
20.8.14880182395101510812616281.1	x^20 - x^19 - 7x^18 + 12x^17 + 19x^16 - 58x^15 - 30x^14 + 152x^13 + 41x^12 - 241x^11 - 49x^10 + 241x^9 + 41x^8 - 152x^7 - 30x^6 + 58x^5 + 19x^4 - 12x^3 - 7x^2 + x + 1	\( 23^{2}\cdot 97\cdot 9497\cdot 13219^{4} \)	20T1015	Trivial (GRH)
20.0.17510262944798593002279973.1	x^20 - 4x^19 + 8x^18 - 12x^17 + 16x^16 - 16x^15 + 13x^14 - 8x^13 + 3x^12 + x^11 - 3x^10 + x^9 + 3x^8 - 8x^7 + 13x^6 - 16x^5 + 16x^4 - 12x^3 + 8x^2 - 4x + 1	\( 17^{4}\cdot 67^{2}\cdot 157\cdot 4153^{4} \)	20T1015	Trivial (GRH)
20.8.22993730893173532944527721.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 160x^16 + 260x^15 + 251x^14 - 799x^13 - 123x^12 + 1297x^11 - 52x^10 - 1396x^9 + 42x^8 + 1031x^7 + 58x^6 - 475x^5 - 69x^4 + 110x^3 + 20x^2 - 7x - 1	\( 3^{6}\cdot 61\cdot 11119^{4}\cdot 33829 \)	20T1015	Trivial (GRH)
20.4.28889461328079508383727616.1	x^20 - 8x^19 + 32x^18 - 82x^17 + 140x^16 - 156x^15 + 110x^14 - 102x^13 + 279x^12 - 524x^11 + 572x^10 - 496x^9 + 596x^8 - 1090x^7 + 1552x^6 - 1204x^5 + 440x^4 - 68x^3 + 12x^2 + 4x - 7	\( 2^{30}\cdot 29\cdot 5519^{4} \)	20T1015	Trivial (GRH)
20.2.29415552451032758542173184.1	x^20 - 2x^19 - 5x^18 + 11x^17 + 4x^16 + 7x^15 - 24x^14 - 114x^13 + 265x^12 - 158x^11 + 42x^10 - 13x^9 - 441x^8 + 1555x^7 - 2024x^6 + 800x^5 + 522x^4 - 426x^3 - 53x^2 + 68x + 17	\( -\,2^{10}\cdot 17^{4}\cdot 61^{4}\cdot 397^{4} \)	20T1015	Trivial (GRH)
20.8.30631371843819989683233329.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 434x^16 - 820x^15 + 1178x^14 - 1240x^13 + 828x^12 - 80x^11 - 576x^10 + 762x^9 - 484x^8 + 78x^7 + 143x^6 - 138x^5 + 49x^4 + 6x^3 - 11x^2 + 3x + 1	\( 163^{2}\cdot 521\cdot 38569^{4} \)	20T1015	Trivial (GRH)
20.6.35928362269592569788867371.1	x^20 - 10x^19 + 50x^18 - 165x^17 + 396x^16 - 720x^15 + 998x^14 - 1016x^13 + 647x^12 - 8x^11 - 565x^10 + 762x^9 - 549x^8 + 168x^7 + 95x^6 - 145x^5 + 76x^4 - 12x^3 - 8x^2 + 5x - 1	\( -\,29^{2}\cdot 61^{4}\cdot 223\cdot 397^{4}\cdot 557 \)	20T1015	Trivial (GRH)
20.10.36757053453857337692075119.1	x^20 - 10x^19 + 37x^18 - 48x^17 - 57x^16 + 252x^15 - 222x^14 - 204x^13 + 562x^12 - 304x^11 - 307x^10 + 517x^9 - 173x^8 - 184x^7 + 202x^6 - 49x^5 - 37x^4 + 34x^3 - 7x^2 - 3x + 1	\( -\,317\cdot 443\cdot 673^{2}\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.4.40408215650726661388383232.1	x^20 - 8x^19 + 26x^18 - 56x^17 + 102x^16 - 85x^15 - 82x^14 + 77x^13 + 226x^12 - 97x^11 - 302x^10 + 100x^9 + 54x^8 + 151x^7 - 86x^6 + 45x^5 - 95x^4 + 16x^3 - x^2 + 12x + 1	\( 2^{10}\cdot 17^{2}\cdot 61^{4}\cdot 397^{5} \)	20T1015	Trivial (GRH)
20.0.40408215650726661388383232.1	x^20 - x^19 - 2x^18 + 2x^17 + 4x^16 + x^15 - 3x^14 - 11x^13 + 35x^12 + 47x^11 - 82x^10 - 101x^9 + 90x^8 - 10x^7 - 120x^6 - 240x^5 + 194x^4 + 212x^3 + 121x^2 + 141x + 113	\( 2^{10}\cdot 17^{2}\cdot 61^{4}\cdot 397^{5} \)	20T1015	Trivial (GRH)
20.2.41031511676617598527730683.1	x^20 - 2x^19 + x^18 - 2x^17 + 4x^16 - 4x^15 + 3x^14 - 4x^13 + 6x^12 - 5x^11 + 3x^10 - 5x^9 + 6x^8 - 4x^7 + 3x^6 - 4x^5 + 4x^4 - 2x^3 + x^2 - 2x + 1	\( -\,17^{4}\cdot 67\cdot 157^{2}\cdot 4153^{4} \)	20T1015	Trivial (GRH)
20.4.72275965427677164931490989.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 566x^16 - 1264x^15 + 2296x^14 - 3438x^13 + 4260x^12 - 4344x^11 + 3564x^10 - 2206x^9 + 788x^8 + 240x^7 - 706x^6 + 707x^5 - 474x^4 + 226x^3 - 73x^2 + 14x - 1	\( 601^{2}\cdot 5783^{4}\cdot 178909 \)	20T1015	Trivial (GRH)
20.6.90352121196396365629490176.1	x^20 - 5x^18 + x^16 + 20x^14 - 13x^12 - 27x^10 + 18x^8 + 17x^6 - 6x^4 - 6x^2 - 1	\( -\,2^{10}\cdot 223^{2}\cdot 36497^{4} \)	20T1015	Trivial (GRH)
20.6.97907636384234445551929843.1	x^20 - 5x^19 + 16x^18 - 34x^17 + 49x^16 - 74x^15 + 105x^14 - 152x^13 + 165x^12 - 33x^11 + 54x^10 - 156x^9 - 129x^8 + 77x^7 + 99x^6 + 127x^5 - 16x^4 - 21x^3 - 21x^2 - 4x + 1	\( -\,163\cdot 521^{2}\cdot 38569^{4} \)	20T1015	Trivial (GRH)
20.8.117075722390787720974547281.1	x^20 - 10x^19 + 37x^18 - 48x^17 - 51x^16 + 204x^15 - 96x^14 - 246x^13 + 206x^12 + 194x^11 - 127x^10 - 229x^9 + 69x^8 + 222x^7 - 84x^6 - 105x^5 + 61x^4 + 18x^3 - 17x^2 + x + 1	\( 673^{2}\cdot 5519^{4}\cdot 278609 \)	20T1015	Trivial (GRH)
20.8.159124297307864817454651709.1	x^20 - 10x^19 + 48x^18 - 147x^17 + 314x^16 - 472x^15 + 453x^14 - 113x^13 - 472x^12 + 947x^11 - 935x^10 + 412x^9 + 219x^8 - 517x^7 + 410x^6 - 156x^5 - x^4 + 30x^3 - 11x^2 + 1	\( 557^{2}\cdot 5519^{4}\cdot 552821 \)	20T1015	Trivial (GRH)
20.2.249238158195972964709564416.1	x^20 + 11x^18 + 51x^16 + 127x^14 + 176x^12 + 118x^10 - 58x^6 - 41x^4 - 11x^2 - 1	\( -\,2^{20}\cdot 461^{2}\cdot 5783^{4} \)	20T1015	Trivial (GRH)
20.6.274459087255890164762804224.1	x^20 - 2x^18 - 6x^16 + 12x^14 + 13x^12 - 25x^10 - 13x^8 + 20x^6 + 6x^4 - 4x^2 - 1	\( -\,2^{20}\cdot 673^{2}\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.2.274459087255890164762804224.1	x^20 + 4x^18 + x^16 - 15x^14 - 16x^12 + 33x^10 + 92x^8 + 79x^6 + 21x^4 - 2x^2 - 1	\( -\,2^{20}\cdot 673^{2}\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.6.274459087255890164762804224.2	x^20 + 2x^18 - 6x^16 - 12x^14 + 13x^12 + 25x^10 - 13x^8 - 20x^6 + 6x^4 + 4x^2 - 1	\( -\,2^{20}\cdot 673^{2}\cdot 4903^{4} \)	20T1015	Trivial (GRH)