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 matches 1-50 of 54)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.231472847376679145996221.1	x^20 + 4x^18 - 5x^17 - 19x^15 + 3x^14 - 5x^13 + 51x^12 + 28x^11 + 75x^10 - 24x^9 + 25x^8 - 70x^7 + 24x^6 - 32x^5 + 36x^4 - 10x^3 + 6x^2 - 4x + 1	\( 17^{4}\cdot 421^{3}\cdot 439^{4} \)	20T990	Trivial
20.4.231472847376679145996221.1	x^20 - 3x^19 + 3x^18 - 9x^17 + 16x^16 - 18x^15 + 26x^14 - 36x^13 + 36x^12 - 39x^11 + 47x^10 - 39x^9 + 36x^8 - 36x^7 + 26x^6 - 18x^5 + 16x^4 - 9x^3 + 3x^2 - 3x + 1	\( 17^{4}\cdot 421^{3}\cdot 439^{4} \)	20T990	Trivial (GRH)
20.0.324864479268392294429293.1	x^20 - x^19 + 4x^18 - x^16 + 9x^15 + 8x^14 - 9x^13 + 10x^12 + 13x^11 + 11x^10 - 15x^9 + 12x^8 + 15x^7 + 8x^6 - 17x^5 + 9x^4 + 8x^3 - x^2 - 2x + 1	\( 277^{3}\cdot 11119^{4} \)	20T990	Trivial
20.4.324864479268392294429293.1	x^20 - 3x^19 + 7x^18 - 16x^17 + 26x^16 - 31x^15 + 40x^14 - 46x^13 + 43x^12 - 36x^11 - 40x^10 + 134x^9 - 101x^8 + 33x^7 - 44x^6 + 37x^5 - 2x^4 + 2x^3 - 6x^2 + 1	\( 277^{3}\cdot 11119^{4} \)	20T990	Trivial (GRH)
20.4.1730326614766632855421952.1	x^20 - 12x^18 + 64x^16 - 201x^14 + 415x^12 - 596x^10 + 614x^8 - 458x^6 + 242x^4 - 85x^2 + 17	\( 2^{10}\cdot 17^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.4.30693941317011285467987968.1	x^20 - 7x^18 + 12x^16 + 4x^14 - 14x^12 - 87x^10 + 309x^8 - 462x^6 + 393x^4 - 185x^2 + 37	\( 2^{20}\cdot 37^{3}\cdot 4903^{4} \)	20T990	Trivial (GRH)
20.4.30693941317011285467987968.2	x^20 + x^18 - 10x^16 - 32x^14 - 23x^12 + 39x^10 + 91x^8 + 33x^6 - 68x^4 - 44x^2 + 37	\( 2^{20}\cdot 37^{3}\cdot 4903^{4} \)	20T990	Trivial (GRH)
20.2.101752808205409431622035787.1	x^20 - 5x^19 + 8x^18 - 7x^17 + 27x^16 - 77x^15 + 114x^14 - 144x^13 + 93x^12 + 206x^11 - 738x^10 + 1526x^9 - 2601x^8 + 3318x^7 - 3384x^6 + 2752x^5 - 1621x^4 + 622x^3 - 143x^2 + 17x - 1	\( -\,43^{3}\cdot 61^{6}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.0.223873081077610811849965568.1	x^20 + 5x^18 + 23x^16 + 106x^14 + 351x^12 + 924x^10 + 1390x^8 + 1321x^6 + 975x^4 + 317	\( 2^{20}\cdot 317^{3}\cdot 1609^{4} \)	20T990	Trivial (GRH)
20.4.223873081077610811849965568.1	x^20 - 5x^18 + 17x^16 - 77x^14 + 202x^12 - 600x^10 + 1824x^8 - 3294x^6 + 3201x^4 - 1585x^2 + 317	\( 2^{20}\cdot 317^{3}\cdot 1609^{4} \)	20T990	Trivial (GRH)
20.0.223873081077610811849965568.2	x^20 - 7x^18 + 19x^16 + 9x^14 - 223x^12 + 711x^10 - 1250x^8 + 1303x^6 - 778x^4 + 317x^2 + 317	\( 2^{20}\cdot 317^{3}\cdot 1609^{4} \)	20T990	Trivial (GRH)
20.4.223873081077610811849965568.2	x^20 - 5x^18 + 23x^16 - 106x^14 + 351x^12 - 924x^10 + 1390x^8 - 1321x^6 + 975x^4 + 317	\( 2^{20}\cdot 317^{3}\cdot 1609^{4} \)	20T990	Trivial (GRH)
20.2.455293169564857148863676416.1	x^20 + 10x^18 + 44x^16 + 112x^14 + 175x^12 + 154x^10 + 43x^8 - 44x^6 - 43x^4 - 14x^2 - 1	\( -\,2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T990	Trivial (GRH)
20.2.455293169564857148863676416.2	x^20 + 10x^18 + 40x^16 + 80x^14 + 79x^12 + 26x^10 - 10x^8 + 8x^4 - 1	\( -\,2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T990	Trivial (GRH)
20.6.455293169564857148863676416.4	x^20 - 10x^18 + 44x^16 - 112x^14 + 175x^12 - 154x^10 + 43x^8 + 44x^6 - 43x^4 + 14x^2 - 1	\( -\,2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T990	Trivial (GRH)
20.6.455293169564857148863676416.5	x^20 - 10x^18 + 40x^16 - 80x^14 + 79x^12 - 26x^10 - 10x^8 + 8x^4 - 1	\( -\,2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T990	Trivial (GRH)
20.0.500064391667556895216944128.1	x^20 - 3x^19 + 2x^18 + 16x^17 - 57x^16 - 10x^15 + 271x^14 - 148x^13 - 593x^12 + 459x^11 + 901x^10 - 735x^9 - 892x^8 + 747x^7 + 694x^6 - 51x^5 + 665x^4 + 581x^3 + 301x^2 - 157x + 83	\( 2^{10}\cdot 17^{5}\cdot 61^{4}\cdot 397^{4} \)	20T990	$[2]$ (GRH)
20.0.764298486756043147081352192.1	x^20 - 2x^19 + 3x^18 - 8x^17 + 5x^16 - 9x^15 + 21x^14 - 44x^13 + 66x^12 + 52x^11 + 8x^10 - 20x^9 - 11x^8 + 357x^7 + 731x^6 + 471x^5 + 8x^4 - 90x^3 + 100x^2 + 205x + 89	\( 2^{10}\cdot 13^{4}\cdot 347^{4}\cdot 1217^{3} \)	20T990	Trivial (GRH)
20.0.1771854453521032043952078848.1	x^20 - 5x^18 + 12x^16 - x^14 - 54x^12 + 6x^10 + 134x^8 + 218x^6 + 188x^4 + 85x^2 + 17	\( 2^{20}\cdot 17^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.12.1771854453521032043952078848.1	x^20 - 4x^19 - 6x^18 + 26x^17 + 18x^16 - 28x^15 - 47x^14 - 34x^13 - 2x^12 + 44x^11 + 81x^10 + 44x^9 - 2x^8 - 34x^7 - 47x^6 - 28x^5 + 18x^4 + 26x^3 - 6x^2 - 4x + 1	\( 2^{20}\cdot 17^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.4.1771854453521032043952078848.1	x^20 + 5x^18 + 4x^16 - 27x^14 - 16x^12 + 32x^10 - 59x^8 - 23x^6 + 149x^4 - 51x^2 + 17	\( 2^{20}\cdot 17^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.0.8795798548122216674119122944.1	x^20 + 15x^18 + 96x^16 + 346x^14 + 784x^12 + 1185x^10 + 1235x^8 + 894x^6 + 441x^4 + 145x^2 + 29	\( 2^{20}\cdot 29^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.12.8795798548122216674119122944.1	x^20 - 15x^18 + 96x^16 - 346x^14 + 784x^12 - 1185x^10 + 1235x^8 - 894x^6 + 441x^4 - 145x^2 + 29	\( 2^{20}\cdot 29^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.0.18267808596417837598677925888.1	x^20 + 10x^18 + 38x^16 + 67x^14 + 11x^12 - 187x^10 - 283x^8 - 9x^6 + 261x^4 + 185x^2 + 37	\( 2^{20}\cdot 37^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.12.18267808596417837598677925888.1	x^20 - 10x^18 + 38x^16 - 67x^14 + 11x^12 + 187x^10 - 283x^8 + 9x^6 + 261x^4 - 185x^2 + 37	\( 2^{20}\cdot 37^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.2.28673892130286320927844073472.1	x^20 - x^18 - 3x^16 - 22x^14 - 48x^12 + 81x^10 + 210x^8 - 43x^6 - 318x^4 - 215x^2 - 43	\( -\,2^{20}\cdot 43^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.6.28673892130286320927844073472.1	x^20 - 4x^18 - 2x^16 + 23x^14 - 5x^12 + 17x^10 - 209x^8 + 6x^6 - 60x^4 + 215x^2 - 43	\( -\,2^{20}\cdot 43^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.6.28673892130286320927844073472.2	x^20 - 4x^18 - 28x^16 + x^14 + 106x^12 + 44x^10 - 122x^8 - 10x^6 + 80x^4 - 43	\( -\,2^{20}\cdot 43^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.8.31430595908619556319219679232.1	x^20 - 4x^19 - 12x^18 + 60x^17 + 50x^16 - 400x^15 + 64x^14 + 1362x^13 - 1275x^12 - 1910x^11 + 3812x^10 - 430x^9 - 3929x^8 + 3560x^7 - 290x^6 - 1500x^5 + 1231x^4 - 460x^3 + 70x^2 + 2x - 1	\( 2^{30}\cdot 37^{3}\cdot 4903^{4} \)	20T990	Trivial (GRH)
20.8.31430595908619556319219679232.2	x^20 - 2x^19 - 20x^18 + 34x^17 + 134x^16 - 204x^15 - 466x^14 + 676x^13 + 1113x^12 - 1452x^11 - 2308x^10 + 1350x^9 + 3331x^8 + 1018x^7 - 978x^6 - 820x^5 - 219x^4 - 6x^3 + 8x^2 + 2x + 1	\( 2^{30}\cdot 37^{3}\cdot 4903^{4} \)	20T990	Trivial (GRH)
20.0.34698090439479943844932354048.1	x^20 + 21x^18 + 185x^16 + 909x^14 + 2773x^12 + 5502x^10 + 7193x^8 + 6101x^6 + 3185x^4 + 902x^2 + 97	\( 2^{20}\cdot 97^{3}\cdot 13799^{4} \)	20T990	$[2]$ (GRH)
20.12.34698090439479943844932354048.1	x^20 - 21x^18 + 185x^16 - 909x^14 + 2773x^12 - 5502x^10 + 7193x^8 - 6101x^6 + 3185x^4 - 902x^2 + 97	\( 2^{20}\cdot 97^{3}\cdot 13799^{4} \)	20T990	Trivial (GRH)
20.12.91999704660989024218056228864.1	x^20 - 2x^18 - x^16 - 32x^14 + 231x^12 - 809x^10 + 1596x^8 - 1712x^6 + 967x^4 - 269x^2 + 29	\( 2^{20}\cdot 3^{12}\cdot 29^{3}\cdot 1613^{4} \)	20T990	Trivial (GRH)
20.10.378164880003108018831486877696.1	x^20 - 10x^18 + 37x^16 - 56x^14 + 7x^12 + 70x^10 - 55x^8 - 12x^6 + 20x^4 - 1	\( -\,2^{40}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.6.378164880003108018831486877696.1	x^20 + 10x^18 + 37x^16 + 56x^14 + 7x^12 - 70x^10 - 55x^8 + 12x^6 + 20x^4 - 1	\( -\,2^{40}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.6.378622199332328495065595163427.1	x^20 - 9x^18 - 4x^17 + 39x^16 + 19x^15 - 157x^14 - 331x^13 - 622x^12 - 1049x^11 - 1406x^10 - 1926x^9 - 2826x^8 - 3212x^7 - 2216x^6 - 1720x^5 - 1269x^4 - 291x^3 - 38x^2 - 35x + 1	\( -\,43^{3}\cdot 61^{8}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.8.512065937067578260702150787072.2	x^20 - 10x^19 + 49x^18 - 156x^17 + 276x^16 - 128x^15 - 658x^14 + 2084x^13 - 2296x^12 - 2050x^11 + 6773x^10 - 1868x^9 - 5785x^8 + 2530x^7 + 2552x^6 - 104x^5 - 1394x^4 - 352x^3 + 544x^2 + 54x - 61	\( 2^{20}\cdot 17^{5}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.12.1814378960405536813006928740352.1	x^20 - 10x^19 + 26x^18 + 50x^17 - 280x^16 - 70x^15 + 1240x^14 + 578x^13 - 3923x^12 - 4716x^11 + 9160x^10 + 16298x^9 - 10882x^8 - 27234x^7 + 814x^6 + 18908x^5 + 4976x^4 - 4804x^3 - 2018x^2 + 236x + 139	\( 2^{30}\cdot 17^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.8.1814378960405536813006928740352.1	x^20 - 4x^19 - 6x^18 + 26x^17 - 14x^16 - 92x^15 + 28x^14 + 140x^13 + 327x^12 + 410x^11 - 4x^10 + 102x^9 + 34x^8 - 736x^7 - 564x^6 - 552x^5 - 1342x^4 - 946x^3 + 504x^2 + 1306x + 691	\( 2^{30}\cdot 17^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.16.9006897713277149874297981894656.1	x^20 - 30x^18 + 327x^16 - 1502x^14 + 2195x^12 + 1764x^10 - 4164x^8 - 58x^6 + 1405x^4 - 406x^2 + 29	\( 2^{30}\cdot 29^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.4.9006897713277149874297981894656.1	x^20 + 30x^18 + 327x^16 + 1502x^14 + 2195x^12 - 1764x^10 - 4164x^8 + 58x^6 + 1405x^4 + 406x^2 + 29	\( 2^{30}\cdot 29^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.16.18706236002731865701046196109312.1	x^20 - 10x^19 + 20x^18 + 80x^17 - 267x^16 - 232x^15 + 1194x^14 + 246x^13 - 2693x^12 + 186x^11 + 3426x^10 - 878x^9 - 2567x^8 + 1158x^7 + 1168x^6 - 742x^5 - 336x^4 + 198x^3 + 56x^2 - 6x - 1	\( 2^{30}\cdot 37^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.4.18706236002731865701046196109312.1	x^20 - 10x^19 + 46x^18 - 108x^17 + 87x^16 + 210x^15 - 550x^14 + 184x^13 + 789x^12 - 832x^11 + 290x^10 + 984x^9 - 1415x^8 - 158x^7 + 2780x^6 - 972x^5 - 2594x^4 + 1998x^3 - 368x^2 - 1366x - 149	\( 2^{30}\cdot 37^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.10.29362065541413192630112331235328.1	x^20 - 2x^18 - 18x^17 - 55x^16 + 66x^15 + 22x^14 + 610x^13 - 67x^12 - 1062x^11 - 250x^10 - 6076x^9 + 7531x^8 - 4558x^7 + 17274x^6 - 2960x^5 - 10528x^4 - 1164x^3 + 1018x^2 + 260x + 17	\( -\,2^{30}\cdot 43^{3}\cdot 61^{4}\cdot 397^{4} \)	20T990	Trivial (GRH)
20.4.24711106619786220822902825453355008.1	x^20 + 10x^18 + 42x^16 + 96x^14 + 124x^12 + 72x^10 - 22x^8 - 56x^6 - 21x^4 + 6x^2 + 2	\( 2^{59}\cdot 14389^{4} \)	20T990	Trivial (GRH)
20.8.24711106619786220822902825453355008.1	x^20 - 10x^18 + 43x^16 - 104x^14 + 150x^12 - 116x^10 + 16x^8 + 48x^6 - 32x^4 + 2	\( 2^{59}\cdot 14389^{4} \)	20T990	Trivial (GRH)
20.4.24711106619786220822902825453355008.2	x^20 + 6x^18 - 42x^16 - 224x^14 - 176x^12 + 1152x^10 + 3968x^8 + 6144x^6 + 5376x^4 + 2560x^2 + 512	\( 2^{59}\cdot 14389^{4} \)	20T990	Trivial (GRH)
20.8.24711106619786220822902825453355008.2	x^20 - 6x^18 - 21x^16 + 8x^14 + 392x^12 - 864x^8 - 2432x^6 + 2176x^4 + 2560x^2 + 512	\( 2^{59}\cdot 14389^{4} \)	20T990	Trivial (GRH)
20.14.26200187925259114875506183929630664183.1	x^20 - 9x^19 - 112x^18 + 1040x^17 + 5222x^16 - 48453x^15 - 133191x^14 + 1161345x^13 + 2084821x^12 - 15176755x^11 - 21670372x^10 + 105641483x^9 + 151273512x^8 - 347660958x^7 - 583819294x^6 + 258552326x^5 + 713204674x^4 + 774865086x^3 + 997414959x^2 - 333549821x - 869875243	\( -\,61^{6}\cdot 167^{5}\cdot 397^{6} \)	20T990	Trivial (GRH)
20.2.26200187925259114875506183929630664183.1	x^20 - x^19 + 18x^18 + 61x^17 - 538x^16 + 563x^15 - 42096x^14 + 86168x^13 - 1612926x^12 + 3113891x^11 - 27783817x^10 + 41808036x^9 - 262085702x^8 + 324820543x^7 - 1467374347x^6 + 1619970297x^5 - 5144459696x^4 + 4044906852x^3 - 10049936456x^2 + 5066796784x - 9095434144	\( -\,61^{6}\cdot 167^{5}\cdot 397^{6} \)	20T990	$[2]$ (GRH)