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 80)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.23317004278327158203125.1	x^20 - 3x^19 + 5x^18 - 10x^17 + 4x^16 + x^15 - 12x^14 + 30x^13 - 35x^12 + 39x^11 - 25x^10 + 18x^9 + 4x^8 - 15x^7 + 3x^6 - 18x^5 + 3x^3 + 3x^2 + 5x + 1	\( 5^{10}\cdot 601^{4}\cdot 18301 \)	20T876	Trivial (GRH)
20.0.29961623632204865208320.1	x^20 - 2x^18 + 7x^16 - 4x^14 + 7x^12 + 4x^10 + 7x^8 - 6x^6 + 14x^4 - 4x^2 + 5	\( 2^{30}\cdot 5\cdot 29^{4}\cdot 53^{4} \)	20T876	Trivial
20.0.77900221443732649541632.1	x^20 - 2x^18 + 11x^16 - 20x^14 + 39x^12 - 60x^10 + 99x^8 - 134x^6 + 118x^4 - 60x^2 + 13	\( 2^{30}\cdot 13\cdot 29^{4}\cdot 53^{4} \)	20T876	Trivial (GRH)
20.0.495261969594325791015625.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 441x^16 - 876x^15 + 1408x^14 - 1870x^13 + 2089x^12 - 2004x^11 + 1701x^10 - 1328x^9 + 983x^8 - 686x^7 + 435x^6 - 241x^5 + 115x^4 - 47x^3 + 15x^2 - 3x + 1	\( 5^{10}\cdot 31^{4}\cdot 71^{4}\cdot 2161 \)	20T876	Trivial
20.2.956078403407438193359375.1	x^20 - 5x^18 - 2x^17 + 9x^16 + 15x^15 - 5x^14 - 26x^13 - 16x^12 + 12x^11 + 21x^10 + x^9 + 3x^8 + 12x^7 + 23x^6 + 27x^5 + 16x^4 + 4x^3 - 6x^2 - 2x - 1	\( -\,5^{10}\cdot 59\cdot 641^{4}\cdot 9829 \)	20T876	Trivial (GRH)
20.0.980469773530538564453125.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 569x^16 - 1288x^15 + 2404x^14 - 3774x^13 + 5055x^12 - 5838x^11 + 5861x^10 - 5144x^9 + 3957x^8 - 2662x^7 + 1553x^6 - 773x^5 + 320x^4 - 106x^3 + 26x^2 - 4x + 1	\( 5^{10}\cdot 11\cdot 601^{4}\cdot 69959 \)	20T876	Trivial (GRH)
20.2.1335973502986240000000000.3	x^20 + x^18 - 4x^16 - 9x^14 - 2x^12 + 17x^10 + 30x^8 + 26x^6 + 11x^4 + x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 601^{4} \)	20T876	Trivial (GRH)
20.4.4033623052252917587890625.1	x^20 - 3x^19 + x^18 + 10x^17 - 16x^16 - 11x^15 + 49x^14 - 17x^13 - 107x^12 + 128x^11 + 59x^10 - 219x^9 + 159x^8 + 24x^7 - 115x^6 + 81x^5 - 23x^4 - 4x^3 + 6x^2 - 3x + 1	\( 5^{10}\cdot 449\cdot 641^{4}\cdot 5449 \)	20T876	Trivial (GRH)
20.2.151646934959991446669921875.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 483x^16 - 1008x^15 + 1713x^14 - 2409x^13 + 2815x^12 - 2707x^11 + 2077x^10 - 1173x^9 + 362x^8 + 103x^7 - 227x^6 + 178x^5 - 108x^4 + 61x^3 - 28x^2 + 8x - 1	\( -\,5^{10}\cdot 29\cdot 71\cdot 9319^{4} \)	20T876	Trivial (GRH)
20.6.201484463662828739248046875.1	x^20 - 6x^19 + 12x^18 + 5x^17 - 96x^16 + 327x^15 - 739x^14 + 1303x^13 - 1902x^12 + 2366x^11 - 2541x^10 + 2366x^9 - 1902x^8 + 1303x^7 - 739x^6 + 327x^5 - 96x^4 + 5x^3 + 12x^2 - 6x + 1	\( -\,5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.10.201484463662828739248046875.2	x^20 - 3x^19 - 10x^18 + 27x^17 + 45x^16 - 76x^15 - 145x^14 + 98x^13 + 274x^12 - 51x^11 - 339x^10 - 51x^9 + 274x^8 + 98x^7 - 145x^6 - 76x^5 + 45x^4 + 27x^3 - 10x^2 - 3x + 1	\( -\,5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.10.201484463662828739248046875.3	x^20 - 6x^19 + 13x^18 - 6x^17 - 42x^16 + 139x^15 - 198x^14 + 49x^13 + 354x^12 - 720x^11 + 620x^10 + 45x^9 - 811x^8 + 756x^7 - 133x^6 + 66x^5 - 177x^4 + 91x^3 + 8x^2 - 9x + 1	\( -\,5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.6.1242593181789399040000000000.1	x^20 + 3x^18 - 10x^16 - 36x^14 - 28x^12 - x^10 - 16x^8 - 8x^6 + 15x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.10.1242593181789399040000000000.2	x^20 - 7x^18 + 16x^16 - 18x^14 + 29x^12 - 40x^10 + 31x^6 - 15x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.2.1242593181789399040000000000.2	x^20 + 10x^18 + 34x^16 + 36x^14 - 36x^12 - 97x^10 - 46x^8 + 7x^6 - 7x^4 - 10x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.6.1242593181789399040000000000.2	x^20 + 4x^18 + x^16 - 7x^14 + 10x^12 + 22x^10 - 13x^8 - 17x^6 + 6x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.10.1242593181789399040000000000.3	x^20 - 11x^18 + 45x^16 - 92x^14 + 96x^12 - 36x^10 - 19x^8 + 38x^6 - 37x^4 + 15x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.2.1242593181789399040000000000.3	x^20 + 8x^18 + 25x^16 + 45x^14 + 52x^12 + 20x^10 - 31x^8 - 53x^6 - 36x^4 - 11x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.6.1242593181789399040000000000.3	x^20 - 7x^18 + 10x^16 + 23x^14 - 47x^12 - 43x^10 + 59x^8 + 44x^6 - 17x^4 - 13x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.10.1242593181789399040000000000.4	x^20 - 3x^18 + 11x^14 - 31x^12 + 46x^10 - 44x^8 + 51x^6 - 45x^4 + 16x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.2.1242593181789399040000000000.4	x^20 + 4x^18 - 4x^16 - 26x^14 - 26x^12 - 8x^10 - 20x^8 - 49x^6 - 39x^4 - 11x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.6.1242593181789399040000000000.4	x^20 + 2x^18 + x^16 - 4x^14 - 9x^12 - 24x^10 - 85x^8 - 90x^6 + 3x^4 + 25x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.10.1242593181789399040000000000.5	x^20 - 4x^18 - 4x^16 + 26x^14 - 26x^12 + 8x^10 - 20x^8 + 49x^6 - 39x^4 + 11x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.4.2120282838067894597861328125.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 482x^16 - 1000x^15 + 1682x^14 - 2332x^13 + 2684x^12 - 2558x^11 + 1984x^10 - 1192x^9 + 468x^8 + 2x^7 - 199x^6 + 212x^5 - 141x^4 + 63x^3 - 14x^2 - x + 1	\( 5^{10}\cdot 11\cdot 5471^{4}\cdot 22031 \)	20T876	Trivial (GRH)
20.4.2814228080944242854892578125.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 479x^16 - 976x^15 + 1583x^14 - 2059x^13 + 2131x^12 - 1697x^11 + 921x^10 - 123x^9 - 440x^8 + 685x^7 - 667x^6 + 496x^5 - 288x^4 + 127x^3 - 42x^2 + 10x - 1	\( 5^{10}\cdot 61\cdot 4441\cdot 5711^{4} \)	20T876	Trivial (GRH)
20.4.15335718780785077520400390625.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 615x^16 - 1452x^15 + 2850x^14 - 4740x^13 + 6762x^12 - 8332x^11 + 8883x^10 - 8165x^9 + 6390x^8 - 4152x^7 + 2127x^6 - 762x^5 + 121x^4 + 43x^3 - 27x^2 + 3x + 1	\( 5^{10}\cdot 19^{4}\cdot 389^{4}\cdot 526249 \)	20T876	Trivial (GRH)
20.10.18016952829639264630654296875.2	x^20 - 5x^19 + 12x^18 - 13x^17 - 27x^16 + 116x^15 - 349x^14 + 738x^13 - 393x^12 - 1300x^11 + 3217x^10 - 3882x^9 + 2569x^8 - 204x^7 - 1272x^6 + 1316x^5 - 564x^4 - 159x^3 + 312x^2 - 133x + 19	\( -\,5^{10}\cdot 19^{4}\cdot 1699^{5} \)	20T876	Trivial (GRH)
20.10.18016952829639264630654296875.3	x^20 - 3x^19 - 4x^18 + 17x^17 - 6x^16 - 25x^15 + 24x^14 + 219x^13 - 372x^12 - 598x^11 + 1089x^10 + 308x^9 - 418x^8 - 511x^7 + 183x^6 + 133x^5 - 67x^4 + 76x^3 - 15x^2 - 11x - 1	\( -\,5^{10}\cdot 19^{4}\cdot 1699^{5} \)	20T876	Trivial (GRH)
20.10.18016952829639264630654296875.4	x^20 - 5x^19 - 2x^18 + 28x^17 + 52x^16 - 207x^15 - 159x^14 + 547x^13 + 495x^12 - 1050x^11 - 603x^10 + 1720x^9 - 324x^8 - 1385x^7 + 575x^6 + 473x^5 - 44x^4 - 153x^3 - x^2 + 12x + 1	\( -\,5^{10}\cdot 19^{4}\cdot 1699^{5} \)	20T876	Trivial (GRH)
20.12.18636916201364268160000000000.1	x^20 - 10x^19 + 32x^18 - 3x^17 - 187x^16 + 272x^15 + 348x^14 - 974x^13 - 148x^12 + 1616x^11 - 266x^10 - 1558x^9 + 287x^8 + 996x^7 - 22x^6 - 443x^5 - 62x^4 + 114x^3 + 18x^2 - 11x - 1	\( 2^{16}\cdot 5^{10}\cdot 191\cdot 499^{4}\cdot 2459 \)	20T876	Trivial (GRH)
20.10.18993732228844275002500000000.1	x^20 + 4x^18 - 39x^16 - 72x^14 + 560x^12 - 55x^10 - 2087x^8 + 1616x^6 + 757x^4 - 263x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.14.18993732228844275002500000000.1	x^20 - 18x^18 + 116x^16 - 292x^14 + 78x^12 + 601x^10 - 298x^8 - 180x^6 + 94x^4 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.14.18993732228844275002500000000.2	x^20 - 7x^18 - 12x^16 + 171x^14 - 318x^12 - 12x^10 + 371x^8 - 140x^6 - 55x^4 + 18x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.12.29933917472746554501569183744.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 209x^16 + 244x^15 + 532x^14 - 1058x^13 - 716x^12 + 2190x^11 + 642x^10 - 2732x^9 - 616x^8 + 2132x^7 + 697x^6 - 958x^5 - 525x^4 + 184x^3 + 171x^2 - 6x - 17	\( 2^{30}\cdot 7\cdot 1583^{4}\cdot 634223 \)	20T876	Trivial (GRH)
20.8.44189987327288033351962890625.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 606x^16 - 1380x^15 + 2526x^14 - 3732x^13 + 4397x^12 - 3970x^11 + 2439x^10 - 486x^9 - 942x^8 + 1344x^7 - 952x^6 + 372x^5 - 26x^4 - 56x^3 + 24x^2 - 1	\( 5^{10}\cdot 151\cdot 1231\cdot 12491^{4} \)	20T876	Trivial (GRH)
20.0.56363984514599954560000000000.1	x^20 - 10x^19 + 62x^18 - 273x^17 + 947x^16 - 2680x^15 + 6372x^14 - 12902x^13 + 22490x^12 - 33904x^11 + 44326x^10 - 50212x^9 + 49181x^8 - 41436x^7 + 29870x^6 - 18257x^5 + 9382x^4 - 3972x^3 + 1338x^2 - 323x + 41	\( 2^{16}\cdot 5^{10}\cdot 499^{4}\cdot 1420429 \)	20T876	Trivial (GRH)
20.14.72735891382281174868544921875.1	x^20 - 6x^19 - 6x^18 + 104x^17 - 119x^16 - 601x^15 + 1425x^14 + 922x^13 - 5543x^12 + 2934x^11 + 7806x^10 - 10328x^9 - 227x^8 + 7303x^7 - 4163x^6 + 143x^5 + 484x^4 - 188x^3 + 68x^2 - 7x - 1	\( -\,5^{10}\cdot 19^{7}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.6.72735891382281174868544921875.1	x^20 - 6x^19 + 9x^18 + 10x^17 - 38x^16 + 17x^15 + 63x^14 + 9x^13 - 342x^12 + 63x^11 + 437x^10 + 1147x^9 - 1947x^8 - 671x^7 + 178x^6 + 2329x^5 + 828x^4 - 3684x^3 + 1766x^2 - 379x + 191	\( -\,5^{10}\cdot 19^{7}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.14.72735891382281174868544921875.2	x^20 - x^19 - 22x^18 + 12x^17 + 158x^16 - 61x^15 - 475x^14 + 121x^13 + 691x^12 + 24x^11 - 877x^10 + 24x^9 + 691x^8 + 121x^7 - 475x^6 - 61x^5 + 158x^4 + 12x^3 - 22x^2 - x + 1	\( -\,5^{10}\cdot 19^{7}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.6.72735891382281174868544921875.2	x^20 - 8x^19 + 25x^18 - 39x^17 + 2x^16 + 148x^15 - 435x^14 + 701x^13 - 490x^12 - 428x^11 + 1899x^10 - 3319x^9 + 3947x^8 - 3146x^7 + 647x^6 + 2446x^5 - 3871x^4 + 3055x^3 - 1396x^2 + 269x + 11	\( -\,5^{10}\cdot 19^{7}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.0.233342046772928706560000000000.1	x^20 + 20x^18 + 175x^16 + 880x^14 + 2808x^12 + 5921x^10 + 8325x^8 + 7675x^6 + 4411x^4 + 1404x^2 + 179	\( 2^{20}\cdot 5^{10}\cdot 179\cdot 3359^{4} \)	20T876	Trivial (GRH)
20.4.410094814925296679994736328125.1	x^20 - 10x^19 + 60x^18 - 255x^17 + 844x^16 - 2264x^15 + 5049x^14 - 9493x^13 + 15155x^12 - 20587x^11 + 23707x^10 - 22929x^9 + 18257x^8 - 11521x^7 + 5256x^6 - 1217x^5 - 410x^4 + 558x^3 - 266x^2 + 65x - 5	\( 5^{10}\cdot 31\cdot 12511^{4}\cdot 55291 \)	20T876	Trivial (GRH)
20.8.411298343172291082240000000000.1	x^20 - 41x^16 + 48x^14 + 458x^12 - 1136x^10 + 814x^8 - 688x^6 - 539x^4 + 1776x^2 + 331	\( 2^{20}\cdot 5^{10}\cdot 331\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.6.1898135124043641651200000000000.1	x^20 + 15x^18 + 29x^16 - 218x^14 - 967x^12 - 1411x^10 - 781x^8 - 6x^6 + 119x^4 + 15x^2 - 5	\( -\,2^{28}\cdot 5^{11}\cdot 3469^{4} \)	20T876	Trivial (GRH)
20.8.3325450063227604080640000000000.1	x^20 - 20x^18 + 145x^16 - 574x^14 + 1188x^12 + 12x^10 - 5991x^8 + 12249x^6 - 8328x^4 - 1112x^2 + 2551	\( 2^{20}\cdot 5^{10}\cdot 2551\cdot 3359^{4} \)	20T876	Trivial (GRH)
20.8.4124166770359015413760000000000.1	x^20 - 19x^18 + 151x^16 - 642x^14 + 1526x^12 - 1790x^10 - 127x^8 + 4180x^6 - 6880x^4 + 2182x^2 + 3319	\( 2^{20}\cdot 5^{10}\cdot 3319^{5} \)	20T876	$[2]$ (GRH)
20.18.4862395450584134400640000000000.1	x^20 - 18x^18 + 130x^16 - 474x^14 + 873x^12 - 558x^10 - 629x^8 + 1349x^6 - 893x^4 + 236x^2 - 16	\( -\,2^{16}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.18.4862395450584134400640000000000.2	x^20 - 19x^18 + 124x^16 - 189x^14 - 1489x^12 + 8215x^10 - 16848x^8 + 15489x^6 - 5721x^4 + 604x^2 - 16	\( -\,2^{16}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.12.5214117947074988109022362599424.1	x^20 - 10x^19 + 39x^18 - 66x^17 - 2x^16 + 220x^15 - 406x^14 + 216x^13 + 376x^12 - 800x^11 + 508x^10 + 226x^9 - 608x^8 + 342x^7 + 81x^6 - 188x^5 + 68x^4 + 18x^3 - 17x^2 + 2x + 1	\( 2^{20}\cdot 3^{10}\cdot 7561\cdot 10273^{4} \)	20T876	Trivial (GRH)
20.2.6074032396939653283840000000000.1	x^20 + 23x^18 + 207x^16 + 920x^14 + 2053x^12 + 1899x^10 - 177x^8 - 1192x^6 - 507x^4 - 45x^2 - 1	\( -\,2^{32}\cdot 5^{10}\cdot 3469^{4} \)	20T876	$[3]$ (GRH)