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 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.2531491036246028598272.1	x^20 - x^19 - 3x^18 + 7x^17 + 2x^16 - 17x^15 + 19x^14 - 17x^12 + 9x^11 + 34x^10 - 34x^9 - x^8 + 32x^7 - 4x^6 + 4x^5 + 3x^3 - 3x + 1	\( 2^{10}\cdot 47^{11} \)	20T423	Trivial
20.0.81007713159872915144704.1	x^20 - x^19 + 4x^18 - 7x^17 + 3x^16 - 19x^15 - 11x^14 - 12x^13 - 7x^12 + 37x^11 + 70x^10 + 146x^9 + 192x^8 + 244x^7 + 307x^6 + 213x^5 + 155x^4 + 121x^3 + 21x^2 - 11x + 1	\( 2^{15}\cdot 47^{11} \)	20T423	Trivial (GRH)
20.10.40745808166212682337450316379.1	x^20 - 4x^19 + 6x^18 - 5x^17 - 9x^16 + 68x^15 - 198x^14 + 39x^13 + 232x^12 - 280x^11 - 29x^10 + 123x^9 + 273x^8 + 80x^7 - 193x^6 - 41x^5 - 11x^4 + 28x^3 + 10x^2 - 8x + 1	\( -\,379\cdot 401^{10} \)	20T423	Trivial (GRH)
20.14.110088938158843764415696897024.1	x^20 - 16x^18 - 5x^17 + 89x^16 + 111x^15 - 299x^14 - 527x^13 + 427x^12 + 1313x^11 + 119x^10 - 2063x^9 - 704x^8 + 1326x^7 + 1326x^6 - 781x^5 - 683x^4 + 303x^3 + 105x^2 - 42x - 1	\( -\,2^{10}\cdot 401^{10} \)	20T423	Trivial (GRH)
20.6.110088938158843764415696897024.1	x^20 + 10x^18 + 14x^16 - 105x^14 - 242x^12 + 304x^10 + 797x^8 - 165x^6 - 281x^4 - 44x^2 - 1	\( -\,2^{10}\cdot 401^{10} \)	20T423	Trivial (GRH)
20.10.110088938158843764415696897024.2	x^20 - 4x^18 - 18x^16 + 67x^14 + 98x^12 - 339x^10 - 141x^8 + 504x^6 - 27x^4 - 59x^2 - 1	\( -\,2^{10}\cdot 401^{10} \)	20T423	Trivial (GRH)
20.10.38933334597022895851373555971984.1	x^20 + 18x^18 + 89x^16 - 10x^14 - 685x^12 + 38x^10 + 1033x^8 - 292x^6 - 191x^4 + 64x^2 - 1	\( -\,2^{4}\cdot 1093^{10} \)	20T423	Trivial (GRH)
20.14.44145664201696349530694455706624.1	x^20 - 15x^18 + 13x^16 + 708x^14 - 2899x^12 - 3375x^10 + 33596x^8 - 57207x^6 + 32794x^4 - 2406x^2 - 401	\( -\,2^{10}\cdot 401^{11} \)	20T423	Trivial (GRH)
20.6.44145664201696349530694455706624.1	x^20 + 19x^18 + 92x^16 - 226x^14 - 2591x^12 - 2721x^10 + 14053x^8 + 25444x^6 + 4265x^4 - 5614x^2 - 401	\( -\,2^{10}\cdot 401^{11} \)	20T423	Trivial (GRH)
20.10.44145664201696349530694455706624.2	x^20 - 10x^18 - 56x^16 + 531x^14 + 897x^12 - 7444x^10 - 7334x^8 + 34068x^6 + 26408x^4 - 46917x^2 - 32481	\( -\,2^{10}\cdot 401^{11} \)	20T423	Trivial (GRH)
20.14.44145664201696349530694455706624.2	x^20 - 22x^18 - 10x^17 + 108x^16 + 141x^15 - 265x^14 - 665x^13 + 1441x^12 - 395x^11 - 2044x^10 + 2370x^9 + 544x^8 - 2331x^7 + 592x^6 + 1112x^5 - 344x^4 - 277x^3 + 35x^2 + 19x - 1	\( -\,2^{10}\cdot 401^{11} \)	20T423	Trivial (GRH)
20.6.44145664201696349530694455706624.2	x^20 + 26x^18 + 225x^16 + 655x^14 - 803x^12 - 7130x^10 - 7409x^8 + 8851x^6 + 11937x^4 + 401x^2 - 401	\( -\,2^{10}\cdot 401^{11} \)	20T423	Trivial (GRH)
20.10.44145664201696349530694455706624.3	x^20 - 5x^18 - 27x^17 - 62x^16 + 423x^15 + 777x^14 - 2789x^13 - 4392x^12 + 9673x^11 + 15480x^10 - 15437x^9 - 34067x^8 + 2410x^7 + 40199x^6 + 17493x^5 - 13433x^4 - 13515x^3 - 3557x^2 + 81	\( -\,2^{10}\cdot 401^{11} \)	20T423	Trivial (GRH)
20.14.112731072674656014761673622552576.1	x^20 - 17x^18 + 82x^16 - 28x^14 - 618x^12 + 944x^10 + 690x^8 - 1339x^6 - 124x^4 + 73x^2 - 1	\( -\,2^{20}\cdot 401^{10} \)	20T423	Trivial (GRH)
20.18.112731072674656014761673622552576.1	x^20 - 16x^18 + 85x^16 - 107x^14 - 588x^12 + 2563x^10 - 4254x^8 + 3481x^6 - 1369x^4 + 206x^2 - 1	\( -\,2^{20}\cdot 401^{10} \)	20T423	Trivial (GRH)
20.2.112731072674656014761673622552576.1	x^20 + 16x^18 + 85x^16 + 107x^14 - 588x^12 - 2563x^10 - 4254x^8 - 3481x^6 - 1369x^4 - 206x^2 - 1	\( -\,2^{20}\cdot 401^{10} \)	20T423	$[2]$ (GRH)
20.6.112731072674656014761673622552576.1	x^20 + 5x^18 - 37x^16 - 327x^14 - 839x^12 - 700x^10 + 371x^8 + 903x^6 + 469x^4 + 74x^2 - 1	\( -\,2^{20}\cdot 401^{10} \)	20T423	Trivial (GRH)
20.8.1647390279091035299662162868290417.1	x^20 - 2x^19 - 7x^18 + 2x^17 + 11x^16 + 20x^15 + 33x^14 + 105x^13 + 26x^12 - 127x^11 - 259x^10 - 378x^9 - 64x^8 + 93x^7 + 124x^6 + 212x^5 + 120x^4 + 47x^3 + 17x^2 + 6x + 1	\( 19^{10}\cdot 43^{10}\cdot 12433 \)	20T423	Trivial (GRH)
20.16.2493717533286270302952039845951489.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 179x^16 + 412x^15 - 128x^14 - 806x^13 + 1290x^12 - 174x^11 - 1615x^10 + 1623x^9 + 321x^8 - 1490x^7 + 656x^6 + 535x^5 - 507x^4 - 110x^3 + 127x^2 + 33x + 1	\( 401^{10}\cdot 2281\cdot 10169 \)	20T423	Trivial (GRH)
20.10.2577947821925133337909357416991744.1	x^20 - 11x^18 - 42x^16 + 662x^14 - 804x^12 - 2768x^10 + 2948x^8 + 1427x^6 - 1022x^4 - 323x^2 - 19	\( -\,2^{10}\cdot 19^{11}\cdot 43^{10} \)	20T423	Trivial (GRH)
20.18.2577947821925133337909357416991744.1	x^20 - 42x^18 + 618x^16 - 3789x^14 + 8961x^12 - 1682x^10 - 20616x^8 + 23886x^6 - 9370x^4 + 1235x^2 - 19	\( -\,2^{10}\cdot 19^{11}\cdot 43^{10} \)	20T423	Trivial (GRH)
20.2.2577947821925133337909357416991744.1	x^20 + 27x^18 + 135x^16 - 362x^14 - 4917x^12 - 16797x^10 - 28278x^8 - 25575x^6 - 11870x^4 - 2242x^2 - 19	\( -\,2^{10}\cdot 19^{11}\cdot 43^{10} \)	20T423	$[4]$ (GRH)
20.12.5834302965409512291058019417402368.1	x^20 - 8x^19 + 23x^18 - 28x^17 - 147x^16 + 1401x^15 - 4324x^14 + 4404x^13 + 4324x^12 - 15674x^11 + 18559x^10 - 14075x^9 + 10908x^8 + 10703x^7 - 60667x^6 + 43458x^5 + 8721x^4 + 10775x^3 - 4300x^2 - 2500x + 625	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.16.5834302965409512291058019417402368.1	x^20 - 20x^18 + 60x^16 + 1399x^14 - 13780x^12 + 39077x^10 + 46329x^8 - 454820x^6 + 792591x^4 - 435461x^2 + 15523	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.4.5834302965409512291058019417402368.1	x^20 - 8x^19 + 29x^18 - 47x^17 - 49x^16 + 385x^15 - 656x^14 + 220x^13 + 2285x^12 - 7382x^11 + 9935x^10 + 667x^9 - 24088x^8 + 64517x^7 - 35816x^6 + 37128x^5 + 7036x^4 - 185493x^3 - 34122x^2 + 42028x + 23471	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.8.5834302965409512291058019417402368.1	x^20 - 8x^19 + 12x^18 + 80x^17 - 290x^16 - 183x^15 + 2154x^14 - 1376x^13 - 8255x^12 + 12715x^11 + 11704x^10 - 36967x^9 + 3675x^8 + 48318x^7 - 3411x^6 - 61608x^5 - 23582x^4 + 88692x^3 + 7239x^2 - 48735x + 9025	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.12.5834302965409512291058019417402368.2	x^20 + 4x^18 - 170x^16 - 329x^14 + 4546x^12 + 223x^10 - 29905x^8 + 29594x^6 - 3381x^4 - 645x^2 + 43	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.16.5834302965409512291058019417402368.2	x^20 - x^18 - 119x^16 + 846x^14 - 1509x^12 - 4889x^10 + 26764x^8 - 48469x^6 + 39585x^4 - 12083x^2 + 43	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.4.5834302965409512291058019417402368.2	x^20 - 4x^19 + 9x^18 - 23x^17 - 73x^16 + 128x^15 - 67x^14 + 318x^13 + 1428x^12 + 2366x^11 + 4792x^10 + 8162x^9 + 13098x^8 + 17165x^7 + 17760x^6 + 25222x^5 + 32482x^4 + 30702x^3 + 20825x^2 + 9261x + 2401	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.8.5834302965409512291058019417402368.2	x^20 + 5x^18 - 46x^16 - 214x^14 + 624x^12 + 2642x^10 - 2143x^8 - 8949x^6 + 1584x^4 + 6536x^2 + 43	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.12.5834302965409512291058019417402368.3	x^20 - 4x^19 - 17x^18 + 69x^17 + 5x^16 - 227x^15 + 1228x^14 - 586x^13 - 4342x^12 - 622x^11 - 23958x^10 - 11581x^9 + 67699x^8 + 99646x^7 + 254736x^6 + 399520x^5 + 168164x^4 - 129423x^3 - 145395x^2 - 37560x + 311	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.16.5834302965409512291058019417402368.3	x^20 - 4x^19 - 24x^18 + 68x^17 + 299x^16 - 335x^15 - 2039x^14 - 396x^13 + 6349x^12 + 7150x^11 - 4637x^10 - 15385x^9 - 12748x^8 + 1428x^7 + 15704x^6 + 15177x^5 + 3975x^4 - 1592x^3 - 791x^2 - 22x + 1	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.4.5834302965409512291058019417402368.3	x^20 + 10x^18 - 317x^14 - 1329x^12 - 1828x^10 + 522x^8 + 3554x^6 + 2852x^4 + 645x^2 + 43	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.8.5834302965409512291058019417402368.3	x^20 + 22x^18 + 112x^16 - 320x^14 - 2581x^12 + 1949x^10 + 15379x^8 - 3714x^6 - 24436x^4 - 6880x^2 + 43	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.12.5834302965409512291058019417402368.4	x^20 + 4x^18 - 126x^16 - 334x^14 + 3071x^12 + 2798x^10 - 25562x^8 + 6176x^6 + 64282x^4 - 63726x^2 + 15523	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.8.5834302965409512291058019417402368.4	x^20 - 8x^19 + 14x^18 + 44x^17 - 159x^16 + 123x^15 - 277x^14 + 249x^13 + 3416x^12 - 4478x^11 - 8682x^10 + 6255x^9 + 18913x^8 + 6575x^7 - 32434x^6 - 20027x^5 + 24522x^4 + 16488x^3 - 3048x^2 - 3280x - 800	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.12.5834302965409512291058019417402368.5	x^20 - 15x^18 - 108x^16 + 1156x^14 + 3500x^12 - 10498x^10 + 1081x^8 + 4853x^6 - 1418x^4 - 172x^2 + 43	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.8.5834302965409512291058019417402368.5	x^20 + 18x^18 + 38x^16 - 710x^14 - 2589x^12 + 3163x^10 + 2443x^8 - 1950x^6 - 734x^4 + 258x^2 + 43	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.12.5834302965409512291058019417402368.6	x^20 - 4x^19 - 5x^18 + 13x^17 - 80x^16 + 399x^15 + 381x^14 - 2097x^13 - 44x^12 + 2179x^11 - 2220x^10 - 462x^9 + 8206x^8 - 1006x^7 - 6228x^6 - 6958x^5 + 6088x^4 + 5123x^3 - 2767x^2 - 567x + 49	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.8.5834302965409512291058019417402368.6	x^20 - 4x^19 + 3x^18 - 3x^17 - 175x^16 + 407x^15 - 757x^14 + 1536x^13 - 1806x^12 + 4873x^11 - 4798x^10 + 9558x^9 - 11525x^8 + 9281x^7 - 10351x^6 - 13435x^5 + 17591x^4 - 20279x^3 + 25882x^2 - 8661x - 829	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.12.5834302965409512291058019417402368.7	x^20 - 94x^16 + 322x^14 + 1064x^12 - 5502x^10 + 2121x^8 + 9198x^6 - 796x^4 - 1204x^2 + 43	\( 2^{10}\cdot 19^{10}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.4.9356679031996449225218910671863808.1	x^20 + 22x^18 + 196x^16 + 926x^14 + 2505x^12 + 3797x^10 + 2625x^8 - 322x^6 - 1456x^4 - 470x^2 + 83	\( 2^{20}\cdot 83\cdot 401^{10} \)	20T423	$[2]$ (GRH)
20.10.42725076543694629594674302947426304.1	x^20 - 12x^18 - 82x^16 + 534x^14 + 1835x^12 - 6705x^10 - 14401x^8 + 33006x^6 + 41290x^4 - 54900x^2 - 30699	\( -\,2^{20}\cdot 379\cdot 401^{10} \)	20T423	Trivial (GRH)
20.10.42725076543694629594674302947426304.2	x^20 + 12x^18 - 82x^16 - 534x^14 + 1835x^12 + 6705x^10 - 14401x^8 - 33006x^6 + 41290x^4 + 54900x^2 - 30699	\( -\,2^{20}\cdot 379\cdot 401^{10} \)	20T423	Trivial (GRH)
20.0.891364591638505108720553333523218432.1	x^20 + 32x^18 + 439x^16 + 3406x^14 + 16533x^12 + 52273x^10 + 108297x^8 + 143602x^6 + 114644x^4 + 48425x^2 + 7907	\( 2^{20}\cdot 401^{10}\cdot 7907 \)	20T423	$[2, 2604]$ (GRH)
20.20.891364591638505108720553333523218432.1	x^20 - 32x^18 + 439x^16 - 3406x^14 + 16533x^12 - 52273x^10 + 108297x^8 - 143602x^6 + 114644x^4 - 48425x^2 + 7907	\( 2^{20}\cdot 401^{10}\cdot 7907 \)	20T423	Trivial (GRH)
20.12.2106183370512833937071945009682254848.1	x^20 - 8x^19 - 5x^18 + 222x^17 - 574x^16 - 2030x^15 + 11793x^14 + 4334x^13 - 104402x^12 + 38920x^11 + 512568x^10 - 267232x^9 - 1454928x^8 + 576352x^7 + 2268740x^6 - 159284x^5 - 1691906x^4 - 756560x^3 + 346947x^2 + 508220x + 7775	\( 2^{10}\cdot 19^{12}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.8.2106183370512833937071945009682254848.1	x^20 - 4x^19 + 5x^18 - 81x^17 + 197x^16 + 814x^15 - 1548x^14 + 3573x^13 - 48227x^12 + 108760x^11 - 15946x^10 - 30992x^9 - 122359x^8 - 83236x^7 + 315447x^6 - 34374x^5 - 148930x^4 + 28599x^3 - 1163x^2 + 11642x - 953	\( 2^{10}\cdot 19^{12}\cdot 43^{11} \)	20T423	Trivial (GRH)
20.0.3547256202968983472963275805780639744.1	x^20 - 4x^19 + 31x^18 - 110x^17 + 345x^16 - 1180x^15 + 1885x^14 - 4747x^13 + 11112x^12 + 13337x^11 + 84784x^10 + 194067x^9 + 262887x^8 + 519267x^7 + 99143x^6 + 368252x^5 + 132457x^4 + 209487x^3 + 887494x^2 - 725088x + 1164241	\( 2^{15}\cdot 19^{11}\cdot 43^{11} \)	20T423	$[2, 1134]$ (GRH)
20.20.3547256202968983472963275805780639744.1	x^20 - 4x^19 - 49x^18 + 238x^17 + 698x^16 - 4834x^15 - 1026x^14 + 41062x^13 - 42369x^12 - 139914x^11 + 283437x^10 + 91048x^9 - 605673x^8 + 353964x^7 + 321800x^6 - 437006x^5 + 121081x^4 + 36702x^3 - 20724x^2 + 1528x + 83	\( 2^{15}\cdot 19^{11}\cdot 43^{11} \)	20T423	Trivial (GRH)