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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.7857627321843320792892969664512.1	x^21 + 3x^19 + 18x^17 - 54x^16 + 58x^15 - 90x^14 - 75x^13 + 288x^12 - 486x^11 + 1380x^10 - 1915x^9 + 2988x^8 - 3399x^7 + 1690x^6 - 2232x^5 - 384x^4 - 1344x^3 - 384x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 71^{9} \)	21T131	Trivial (GRH)
21.1.7857627321843320792892969664512.1	x^21 - 3x^19 - 2x^18 - 9x^17 - 12x^16 + 23x^15 + 54x^14 - 45x^13 - 208x^12 - 459x^11 - 906x^10 + 362x^9 + 5112x^8 + 11667x^7 + 18814x^6 + 24732x^5 + 23832x^4 + 15248x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 71^{9} \)	21T131	Trivial (GRH)
21.1.7857627321843320792892969664512.2	x^21 + 6x^19 - 2x^18 + 36x^17 + 18x^16 + 135x^15 + 18x^14 + 300x^13 + 448x^12 + 1620x^11 + 2160x^10 + 2722x^9 + 2538x^8 + 3087x^7 + 3382x^6 + 1944x^5 - 168x^4 - 608x^3 - 576x^2 - 192x - 128	\( 2^{14}\cdot 3^{21}\cdot 71^{9} \)	21T131	Trivial (GRH)
21.3.86433900540276528721822666309632.1	x^21 - 2x^18 - 18x^17 + 12x^16 + 93x^15 + 252x^14 + 756x^13 + 424x^12 - 846x^11 - 3942x^10 - 12420x^9 - 20592x^8 - 30729x^7 - 35272x^6 - 30168x^5 - 18600x^4 - 8512x^3 - 2880x^2 - 768x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 11\cdot 71^{9} \)	21T131	Trivial (GRH)
21.11.1214922588597965135114544770664959361024.1	x^21 - 21x^19 - 12x^18 + 189x^17 + 216x^16 - 925x^15 - 1620x^14 + 2535x^13 + 6616x^12 - 3303x^11 - 16212x^10 - 665x^9 + 24840x^8 + 9225x^7 - 23660x^6 - 14796x^5 + 12360x^4 + 11024x^3 - 2016x^2 - 3264x - 640	\( -\,2^{14}\cdot 3^{21}\cdot 577^{9} \)	21T131	Trivial (GRH)
21.11.6074612942989825675572723853324796805120.1	x^21 - 6x^19 - 4x^18 - 63x^17 - 84x^16 + 242x^15 + 540x^14 + 1413x^13 + 2888x^12 + 378x^11 - 6852x^10 - 11321x^9 - 10116x^8 - 5073x^7 + 5566x^6 + 18252x^5 + 22104x^4 + 15056x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 5\cdot 577^{9} \)	21T131	Trivial (GRH)
21.9.30373064714949128377863619266623984025600.1	x^21 + 15x^19 - 10x^18 + 18x^17 - 24x^16 - 532x^15 + 1080x^14 - 2502x^13 + 4912x^12 - 2322x^11 - 5988x^10 + 23570x^9 - 59688x^8 + 100815x^7 - 129110x^6 + 140940x^5 - 123768x^4 + 76752x^3 - 30240x^2 + 6720x - 640	\( 2^{14}\cdot 3^{21}\cdot 5^{2}\cdot 577^{9} \)	21T131	Trivial (GRH)
21.15.59531206841300291620612693762583008690176.1	x^21 - 27x^19 - 18x^18 + 234x^17 + 312x^16 - 436x^15 - 1080x^14 - 2502x^13 - 4912x^12 + 2538x^11 + 22188x^10 + 33506x^9 + 27432x^8 + 1611x^7 - 61842x^6 - 138564x^5 - 157608x^4 - 105712x^3 - 42336x^2 - 9408x - 896	\( -\,2^{14}\cdot 3^{21}\cdot 7^{2}\cdot 577^{9} \)	21T131	Trivial (GRH)
21.9.100838574853631106214507215965191626964992.1	x^21 - 21x^19 - 136x^18 + 189x^17 + 2448x^16 + 843x^15 - 18360x^14 - 23985x^13 + 63864x^12 + 155817x^11 - 50328x^10 - 452969x^9 - 318816x^8 + 499761x^7 + 907384x^6 + 232092x^5 - 609576x^4 - 663824x^3 - 249120x^2 - 8256x + 12416	\( 2^{14}\cdot 3^{21}\cdot 83\cdot 577^{9} \)	21T131	Trivial (GRH)
21.7.117847491094002618106110842754501058019328.1	x^21 + 36x^19 - 24x^18 + 477x^17 - 636x^16 + 2912x^15 - 5400x^14 + 7893x^13 - 12248x^12 - 3132x^11 + 43512x^10 - 108421x^9 + 221076x^8 - 313047x^7 + 275646x^6 - 152172x^5 + 57816x^4 - 19024x^3 + 6048x^2 - 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 97\cdot 577^{9} \)	21T131	Trivial (GRH)
21.13.185774792348382807570141316603039633686528.1	x^21 - 24x^19 - 16x^18 + 162x^17 + 216x^16 - 9x^15 - 162x^14 - 1890x^13 - 4776x^12 - 3780x^11 + 1128x^10 + 9800x^9 + 26208x^8 + 42027x^7 + 44894x^6 + 37692x^5 + 27288x^4 + 15632x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 1009^{9} \)	21T131	Trivial (GRH)
21.17.780359536423698568398593575601369133108096.1	x^21 - 21x^19 - 41x^18 + 189x^17 + 738x^16 - 1010x^15 - 5535x^14 + 3810x^13 + 22384x^12 - 10953x^11 - 52743x^10 + 23361x^9 + 72954x^8 - 34884x^7 - 55577x^6 + 34911x^5 + 15780x^4 - 18860x^3 + 5976x^2 - 768x + 32	\( 2^{7}\cdot 3^{21}\cdot 2029^{9} \)	21T131	Trivial (GRH)
21.19.1026609587365280539171790331211890660065280.1	x^21 - 96x^19 - 64x^18 + 3636x^17 + 4848x^16 - 67504x^15 - 138240x^14 + 598608x^13 + 1821568x^12 - 1579392x^11 - 10586112x^10 - 8211520x^9 + 17296128x^8 + 38704512x^7 + 23209216x^6 - 13644288x^5 - 32320512x^4 - 24557568x^3 - 10063872x^2 - 2236416x - 212992	\( -\,2^{14}\cdot 3^{21}\cdot 5\cdot 13^{2}\cdot 577^{9} \)	21T131	Trivial (GRH)
21.15.1315969325517029136527144953243469517078528.1	x^21 - 27x^19 - 18x^18 + 171x^17 + 228x^16 + 1129x^15 + 2106x^14 - 14553x^13 - 42240x^12 + 16497x^11 + 177918x^10 + 192220x^9 - 93312x^8 - 395361x^7 - 420282x^6 - 259956x^5 - 121032x^4 - 51248x^3 - 18144x^2 - 4032x - 384	\( -\,2^{14}\cdot 3^{19}\cdot 1601^{9} \)	21T131	Trivial (GRH)
21.17.1437253422311392754840506463696646924091392.1	x^21 - 48x^19 - 32x^18 + 909x^17 + 1212x^16 - 8236x^15 - 17280x^14 + 31653x^13 + 112568x^12 + 8208x^11 - 305232x^10 - 359509x^9 + 111852x^8 + 580389x^7 + 488282x^6 + 52164x^5 - 210168x^4 - 187152x^3 - 78624x^2 - 17472x - 1664	\( 2^{14}\cdot 3^{21}\cdot 7\cdot 13^{2}\cdot 577^{9} \)	21T131	Trivial (GRH)
21.13.9211785278619203955690014672704286619549696.1	x^21 - 6x^19 - 4x^18 - 126x^17 - 168x^16 + 862x^15 + 1836x^14 + 1548x^13 + 1136x^12 - 8370x^11 - 30396x^10 - 35873x^9 - 6948x^8 + 27087x^7 + 39230x^6 + 35532x^5 + 26712x^4 + 15568x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{19}\cdot 7\cdot 1601^{9} \)	21T131	Trivial (GRH)
21.15.199772041324466833510039955353950498075672576.1	x^21 - 21x^19 - 4x^18 + 189x^17 + 72x^16 - 1045x^15 - 540x^14 + 4335x^13 + 1944x^12 - 14103x^11 - 2268x^10 + 32519x^9 - 5832x^8 - 46431x^7 + 21084x^6 + 35532x^5 - 21528x^4 - 11616x^3 + 6048x^2 + 1152x - 512	\( -\,2^{15}\cdot 3^{21}\cdot 2029^{9} \)	21T131	Trivial (GRH)
21.15.20348294776519408952081501076010566466441494528.1	x^21 - 48x^19 - 32x^18 + 846x^17 + 1128x^16 - 6266x^15 - 13284x^14 + 12042x^13 + 53760x^12 + 51354x^11 + 10188x^10 - 87483x^9 - 301644x^8 - 426411x^7 - 152694x^6 + 337284x^5 + 555336x^4 + 401904x^3 + 163296x^2 + 36288x + 3456	\( -\,2^{14}\cdot 3^{36}\cdot 587^{9} \)	21T131	Trivial (GRH)
21.21.38980223886316836110432070474377320562433441792.1	x^21 - 69x^19 - 46x^18 + 1962x^17 + 2616x^16 - 28828x^15 - 59400x^14 + 217818x^13 + 677648x^12 - 584442x^11 - 3931212x^10 - 2306846x^9 + 9397224x^8 + 17247063x^7 + 3299494x^6 - 22317012x^5 - 33030216x^4 - 23464624x^3 - 9501408x^2 - 2111424x - 201088	\( 2^{14}\cdot 3^{21}\cdot 13\cdot 577^{9}\cdot 1571^{2} \)	21T131	Trivial (GRH)
21.7.48616921823410934076113073180784620976351592448.1	x^21 + 57x^19 - 38x^18 + 1314x^17 - 1752x^16 + 16244x^15 - 31320x^14 + 122778x^13 - 276368x^12 + 619218x^11 - 1279068x^10 + 2090866x^9 - 3134952x^8 + 4064259x^7 - 4154782x^6 + 3539484x^5 - 2615832x^4 + 1512848x^3 - 586656x^2 + 130368x - 12416	\( -\,2^{14}\cdot 3^{21}\cdot 97^{2}\cdot 577^{9}\cdot 4253 \)	21T131	Trivial (GRH)
21.19.1146287272410593370967257893948595244276204191744.1	x^21 - 69x^19 - 46x^18 + 1899x^17 + 2532x^16 - 25913x^15 - 53514x^14 + 169821x^13 + 540064x^12 - 294975x^11 - 2566338x^10 - 2052556x^9 + 4115808x^8 + 9081111x^7 + 4512310x^6 - 5450004x^5 - 10192392x^4 - 7520688x^3 - 3066336x^2 - 681408x - 64896	\( -\,2^{14}\cdot 3^{35}\cdot 13^{2}\cdot 587^{9} \)	21T131	Trivial (GRH)
21.21.2414563091823149581136287358490706306288929226752.1	x^21 - 66x^19 - 44x^18 + 1782x^17 + 2376x^16 - 24669x^15 - 50922x^14 + 173574x^13 + 545848x^12 - 410832x^11 - 2968128x^10 - 1876656x^9 + 6614208x^8 + 12455691x^7 + 2810462x^6 - 15172164x^5 - 22782312x^4 - 16227568x^3 - 6574176x^2 - 1460928x - 139136	\( 2^{14}\cdot 3^{21}\cdot 11\cdot 1009^{9}\cdot 1087^{2} \)	21T131	Trivial (GRH)