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 all 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.1.116234663759754077598636637937221632.1	x^21 + 12x^19 - 8x^18 + 108x^17 - 144x^16 + 642x^15 - 1188x^14 + 3222x^13 - 6656x^12 + 13527x^11 - 26370x^10 + 44193x^9 - 70452x^8 + 102702x^7 - 135604x^6 + 159192x^5 - 145872x^4 + 91808x^3 - 36288x^2 + 8064x - 768	\( 2^{14}\cdot 3^{17}\cdot 11^{9}\cdot 13^{12} \)	21T142	Trivial (GRH)
21.3.2353751941135020071372391918228738048.1	x^21 - 6x^19 - 4x^18 - 18x^17 - 24x^16 + 19x^15 + 54x^14 + 522x^13 + 1304x^12 + 1296x^11 + 576x^10 - 633x^9 - 2916x^8 - 13608x^7 - 45144x^6 - 83808x^5 - 91296x^4 - 60544x^3 - 24192x^2 - 5376x - 512	\( -\,2^{12}\cdot 3^{21}\cdot 11^{9}\cdot 13^{12} \)	21T142	Trivial (GRH)
21.3.2788191129777993959351061126655770624.1	x^21 - 4374x^7 - 20412x^6 - 40824x^5 - 45360x^4 - 30240x^3 - 12096x^2 - 2688x - 256	\( -\,2^{32}\cdot 3^{19}\cdot 7^{21} \)	21T142	Trivial (GRH)
21.1.36353874781068335688593663064000000000.1	x^21 + 63x^17 - 84x^16 + 28x^15 + 1134x^13 - 3024x^12 + 3024x^11 - 1344x^10 + 5327x^9 - 20412x^8 + 31833x^7 - 20034x^6 - 5292x^5 + 18648x^4 - 14672x^3 + 6048x^2 - 1344x + 128	\( 2^{12}\cdot 3^{19}\cdot 5^{9}\cdot 7^{22} \)	21T142	Trivial (GRH)
21.11.329274195048166752324572139831383256839602176.1	x^21 + 36x^19 - 24x^18 + 108x^17 - 144x^16 - 6648x^15 + 13392x^14 - 50400x^13 + 112576x^12 + 83808x^11 - 598848x^10 + 1555648x^9 - 3375360x^8 + 2618112x^7 + 6278144x^6 - 18828288x^5 + 22671360x^4 - 15421440x^3 + 6193152x^2 - 1376256x + 131072	\( -\,2^{14}\cdot 3^{21}\cdot 7^{12}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.9.6914758096011501798816014936459048393631645696.1	x^21 + 18x^19 - 12x^18 + 27x^17 - 36x^16 - 825x^15 + 1674x^14 - 3708x^13 + 7160x^12 - 837x^11 - 17178x^10 + 37423x^9 - 61740x^8 + 61404x^7 + 16048x^6 - 130896x^5 + 172800x^4 - 120000x^3 + 48384x^2 - 10752x + 1024	\( 2^{14}\cdot 3^{22}\cdot 7^{13}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.15.14817338777167503854605746292412246557782097920.1	x^21 - 24x^19 - 16x^18 + 135x^17 + 180x^16 + 573x^15 + 1026x^14 - 4500x^13 - 13672x^12 - 13581x^11 - 5334x^10 + 43067x^9 + 172764x^8 + 247614x^7 + 71204x^6 - 239976x^5 - 374256x^4 - 268384x^3 - 108864x^2 - 24192x - 2304	\( -\,2^{14}\cdot 3^{23}\cdot 5\cdot 7^{12}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.13.16463709752408337616228606991569162841980108800.1	x^21 - 3x^19 - 2x^18 - 108x^17 - 144x^16 + 195x^15 + 486x^14 + 3321x^13 + 8064x^12 + 1674x^11 - 17508x^10 - 42797x^9 - 79956x^8 - 97365x^7 - 40522x^6 + 56700x^5 + 101304x^4 + 74256x^3 + 30240x^2 + 6720x + 640	\( 2^{15}\cdot 3^{21}\cdot 5^{2}\cdot 7^{12}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.17.190320484737840382843602696822539522453290057728.1	x^21 - 45x^19 - 30x^18 + 756x^17 + 1008x^16 - 5361x^15 - 11394x^14 + 9009x^13 + 42592x^12 + 48168x^11 + 32640x^10 - 38489x^9 - 224676x^8 - 426999x^7 - 522910x^6 - 521964x^5 - 432216x^4 - 262224x^3 - 102816x^2 - 22848x - 2176	\( 2^{15}\cdot 3^{21}\cdot 7^{12}\cdot 17^{2}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.15.501566917607120005478404511998154545980924014592.1	x^21 - 48x^19 - 32x^18 + 540x^17 + 720x^16 + 4344x^15 + 8208x^14 - 77472x^13 - 219968x^12 - 213408x^11 - 72384x^10 + 2770880x^9 + 11033856x^8 + 13320192x^7 - 7201280x^6 - 38873088x^5 - 50079744x^4 - 34594816x^3 - 13934592x^2 - 3096576x - 294912	\( -\,2^{12}\cdot 3^{23}\cdot 7^{12}\cdot 173^{9}\cdot 677 \)	21T142	Trivial (GRH)
21.9.885089036289472230248449911866758194384850649088.1	x^21 + 57x^19 - 38x^18 + 945x^17 - 1260x^16 + 1149x^15 - 1458x^14 - 88857x^13 + 239328x^12 - 701973x^11 + 1647894x^10 - 1948325x^9 + 871524x^8 + 376527x^7 - 688030x^6 + 389772x^5 - 121176x^4 + 26064x^3 - 6048x^2 + 1344x - 128	\( 2^{21}\cdot 3^{22}\cdot 7^{13}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.17.889138920626346923563285121178114921239572119552.1	x^21 - 21x^19 - 63x^18 + 189x^17 + 1134x^16 - 825x^15 - 8505x^14 + 1035x^13 + 34584x^12 + 5697x^11 - 83313x^10 - 29457x^9 + 122310x^8 + 65853x^7 - 104151x^6 - 87480x^5 + 29556x^4 + 56976x^3 + 24192x^2 + 4032x + 192	\( 2^{33}\cdot 3^{39}\cdot 13^{15}\cdot 499 \)	21T142	Trivial (GRH)
21.15.1026340717997546749443792043684557504276540162048.1	x^21 - 27x^19 - 18x^18 + 216x^17 + 288x^16 - 66x^15 - 324x^14 - 3861x^13 - 9768x^12 - 4617x^11 + 12690x^10 + 37269x^9 + 76356x^8 + 100539x^7 + 60774x^6 - 15876x^5 - 55944x^4 - 44016x^3 - 18144x^2 - 4032x - 384	\( -\,2^{39}\cdot 3^{41}\cdot 13^{15} \)	21T142	Trivial (GRH)
21.13.1482492148218678638085477396433249728399446900736.1	x^21 - 6x^19 - 4x^18 - 81x^17 - 108x^16 + 342x^15 + 756x^14 + 2610x^13 + 5728x^12 - 216x^11 - 16944x^10 - 42271x^9 - 84348x^8 - 108792x^7 - 59304x^6 + 31968x^5 + 77472x^4 + 59008x^3 + 24192x^2 + 5376x + 512	\( 2^{39}\cdot 3^{39}\cdot 13^{16} \)	21T142	Trivial (GRH)
21.11.5170674349462897470243377350710078541633750155264.1	x^21 - 3x^19 - 2x^18 - 207x^17 - 276x^16 + 745x^15 + 1674x^14 + 7029x^13 + 16016x^12 - 999x^11 - 48882x^10 - 79184x^9 - 73008x^8 - 35757x^7 + 55086x^6 + 166428x^5 + 199512x^4 + 135568x^3 + 54432x^2 + 12096x + 1152	\( -\,2^{14}\cdot 3^{23}\cdot 13\cdot 31^{12}\cdot 41^{9} \)	21T142	Trivial (GRH)
21.13.7581538340984039472273273519617599488731840102400.1	x^21 - 6x^19 - 4x^18 - 432x^17 - 576x^16 + 1752x^15 + 3888x^14 + 50544x^13 + 128448x^12 - 74304x^11 - 617088x^10 - 1868864x^9 - 4518144x^8 - 5331840x^7 + 699136x^6 + 10160640x^5 + 13741056x^4 + 9590784x^3 + 3870720x^2 + 860160x + 81920	\( 2^{14}\cdot 3^{22}\cdot 5^{2}\cdot 7^{12}\cdot 173^{9}\cdot 307 \)	21T142	Trivial (GRH)
21.13.8830806594437225156672627375869213526379397644288.1	x^21 - 12x^19 - 8x^18 - 324x^17 - 432x^16 + 2880x^15 + 6048x^14 + 37728x^13 + 90752x^12 - 96768x^11 - 582144x^10 - 1895872x^9 - 4845312x^8 - 6218496x^7 - 1158144x^6 + 7271424x^5 + 10764288x^4 + 7647232x^3 + 3096576x^2 + 688128x + 65536	\( 2^{35}\cdot 3^{40}\cdot 7\cdot 13^{15}\cdot 59 \)	21T142	Trivial (GRH)
21.7.26496011938148351603082366412208086506763670519808.1	x^21 + 42x^19 - 28x^18 + 630x^17 - 840x^16 + 4060x^15 - 7560x^14 + 9576x^13 - 13216x^12 - 15120x^11 + 85344x^10 - 160888x^9 + 243936x^8 - 303414x^7 + 265916x^6 - 161784x^5 + 77616x^4 - 33824x^3 + 12096x^2 - 2688x + 256	\( -\,2^{32}\cdot 3^{22}\cdot 7^{15}\cdot 37\cdot 47^{9} \)	21T142	Trivial (GRH)
21.15.60489956066980411545343493574658607908298585800704.1	x^21 - 54x^19 - 36x^18 + 864x^17 + 1152x^16 - 912x^15 - 2592x^14 - 60048x^13 - 155904x^12 + 7776x^11 + 475200x^10 + 1694016x^9 + 4402944x^8 + 5853312x^7 + 1908480x^6 - 4935168x^5 - 7934976x^4 - 5720064x^3 - 2322432x^2 - 516096x - 49152	\( -\,2^{35}\cdot 3^{41}\cdot 13^{15}\cdot 23\cdot 41 \)	21T142	Trivial (GRH)
21.7.141295796391428497217987790912262400704772214620160.1	x^21 + 60x^19 - 40x^18 + 1386x^17 - 1848x^16 + 15898x^15 - 30564x^14 + 99351x^13 - 215128x^12 + 347166x^11 - 548820x^10 + 461451x^9 + 239796x^8 - 1359084x^7 + 2896288x^6 - 4396464x^5 + 4481856x^4 - 2917184x^3 + 1161216x^2 - 258048x + 24576	\( -\,2^{41}\cdot 3^{23}\cdot 5\cdot 7^{12}\cdot 31^{9}\cdot 373 \)	21T142	Trivial (GRH)
21.21.661001474699906019511835222071349858115923781431046144.1	x^21 - 87x^19 - 58x^18 + 3132x^17 + 4176x^16 - 58845x^15 - 120474x^14 + 584937x^13 + 1756160x^12 - 2422602x^11 - 13200252x^10 - 4585357x^9 + 43304940x^8 + 69983079x^7 - 5573938x^6 - 133907796x^5 - 183652200x^4 - 128551600x^3 - 51909984x^2 - 11535552x - 1098624	\( 2^{12}\cdot 3^{23}\cdot 7^{12}\cdot 109\cdot 173^{9}\cdot 2861^{2} \)	21T142	Trivial (GRH)
21.19.1246717509268840429748140354675211188979247111456423936.1	x^21 - 69x^19 - 46x^18 + 1944x^17 + 2592x^16 - 27918x^15 - 57564x^14 + 201627x^13 + 631480x^12 - 479007x^11 - 3445602x^10 - 2239627x^9 + 7429860x^8 + 14247297x^7 + 3841026x^6 - 15902028x^5 - 24390360x^4 - 17439440x^3 - 7070112x^2 - 1571136x - 149632	\( -\,2^{42}\cdot 3^{39}\cdot 7^{2}\cdot 13^{15}\cdot 167^{2} \)	21T142	Trivial (GRH)
21.21.24534552729185913337390664993026148677387683665478156288.1	x^21 - 90x^19 - 60x^18 + 3375x^17 + 4500x^16 - 66702x^15 - 136404x^14 + 709506x^13 + 2114304x^12 - 3312576x^11 - 17208288x^10 - 4169151x^9 + 63388548x^8 + 97143804x^7 - 23005920x^6 - 221306256x^5 - 295641792x^4 - 205821888x^3 - 83026944x^2 - 18450432x - 1757184	\( 2^{39}\cdot 3^{41}\cdot 7\cdot 11^{2}\cdot 13^{17}\cdot 167 \)	21T142	$[3]$ (GRH)
21.19.52483781054437666614504054423280523869246083235156328448.1	x^21 - 117x^19 - 78x^18 + 5481x^17 + 7308x^16 - 128865x^15 - 262602x^14 + 1530063x^13 + 4508112x^12 - 7197903x^11 - 37128834x^10 - 13019517x^9 + 120573468x^8 + 200437749x^7 + 9686586x^6 - 322807356x^5 - 455863032x^4 - 320959248x^3 - 129747744x^2 - 28832832x - 2745984	\( -\,2^{39}\cdot 3^{41}\cdot 13^{15}\cdot 7151^{2} \)	21T142	Trivial (GRH)