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 13 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.5.1387347928027439932553142925836288.1	x^21 - 6x^19 - 4x^18 - 9x^17 - 12x^16 + 104x^15 + 216x^14 + 144x^13 + 32x^12 - 729x^11 - 2430x^10 - 3969x^9 - 5076x^8 - 3393x^7 + 5790x^6 + 18252x^5 + 22104x^4 + 15056x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 109^{6} \)	21T136	Trivial (GRH)
21.7.91178360615058506586326215629471744.1	x^21 - 9x^19 - 6x^18 + 27x^17 + 36x^16 - 15x^15 - 54x^14 - 441x^13 - 1088x^12 + 135x^11 + 3570x^10 + 7507x^9 + 12348x^8 + 13593x^7 + 2914x^6 - 13932x^5 - 20952x^4 - 14928x^3 - 6048x^2 - 1344x - 128	\( -\,2^{33}\cdot 3^{21}\cdot 317^{6} \)	21T136	Trivial (GRH)
21.5.8701446204588103256973312430845198336.1	x^21 + 6x^19 - 16x^18 - 36x^17 - 144x^16 - 390x^15 - 270x^14 - 2019x^13 - 784x^12 - 9594x^11 - 2886x^10 - 15678x^9 + 10368x^8 + 15135x^7 + 33164x^6 + 52632x^5 + 28944x^4 + 22256x^3 + 12096x^2 + 5376x + 896	\( 2^{21}\cdot 3^{21}\cdot 7^{2}\cdot 13^{6}\cdot 109^{6} \)	21T136	Trivial (GRH)
21.9.13096950897107618944566483939232950779904.1	x^21 - 51x^19 - 34x^18 + 1107x^17 + 1476x^16 - 12765x^15 - 26514x^14 + 76527x^13 + 247280x^12 - 142695x^11 - 1201362x^10 - 843421x^9 + 2387484x^8 + 4706427x^7 + 1346134x^6 - 5103108x^5 - 7893576x^4 - 5652464x^3 - 2292192x^2 - 509376x - 48512	\( 2^{33}\cdot 3^{21}\cdot 317^{6}\cdot 379^{2} \)	21T136	Trivial (GRH)
21.3.14978582190038884880930805105486631888339.1	x^21 - 3x^20 - 5x^19 - 43x^18 + 287x^17 - 286x^16 + 309x^15 - 5832x^14 + 14849x^13 + 23772x^12 - 100540x^11 + 251238x^10 - 954894x^9 - 83566x^8 + 3314973x^7 + 1174509x^6 + 5584313x^5 - 34579327x^4 - 21371158x^3 + 98029199x^2 + 27253836x - 127427549	\( -\,7^{3}\cdot 13^{7}\cdot 109^{6}\cdot 644179747^{2} \)	21T136	$[3]$ (GRH)
21.7.528430645588489921205792011738671012618729507.1	x^21 - 10x^20 - 71x^19 + 1071x^18 + 520x^17 - 46776x^16 + 103735x^15 + 989586x^14 - 4517658x^13 - 7586285x^12 + 82754841x^11 - 79517644x^10 - 682235084x^9 + 2028465624x^8 + 866153091x^7 - 13441984314x^6 + 21009463100x^5 + 13056475367x^4 - 88309703262x^3 + 131356776913x^2 - 91887618149x + 26232068501	\( -\,3^{5}\cdot 421^{2}\cdot 2741^{6}\cdot 170091127^{2} \)	21T136	$[3]$ (GRH)
21.9.669989641990779134661554841839710781441002093.1	x^21 - 8x^20 - 44x^19 + 177x^18 + 930x^17 + 13477x^16 - 123876x^15 - 187878x^14 + 6288822x^13 - 11318947x^12 - 109350935x^11 + 301750779x^10 + 715568742x^9 - 1607781301x^8 + 156769574x^7 - 6541085155x^6 - 34174260492x^5 - 24325229292x^4 + 54837372042x^3 - 11194152858x^2 - 181242408040x + 76054217719	\( 7^{4}\cdot 13^{7}\cdot 109^{6}\cdot 307^{2}\cdot 167732941^{2} \)	21T136	Trivial (GRH)
21.7.6157833349011271592152423961007508818954041688064.1	x^21 - 3x^20 - 68x^19 + 120x^18 + 2168x^17 - 1012x^16 - 39719x^15 - 28995x^14 + 416063x^13 + 787937x^12 - 2030115x^11 - 7492247x^10 - 1407263x^9 + 25538455x^8 + 48627612x^7 + 35727432x^6 - 39940417x^5 - 222181433x^4 - 460960453x^3 - 615417925x^2 - 623609988x - 374722982	\( -\,2^{26}\cdot 4457^{6}\cdot 3421339093^{2} \)	21T136	$[3]$ (GRH)
21.15.248963880921721405280252120945881577616987438186496.1	x^21 - 10x^20 - 137x^19 + 1872x^18 + 3512x^17 - 125638x^16 + 254464x^15 + 3804068x^14 - 18436401x^13 - 41021470x^12 + 471129383x^11 - 504783236x^10 - 5179107104x^9 + 17759404554x^8 + 7828934422x^7 - 152839367696x^6 + 283190814248x^5 + 156238042640x^4 - 1431442633860x^3 + 2489193126240x^2 - 2022049207736x + 669652484632	\( -\,2^{22}\cdot 19^{2}\cdot 37^{4}\cdot 4129^{6}\cdot 4207717^{2} \)	21T136	Trivial (GRH)
21.13.548703534888016451766579057903649447556780593774592.1	x^21 - 4x^20 - 119x^19 + 594x^18 + 5185x^17 - 34100x^16 - 85945x^15 + 948642x^14 - 328631x^13 - 12572436x^12 + 28717465x^11 + 49351730x^10 - 303320137x^9 + 413424460x^8 + 453601517x^7 - 2810189586x^6 + 5024882686x^5 - 3804363432x^4 - 428469094x^3 + 3845381132x^2 - 4627265616x + 2209117384	\( 2^{37}\cdot 809^{6}\cdot 3391^{2}\cdot 35191729^{2} \)	21T136	$[3]$ (GRH)
21.15.6794371816936220522300136015552507232390662697517056.1	x^21 - 5x^20 - 147x^19 + 855x^18 + 8313x^17 - 59101x^16 - 213419x^15 + 2133399x^14 + 1553594x^13 - 42723266x^12 + 42772372x^11 + 449457876x^10 - 1079884938x^9 - 1761084678x^8 + 8758478200x^7 - 5404777968x^6 - 17906984544x^5 + 38312104852x^4 - 48599758344x^3 + 67992573696x^2 - 64614140288x + 23767712416	\( -\,2^{22}\cdot 4129^{6}\cdot 571755108853^{2} \)	21T136	$[3]$ (GRH)
21.21.3774397644894044347142955656438221553789875050264299307008.1	x^21 - 8x^20 - 220x^19 + 1884x^18 + 17660x^17 - 160612x^16 - 676136x^15 + 6150204x^14 + 16330229x^13 - 110645300x^12 - 335529492x^11 + 831687320x^10 + 4351522002x^9 + 2422126064x^8 - 19214679456x^7 - 56774917712x^6 - 80223794180x^5 - 68940926608x^4 - 37807761952x^3 - 12977116160x^2 - 2548044728x - 218815936	\( 2^{43}\cdot 61^{2}\cdot 157^{2}\cdot 163^{2}\cdot 809^{6}\cdot 1987^{2}\cdot 12613^{2} \)	21T136	$[3]$ (GRH)
21.21.103824735093241618527929042484657707192669185678662729728000.1	x^21 - 7x^20 - 272x^19 + 1288x^18 + 31411x^17 - 79101x^16 - 1977903x^15 + 1081747x^14 + 72271854x^13 + 83688934x^12 - 1473025353x^11 - 4114370323x^10 + 13215711831x^9 + 71791433797x^8 + 25816033011x^7 - 438197404399x^6 - 1026938609748x^5 - 471523044618x^4 + 1452614355659x^3 + 2619148572733x^2 + 1750594810270x + 436671618380	\( 2^{18}\cdot 5^{3}\cdot 7^{2}\cdot 97^{2}\cdot 7607^{6}\cdot 188328230263^{2} \)	21T136	$[3]$ (GRH)