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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.1078228439505013455412874919936.1	x^21 - 6x^19 - 6x^18 + 36x^17 + 30x^16 - 138x^15 - 36x^14 + 447x^13 - 10x^12 - 1071x^11 + 888x^10 + 1111x^9 - 3042x^8 + 993x^7 + 2302x^6 - 1764x^5 + 648x^4 - 800x^3 + 864x^2 - 576x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 184607^{3} \)	21T152	$[2]$ (GRH)
21.3.1078228439505013455412874919936.2	x^21 - 3x^19 - 2x^18 - 9x^17 - 12x^16 - 4x^15 + 81x^13 + 216x^12 + 459x^11 + 906x^10 + 367x^9 - 2196x^8 - 6807x^7 - 14494x^6 - 22572x^5 - 23256x^4 - 15184x^3 - 6048x^2 - 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 184607^{3} \)	21T152	Trivial (GRH)
21.1.1078228439505013455412874919936.1	x^21 - 3x^19 - 2x^18 - 9x^17 - 12x^16 + 23x^15 + 54x^14 + 36x^13 + 8x^12 - 243x^11 - 810x^10 - 351x^9 + 2196x^8 + 6807x^7 + 14494x^6 + 22572x^5 + 23256x^4 + 15184x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 184607^{3} \)	21T152	Trivial (GRH)
21.1.1078228439505013455412874919936.2	x^21 + 3x^19 - 2x^18 - 27x^17 + 12x^16 - 27x^15 - 36x^14 + 381x^13 - 192x^12 - 27x^11 + 198x^10 - 1026x^9 - 954x^8 + 2655x^7 + 98x^6 - 1116x^5 + 480x^4 + 368x^3 - 288x^2 - 192x + 128	\( 2^{14}\cdot 3^{21}\cdot 184607^{3} \)	21T152	Trivial (GRH)
21.5.9333296606842651868186378354688.1	x^21 - 21x^19 - 16x^18 + 189x^17 + 288x^16 - 841x^15 - 2160x^14 + 1275x^13 + 8272x^12 + 4257x^11 - 15024x^10 - 22193x^9 + 3456x^8 + 32877x^7 + 27088x^6 - 4104x^5 - 23856x^4 - 20464x^3 - 8928x^2 - 2112x - 128	\( 2^{14}\cdot 3^{15}\cdot 71^{3}\cdot 173\cdot 8623^{3} \)	21T152	Trivial (GRH)
21.5.39329325008024816253802715725824.1	x^21 - 21x^19 + 189x^17 - 961x^15 + 3075x^13 - 6543x^11 + 9503x^9 - 9387x^7 - 32x^6 + 6048x^5 + 192x^4 - 2352x^3 - 288x^2 + 576x + 128	\( 2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 8623^{3} \)	21T152	Trivial (GRH)
21.7.39394113610756286924826653933568.1	x^21 + 3x^19 - 36x^16 + 51x^15 - 108x^14 - 210x^13 + 1028x^12 - 1872x^11 + 2298x^10 - 147x^9 - 2556x^8 + 3279x^7 - 2508x^6 - 828x^5 + 1272x^4 + 432x^3 + 288x^2 - 192x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 593^{3}\cdot 1033^{3} \)	21T152	Trivial (GRH)
21.7.39394113610756286924826653933568.2	x^21 - 21x^19 - 2x^18 + 189x^17 + 36x^16 - 957x^15 - 270x^14 + 3015x^13 + 1112x^12 - 6183x^11 - 2814x^10 + 8375x^9 + 4644x^8 - 7335x^7 - 5074x^6 + 3780x^5 + 3552x^4 - 864x^3 - 1440x^2 + 128	\( -\,2^{14}\cdot 3^{21}\cdot 593^{3}\cdot 1033^{3} \)	21T152	Trivial (GRH)
21.3.1615158658041007763917892811276288.1	x^21 - 8x^18 - 30x^16 + 89x^15 + 144x^14 + 63x^13 + 64x^12 - 1053x^11 - 810x^10 - 1624x^9 + 144x^8 + 735x^7 + 1794x^6 - 2412x^5 - 936x^4 - 1104x^3 + 288x^2 + 384x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 41\cdot 593^{3}\cdot 1033^{3} \)	21T152	Trivial (GRH)
21.11.2103209751169770458112224890011648.1	x^21 - 21x^19 - 14x^18 + 162x^17 + 216x^16 - 495x^15 - 1134x^14 + 54x^13 + 1992x^12 + 2889x^11 + 3390x^10 - 974x^9 - 15336x^8 - 26253x^7 - 15618x^6 + 7452x^5 + 19224x^4 + 14736x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 107^{3}\cdot 21557^{3} \)	21T152	Trivial (GRH)
21.9.2103209751169770458112224890011648.1	x^21 - 27x^17 - 36x^16 - 39x^15 - 54x^14 + 45x^13 + 208x^12 + 945x^11 + 2526x^10 + 3985x^9 + 5076x^8 + 3393x^7 - 5790x^6 - 18252x^5 - 22104x^4 - 15056x^3 - 6048x^2 - 1344x - 128	\( 2^{14}\cdot 3^{21}\cdot 107^{3}\cdot 21557^{3} \)	21T152	Trivial (GRH)
21.3.2118310801102976905027679213666304.1	x^21 + 15x^19 - 10x^18 + 99x^17 - 132x^16 + 449x^15 - 810x^14 + 1512x^13 - 2712x^12 + 3564x^11 - 4392x^10 + 4512x^9 - 2880x^8 - 1227x^7 + 10078x^6 - 20412x^5 + 22680x^4 - 15120x^3 + 6048x^2 - 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 47\cdot 59^{3}\cdot 10859^{3} \)	21T152	Trivial (GRH)
21.11.2279162600361785110437461456142336.1	x^21 - 21x^19 - 16x^18 + 189x^17 + 288x^16 - 873x^15 - 2160x^14 + 1755x^13 + 8584x^12 + 1377x^11 - 18768x^10 - 14529x^9 + 20304x^8 + 28701x^7 - 5168x^6 - 22680x^5 - 7224x^4 + 4800x^3 + 4032x^2 + 1152x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 239^{3}\cdot 431^{3} \)	21T152	Trivial (GRH)
21.9.2279162600361785110437461456142336.1	x^21 - 3x^19 - 2x^18 - 45x^17 + 6x^16 + 57x^15 - 18x^14 + 384x^13 - 82x^12 - 369x^11 - 114x^10 - 235x^9 + 1422x^8 + 3867x^7 + 1160x^6 - 3312x^5 - 1512x^4 + 112x^3 + 288x^2 + 384x - 128	\( 2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 239^{3}\cdot 431^{3} \)	21T152	Trivial (GRH)
21.7.3071123628635589927498516790591488.1	x^21 - 3x^19 - 2x^18 - 27x^17 - 36x^16 + 96x^15 + 216x^14 + 225x^13 + 248x^12 - 999x^11 - 3954x^10 - 4655x^9 - 684x^8 + 5847x^7 + 14366x^6 + 22572x^5 + 23256x^4 + 15184x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 61^{3}\cdot 42899^{3} \)	21T152	Trivial (GRH)
21.9.13025357904654475011765942398926848.1	x^21 - 30x^19 - 34x^18 + 387x^17 + 954x^16 - 2237x^15 - 10944x^14 - 525x^13 + 63996x^12 + 83790x^11 - 181800x^10 - 495124x^9 + 82314x^8 + 1330701x^7 + 810842x^6 - 1778580x^5 - 1822800x^4 + 1114720x^3 + 1473696x^2 - 332928x - 341632	\( 2^{14}\cdot 3^{21}\cdot 17^{2}\cdot 59^{3}\cdot 10859^{3} \)	21T152	Trivial (GRH)
21.7.35754565769886097787907823130198016.1	x^21 - 21x^19 - 10x^18 + 189x^17 + 180x^16 - 945x^15 - 1350x^14 + 2835x^13 + 5704x^12 - 5103x^11 - 15798x^10 + 4015x^9 + 30996x^8 + 7605x^7 - 39738x^6 - 29376x^5 + 22320x^4 + 33088x^3 + 3456x^2 - 11136x - 4736	\( -\,2^{14}\cdot 3^{21}\cdot 17\cdot 107^{3}\cdot 21557^{3} \)	21T152	Trivial (GRH)
21.5.52420739808321057540061613491273728.1	x^21 - 4x^18 - 36x^17 + 12x^16 - 32x^15 + 198x^14 - 45x^13 + 328x^12 - 1395x^11 - 120x^10 - 551x^9 + 3384x^8 + 135x^7 + 868x^6 - 5328x^5 - 2856x^4 + 1248x^3 + 1152x^2 - 128	\( 2^{14}\cdot 3^{21}\cdot 23^{4}\cdot 239^{3}\cdot 431^{3} \)	21T152	Trivial (GRH)
21.5.77818760793281506950152320930430976.1	x^21 + 21x^19 - 14x^18 + 162x^17 - 216x^16 + 585x^15 - 1026x^14 + 846x^13 - 584x^12 - 1755x^11 + 7098x^10 - 11146x^9 + 12312x^8 - 9693x^7 - 1278x^6 + 16092x^5 - 21528x^4 + 14992x^3 - 6048x^2 + 1344x - 128	\( 2^{14}\cdot 3^{21}\cdot 37\cdot 107^{3}\cdot 21557^{3} \)	21T152	Trivial (GRH)
21.11.1398884674421463279959586376937816064.1	x^21 - 3x^19 - 2x^18 - 54x^17 - 72x^16 + 111x^15 + 270x^14 + 828x^13 + 1768x^12 + 513x^11 - 3282x^10 - 6730x^9 - 9432x^8 - 8733x^7 + 1406x^6 + 16092x^5 + 21528x^4 + 14992x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.15.1398884674421463279959586376937816064.1	x^21 - 24x^19 - 16x^18 + 189x^17 + 252x^16 - 321x^15 - 810x^14 - 1917x^13 - 3792x^12 + 2403x^11 + 18618x^10 + 23083x^9 + 3420x^8 - 20487x^7 - 31006x^6 - 31212x^5 - 25560x^4 - 15440x^3 - 6048x^2 - 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.11.1398884674421463279959586376937816064.2	x^21 - 3x^19 - 2x^18 - 54x^17 - 72x^16 + 84x^15 + 216x^14 + 954x^13 + 2192x^12 + 1188x^11 - 2280x^10 - 7076x^9 - 14544x^8 - 18213x^7 - 7202x^6 + 11772x^5 + 20376x^4 + 14864x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.15.1398884674421463279959586376937816064.2	x^21 - 24x^19 - 16x^18 + 189x^17 + 252x^16 - 348x^15 - 864x^14 - 1467x^13 - 2504x^12 + 1026x^11 + 10284x^10 + 15673x^9 + 12996x^8 + 6033x^7 - 5438x^6 - 18252x^5 - 22104x^4 - 15056x^3 - 6048x^2 - 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.17.1398884674421463279959586376937816064.1	x^21 - 18x^19 - 16x^18 + 36x^17 + 300x^16 + 1080x^15 - 990x^14 - 9240x^13 - 8424x^12 + 32616x^11 + 61062x^10 - 62433x^9 - 127386x^8 + 78735x^7 + 98312x^6 - 51048x^5 - 27456x^4 + 14400x^3 + 1728x^2 - 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.9.1750980878682272844435550706829410304.1	x^21 - 15x^19 - 22x^18 + 27x^17 + 168x^16 + 105x^15 - 54x^14 - 1014x^13 + 1890x^12 + 13563x^11 - 25146x^10 + 13781x^9 + 77688x^8 - 265965x^7 - 246390x^6 + 126756x^5 - 76728x^4 - 22336x^3 + 60768x^2 - 40512x + 27008	\( 2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 211^{2}\cdot 8623^{3} \)	21T152	Trivial (GRH)
21.13.2730915542462327937504442529336180736.1	x^21 - 6x^19 - 4x^18 - 45x^17 - 60x^16 + 223x^15 + 486x^14 + 891x^13 + 1584x^12 - 918x^11 - 7428x^10 - 12146x^9 - 13032x^8 - 9933x^7 + 1246x^6 + 16092x^5 + 21528x^4 + 14992x^3 + 6048x^2 + 1344x + 128	\( 2^{14}\cdot 3^{24}\cdot 8388019^{3} \)	21T152	Trivial (GRH)
21.13.4645990340334022941969904782035730432.1	x^21 - 42x^19 - 28x^18 + 729x^17 + 972x^16 - 6453x^15 - 13554x^14 + 27333x^13 + 94976x^12 - 14553x^11 - 328686x^10 - 312847x^9 + 372276x^8 + 958311x^7 + 546750x^6 - 438804x^5 - 927144x^4 - 695216x^3 - 284256x^2 - 63168x - 6016	\( 2^{14}\cdot 3^{21}\cdot 47^{2}\cdot 107^{3}\cdot 21557^{3} \)	21T152	Trivial (GRH)
21.9.9792192720950242959717104638564712448.1	x^21 + 18x^19 - 12x^18 + 81x^17 - 108x^16 - 99x^15 + 270x^14 - 1557x^13 + 3712x^12 - 4887x^11 + 5682x^10 - 3485x^9 - 5148x^8 + 15567x^7 - 23006x^6 + 26892x^5 - 24408x^4 + 15312x^3 - 6048x^2 + 1344x - 128	\( 2^{14}\cdot 3^{21}\cdot 7\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.13.23781039465164875759312968407942873088.1	x^21 - 21x^19 - 10x^18 + 189x^17 + 180x^16 - 929x^15 - 1350x^14 + 2595x^13 + 5496x^12 - 3663x^11 - 13302x^10 + 495x^9 + 19764x^8 + 6885x^7 - 17594x^6 - 11664x^5 + 7392x^4 + 8032x^3 + 576x^2 - 768x - 128	\( 2^{14}\cdot 3^{21}\cdot 17\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.13.101589114585925847727528969484632342528.1	x^21 - 60x^19 - 8x^18 + 1224x^17 + 192x^16 - 10767x^15 - 4410x^14 + 45264x^13 + 54600x^12 - 156366x^11 - 233310x^10 + 726860x^9 + 270576x^8 - 2019843x^7 - 331208x^6 + 2676384x^5 + 103680x^4 - 922000x^3 + 242208x^2 - 161472x - 107648	\( 2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 29^{2}\cdot 53\cdot 239^{3}\cdot 431^{3} \)	21T152	Trivial (GRH)
21.9.144085121465410717835837396824595054592.1	x^21 - 21x^19 - 20x^18 + 189x^17 + 360x^16 - 809x^15 - 2700x^14 + 795x^13 + 10496x^12 + 7137x^11 - 20652x^10 - 32065x^9 + 12744x^8 + 56925x^7 + 21196x^6 - 45144x^5 - 42288x^4 + 8320x^3 + 26496x^2 + 11328x + 896	\( 2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 103\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.17.740009992768954075098621193400104697856.1	x^21 - 24x^19 - 16x^18 + 117x^17 + 156x^16 + 889x^15 + 1674x^14 - 8037x^13 - 24160x^12 + 135x^11 + 70962x^10 + 105085x^9 + 63972x^8 - 40641x^7 - 244466x^6 - 475956x^5 - 523368x^4 - 347952x^3 - 139104x^2 - 30912x - 2944	\( 2^{14}\cdot 3^{21}\cdot 23^{2}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.19.1459036715421586200997848591146142154752.1	x^21 - 51x^19 - 28x^18 + 900x^17 + 792x^16 - 7128x^15 - 8658x^14 + 26442x^13 + 50482x^12 - 37872x^11 - 167574x^10 - 9596x^9 + 289188x^8 + 73785x^7 - 233564x^6 - 52848x^5 + 82296x^4 + 13584x^3 - 10656x^2 - 1152x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 7\cdot 71^{3}\cdot 149\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.7.8282866840288240634450974191476636172288.1	x^21 + 36x^19 - 24x^18 + 495x^17 - 660x^16 + 3433x^15 - 6426x^14 + 13923x^13 - 26656x^12 + 35424x^11 - 43824x^10 + 40730x^9 - 11304x^8 - 26121x^7 + 55258x^6 - 74196x^5 + 71496x^4 - 45744x^3 + 18144x^2 - 4032x + 384	\( -\,2^{14}\cdot 3^{26}\cdot 337\cdot 8388019^{3} \)	21T152	Trivial (GRH)
21.7.37494305928518480292756793661064283963392.1	x^21 + 39x^19 - 26x^18 + 594x^17 - 792x^16 + 4692x^15 - 8856x^14 + 22266x^13 - 44944x^12 + 68904x^11 - 103632x^10 + 118468x^9 - 86544x^8 + 29091x^7 + 50834x^6 - 134244x^5 + 156456x^4 - 105584x^3 + 42336x^2 - 9408x + 896	\( -\,2^{14}\cdot 3^{21}\cdot 7^{2}\cdot 71^{3}\cdot 547\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.15.112907939754257152540470809754816990560256.1	x^21 - 63x^19 - 42x^18 + 1665x^17 + 2220x^16 - 23155x^15 - 47790x^14 + 168858x^13 + 528168x^12 - 449145x^11 - 3043422x^10 - 1732173x^9 + 7496316x^8 + 13524411x^7 + 1957846x^6 - 18965124x^5 - 27585864x^4 - 19533296x^3 - 7904736x^2 - 1756608x - 167296	\( -\,2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 29\cdot 239^{3}\cdot 431^{3}\cdot 1307^{2} \)	21T152	Trivial (GRH)
21.15.235348967144551450795023528306489080070144.1	x^21 - 63x^19 - 42x^18 + 1674x^17 + 2232x^16 - 23583x^15 - 48654x^14 + 176382x^13 + 549640x^12 - 500931x^11 - 3278442x^10 - 1739618x^9 + 8547336x^8 + 15049899x^7 + 1418766x^6 - 22842756x^5 - 32687784x^4 - 23073776x^3 - 9332064x^2 - 2073792x - 197504	\( -\,2^{14}\cdot 3^{21}\cdot 47\cdot 107^{3}\cdot 1543^{2}\cdot 21557^{3} \)	21T152	Trivial (GRH)
21.19.994744179088530338219805704638291841630208.1	x^21 - 96x^19 - 64x^18 + 3708x^17 + 4944x^16 - 72008x^15 - 147312x^14 + 698832x^13 + 2103616x^12 - 2446848x^11 - 14296320x^10 - 7753344x^9 + 36094464x^8 + 66183552x^7 + 16767744x^6 - 75575808x^5 - 115024896x^4 - 82130944x^3 - 33288192x^2 - 7397376x - 704512	\( -\,2^{14}\cdot 3^{24}\cdot 43^{2}\cdot 197\cdot 8388019^{3} \)	21T152	Trivial (GRH)
21.21.65517556894139629686586965049358339099148288.1	x^21 - 66x^19 - 44x^18 + 1809x^17 + 2412x^16 - 25818x^15 - 53244x^14 + 191061x^13 + 596264x^12 - 507816x^11 - 3438048x^10 - 1989347x^9 + 8337204x^8 + 15167451x^7 + 2522086x^6 - 20511684x^5 - 30066696x^4 - 21320944x^3 - 8630496x^2 - 1917888x - 182656	\( 2^{14}\cdot 3^{21}\cdot 23\cdot 71^{3}\cdot 1427^{2}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.21.93620997925765436584656964317628337389092864.1	x^21 - 66x^19 - 44x^18 + 1809x^17 + 2412x^16 - 25818x^15 - 53244x^14 + 190980x^13 + 596048x^12 - 505845x^11 - 3430854x^10 - 1998597x^9 + 8267868x^8 + 15095739x^7 + 2654998x^6 - 20077956x^5 - 29537352x^4 - 20959728x^3 - 8485344x^2 - 1885632x - 179584	\( 2^{14}\cdot 3^{21}\cdot 17^{4}\cdot 23^{5}\cdot 61^{2}\cdot 64879^{3} \)	21T152	Trivial (GRH)