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 19 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.19.113492159372494552843502595189730127.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 52x^16 - 900x^15 - 368x^14 + 2573x^13 + 1365x^12 - 4383x^11 - 2836x^10 + 4255x^9 + 3280x^8 - 2085x^7 - 1991x^6 + 349x^5 + 561x^4 + 46x^3 - 53x^2 - 14x - 1	\( -\,7^{14}\cdot 1091\cdot 4703\cdot 17431\cdot 1870989140621 \)	21T159	Trivial (GRH)
21.19.583010612856606322911444713539464987.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 51x^16 - 901x^15 - 354x^14 + 2589x^13 + 1292x^12 - 4479x^11 - 2667x^10 + 4522x^9 + 3132x^8 - 2424x^7 - 2000x^6 + 516x^5 + 612x^4 + 26x^3 - 63x^2 - 15x - 1	\( -\,3^{28}\cdot 17^{2}\cdot 73\cdot 1207982452098121811 \)	21T159	Trivial (GRH)
21.19.102724782506109615033478690865109188608.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 52x^16 - 900x^15 - 368x^14 + 2573x^13 + 1365x^12 - 4384x^11 - 2838x^10 + 4261x^9 + 3295x^8 - 2089x^7 - 2019x^6 + 335x^5 + 569x^4 + 53x^3 - 52x^2 - 14x - 1	\( -\,2^{14}\cdot 37^{7}\cdot 66045498523363396992439 \)	21T162	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)
21.19.20096043902376756274484831980765619159040.1	x^21 - 21x^19 - 48x^18 + 189x^17 + 864x^16 - 793x^15 - 6480x^14 + 555x^13 + 25912x^12 + 8577x^11 - 58224x^10 - 36449x^9 + 69552x^8 + 63981x^7 - 33392x^6 - 50760x^5 - 5064x^4 + 13440x^3 + 6624x^2 + 1152x + 64	\( -\,2^{24}\cdot 3^{21}\cdot 5\cdot 73^{12} \)	21T137	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)
21.19.1026609587365280539171790331211890660065280.1	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)
21.19.10467408193573914265348716396525160262037504.1	x^21 - 54x^19 - 107x^18 + 1125x^17 + 4500x^16 - 8107x^15 - 67779x^14 - 36492x^13 + 407759x^12 + 726822x^11 - 648882x^10 - 2751741x^9 - 1664640x^8 + 2055372x^7 + 3207811x^6 + 1305252x^5 - 75792x^4 - 149384x^3 - 17568x^2 + 1632x + 128	\( -\,2^{12}\cdot 3^{21}\cdot 11\cdot 23\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.19.427377791081311923649394333215481320454012928.1	x^21 - 66x^19 - 44x^18 + 1755x^17 + 2340x^16 - 23331x^15 - 48222x^14 + 149211x^13 + 476480x^12 - 237114x^11 - 2187516x^10 - 1872752x^9 + 3043296x^8 + 7287477x^7 + 4627874x^6 - 2062908x^5 - 5531544x^4 - 4256016x^3 - 1747872x^2 - 388416x - 36992	\( -\,2^{14}\cdot 3^{21}\cdot 17^{2}\cdot 29^{18}\cdot 41 \)	21T123	Trivial (GRH)
21.19.476572123064963750340948413604798767327870976.1	x^21 - 90x^19 - 48x^18 + 3114x^17 + 2736x^16 - 55436x^15 - 59544x^14 + 556140x^13 + 626528x^12 - 3161016x^11 - 3364128x^10 + 9540856x^9 + 9086400x^8 - 12948624x^7 - 11248992x^6 + 4643712x^5 + 5262720x^4 + 208896x^3 - 734976x^2 - 200448x - 14848	\( -\,2^{38}\cdot 3^{21}\cdot 19\cdot 29^{2}\cdot 37\cdot 809^{6} \)	21T147	Trivial (GRH)
21.19.884877203125648650803983313687121298332172643.1	x^21 - 4x^20 - 14x^19 + 68x^18 + 66x^17 - 467x^16 - 71x^15 + 1678x^14 - 409x^13 - 3411x^12 + 1633x^11 + 3942x^10 - 2566x^9 - 2423x^8 + 2029x^7 + 621x^6 - 784x^5 + 17x^4 + 120x^3 - 22x^2 - 4x + 1	\( -\,421\cdot 647\cdot 991\cdot 2843\cdot 53357069\cdot 21609969352347848780355937 \)	21T164	Trivial (GRH)
21.19.14820597186060641470356690957661801327808741376.1	x^21 - 63x^19 - 42x^18 + 1629x^17 + 2172x^16 - 21605x^15 - 44658x^14 + 144702x^13 + 458648x^12 - 307962x^11 - 2370636x^10 - 1613130x^9 + 4864824x^8 + 9505014x^7 + 2763308x^6 - 10171656x^5 - 15777936x^4 - 11303904x^3 - 4584384x^2 - 1018752x - 97024	\( -\,2^{45}\cdot 3^{21}\cdot 379^{2}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.19.376684621470118839904470766759029380731469611008.1	x^21 - 66x^19 - 44x^18 + 1755x^17 + 2340x^16 - 23304x^15 - 48168x^14 + 149733x^13 + 477784x^12 - 261576x^11 - 2272800x^10 - 1756043x^9 + 3891348x^8 + 8255907x^7 + 3442422x^6 - 6481188x^5 - 11018952x^4 - 8015728x^3 - 3259872x^2 - 724416x - 68992	\( -\,2^{14}\cdot 3^{45}\cdot 7^{4}\cdot 11^{2}\cdot 547^{6} \)	21T151	Trivial (GRH)
21.19.460953958284049031411201347341619922421861679104.1	x^21 - 45x^19 - 30x^18 + 729x^17 + 972x^16 - 4266x^15 - 9180x^14 - 6687x^13 - 2872x^12 + 131652x^11 + 443208x^10 + 46436x^9 - 1786608x^8 - 2821416x^7 - 29552x^6 + 4752864x^5 + 6645312x^4 + 4669568x^3 + 1886976x^2 + 419328x + 39936	\( -\,2^{15}\cdot 3^{23}\cdot 13^{2}\cdot 313^{12} \)	21T137	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)
21.19.3316408537317672378000348521605478401589071837739.1	x^21 - 4x^20 - 15x^19 + 72x^18 + 74x^17 - 512x^16 - 76x^15 + 1846x^14 - 486x^13 - 3645x^12 + 1761x^11 + 4038x^10 - 2481x^9 - 2456x^8 + 1759x^7 + 747x^6 - 642x^5 - 80x^4 + 111x^3 - 5x^2 - 7x + 1	\( -\,26283423599\cdot 20591059981426849\cdot 6127839564275492002789 \)	21T164	Trivial (GRH)
21.19.23646919820900166782460221000494785041305243194753024.1	x^21 - 111x^19 - 74x^18 + 4833x^17 + 6444x^16 - 102315x^15 - 208926x^14 + 1011159x^13 + 3036896x^12 - 2555901x^11 - 17382342x^10 - 20116901x^9 + 1938204x^8 + 49891719x^7 + 140889166x^6 + 241923564x^5 + 257168664x^4 + 169404496x^3 + 67598496x^2 + 15021888x + 1430656	\( -\,2^{21}\cdot 3^{21}\cdot 29^{18}\cdot 41\cdot 11177^{2} \)	21T123	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)
21.19.52483781054437666614504054423280523869246083235156328448.1	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)