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
21.9.8192746627386983812513327588008542208.1	x^21 + 15x^19 - 10x^18 + 36x^17 - 48x^16 - 281x^15 + 594x^14 - 1368x^13 + 2680x^12 - 1134x^11 - 3708x^10 + 9933x^9 - 18900x^8 + 23553x^7 - 11586x^6 - 9612x^5 + 19800x^4 - 14800x^3 + 6048x^2 - 1344x + 128	\( 2^{14}\cdot 3^{25}\cdot 8388019^{3} \)	21T149	Trivial (GRH)
21.3.13323487817207712485393041038446217904128.1	x^21 - 18x^19 - 2x^18 - 81x^17 + 12x^16 + 1190x^15 - 36x^14 + 16188x^13 + 4536x^12 - 15165x^11 + 44712x^10 - 829793x^9 - 1493568x^8 - 5381199x^7 - 4256218x^6 + 1955916x^5 + 401568x^4 - 1042672x^3 + 684576x^2 + 456384x - 304256	\( -\,2^{14}\cdot 3^{28}\cdot 2377^{2}\cdot 184607^{3} \)	21T149	Trivial (GRH)
21.17.15148388514038533069337142710227794542592.1	x^21 - 48x^19 - 32x^18 + 927x^17 + 1236x^16 - 8795x^15 - 18414x^14 + 37539x^13 + 130112x^12 - 10044x^11 - 417240x^10 - 431286x^9 + 352296x^8 + 1057599x^7 + 691446x^6 - 303156x^5 - 822024x^4 - 633136x^3 - 260064x^2 - 57792x - 5504	\( 2^{14}\cdot 3^{25}\cdot 43^{2}\cdot 8388019^{3} \)	21T149	Trivial (GRH)
21.5.101797990310360609370645863694989201915904.1	x^21 - 27x^19 - 10x^18 + 216x^17 + 210x^16 + 725x^15 + 288x^14 - 19932x^13 - 38346x^12 + 76410x^11 + 234948x^10 + 296881x^9 + 400932x^8 - 2455545x^7 - 3096076x^6 + 984564x^5 + 2353416x^4 - 412432x^3 + 313056x^2 + 208704x - 139136	\( 2^{14}\cdot 3^{28}\cdot 593^{3}\cdot 1033^{3}\cdot 1087^{2} \)	21T149	Trivial (GRH)
21.11.482108591396798180036901678675500279119872.1	x^21 - 12x^19 - 14x^18 - 171x^17 + 762x^16 + 2775x^15 - 11556x^14 - 7095x^13 + 67730x^12 - 4464x^11 - 219000x^10 - 105816x^9 + 1080900x^8 - 492591x^7 - 3230200x^6 + 5102568x^5 - 1202184x^4 - 1646784x^3 + 1253952x^2 - 358272x + 39808	\( -\,2^{14}\cdot 3^{28}\cdot 23^{3}\cdot 239^{3}\cdot 311^{2}\cdot 431^{3} \)	21T149	Trivial (GRH)
21.13.2469302026241064308075329448353362630033408.1	x^21 + 24x^19 - 16x^18 - 297x^17 + 396x^16 - 7881x^15 + 15498x^14 + 14859x^13 - 64880x^12 + 659124x^11 - 2003016x^10 + 1978298x^9 + 876312x^8 - 11936907x^7 + 41795214x^6 - 77901372x^5 + 84911832x^4 - 56319248x^3 + 22504608x^2 - 5001024x + 476288	\( 2^{14}\cdot 3^{29}\cdot 61^{2}\cdot 8388019^{3} \)	21T149	Trivial (GRH)
21.11.23681017647282083374222184484113019484225536.1	x^21 - 21x^19 - 14x^18 - 54x^17 - 72x^16 + 1947x^15 + 3942x^14 - 1098x^13 - 9352x^12 + 129303x^11 + 459714x^10 + 249230x^9 - 1062936x^8 - 7283943x^7 - 25324998x^6 - 47407788x^5 - 51752376x^4 - 34339664x^3 - 13722912x^2 - 3049536x - 290432	\( -\,2^{14}\cdot 3^{28}\cdot 107^{3}\cdot 2269^{2}\cdot 21557^{3} \)	21T149	Trivial (GRH)
21.9.67854082802563294891090125131292002166915072.1	x^21 - 27x^19 - 38x^18 + 207x^17 + 696x^16 - 2407x^15 - 4266x^14 - 2724x^13 + 131902x^12 + 77391x^11 - 1608954x^10 + 8580441x^9 + 6141168x^8 - 51751881x^7 - 35307262x^6 + 20619540x^5 - 13559064x^4 - 1839680x^3 + 8089056x^2 - 5392704x + 3595136	\( 2^{14}\cdot 3^{28}\cdot 71^{3}\cdot 8623^{3}\cdot 28087^{2} \)	21T149	Trivial (GRH)
21.7.118116119077730298829170778650237162465584503.1	x^21 - 5x^20 - 109x^19 + 701x^18 + 4296x^17 - 39756x^16 - 48624x^15 + 1154631x^14 - 1521502x^13 - 17113929x^12 + 59548164x^11 + 83276272x^10 - 794402904x^9 + 960360912x^8 + 3742318991x^7 - 13615721957x^6 + 9795702580x^5 + 34213837684x^4 - 101142508280x^3 + 124128246896x^2 - 77759450304x + 20461436081	\( -\,7^{3}\cdot 4591^{2}\cdot 1057681^{3}\cdot 117508201^{2} \)	21T149	$[3]$ (GRH)
21.7.319818187070222575563949307127106042884938167.1	x^21 - 3x^20 - 121x^19 + 520x^18 + 5673x^17 - 34123x^16 - 113785x^15 + 1128771x^14 + 76521x^13 - 19817069x^12 + 39581265x^11 + 156838536x^10 - 718476095x^9 + 165478618x^8 + 4650794255x^7 - 10553757523x^6 + 58638956x^5 + 39666054316x^4 - 82890643198x^3 + 84623317925x^2 - 45571419390x + 10411723987	\( -\,72871^{2}\cdot 7215127^{3}\cdot 12662833^{2} \)	21T149	$[3]$ (GRH)
21.15.206999357923580597519925622120420920952650317824.1	x^21 - 4x^20 - 135x^19 + 447x^18 + 7426x^17 - 14742x^16 - 235889x^15 + 81863x^14 + 4535217x^13 + 6003126x^12 - 45995423x^11 - 152176849x^10 + 82861724x^9 + 1302489123x^8 + 2491180274x^7 - 865406655x^6 - 12974841396x^5 - 29235206700x^4 - 36570332305x^3 - 28144706275x^2 - 12639229484x - 2567394257	\( -\,2^{14}\cdot 107^{3}\cdot 331^{2}\cdot 21557^{3}\cdot 31033^{2}\cdot 98779^{2} \)	21T149	$[3]$ (GRH)
21.17.210302543645345736468562461003484609741021790208.1	x^21 - 93x^19 - 62x^18 + 3186x^17 + 4248x^16 - 45699x^15 - 94230x^14 + 151668x^13 + 558008x^12 + 1909683x^11 + 4713258x^10 - 6558322x^9 - 46220760x^8 - 64186983x^7 + 10446906x^6 + 132062292x^5 + 178126920x^4 + 124258480x^3 + 50143968x^2 + 11143104x + 1061248	\( 2^{14}\cdot 3^{28}\cdot 71^{3}\cdot 8291^{2}\cdot 283583^{3} \)	21T149	Trivial (GRH)
21.15.264052273254588481010531488175866616732437426978816.1	x^21 - 3x^20 - 209x^19 + 866x^18 + 17488x^17 - 100813x^16 - 699289x^15 + 6055386x^14 + 9100112x^13 - 197774167x^12 + 303373804x^11 + 3145126908x^10 - 13632017727x^9 - 6799234698x^8 + 179226043197x^7 - 434862711589x^6 - 215531886603x^5 + 3436111182819x^4 - 8653636855724x^3 + 11225010417085x^2 - 7833213610116x + 2346733148869	\( -\,2^{14}\cdot 107^{3}\cdot 21557^{3}\cdot 597049^{2}\cdot 60696949^{2} \)	21T149	$[3]$ (GRH)