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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.13.36068680148646461612743213200732662710272.1	x^21 - 3x^19 - 2x^18 - 108x^17 - 144x^16 + 141x^15 + 378x^14 + 2520x^13 + 6104x^12 + 2646x^11 - 8652x^10 - 21233x^9 - 36324x^8 - 49287x^7 - 49534x^6 - 39852x^5 - 27864x^4 - 15696x^3 - 6048x^2 - 1344x - 128	\( 2^{14}\cdot 3^{21}\cdot 29^{18} \)	21T123	Trivial (GRH)
21.17.43978192433421249509929797067247084063789.1	x^21 - 8x^20 - x^19 + 83x^18 + 31x^17 - 219x^16 - 433x^15 - 960x^14 - 206x^13 + 2604x^12 + 2808x^11 + 2203x^10 + 1933x^9 - 7087x^8 - 12004x^7 + 1523x^6 + 9926x^5 + 2591x^4 - 2172x^3 - 923x^2 - 78x - 1	\( 29^{18}\cdot 389\cdot 463^{2}\cdot 1583^{2} \)	21T123	Trivial (GRH)
21.11.756401169658892313445973964168187656575911.1	x^21 - x^20 - 10x^19 + 40x^18 - 74x^17 + 11x^16 + 323x^15 - 1158x^14 + 2738x^13 - 4870x^12 + 7701x^11 - 11657x^10 + 15330x^9 - 18587x^8 + 21309x^7 - 19493x^6 + 16136x^5 - 15807x^4 + 11731x^3 - 3775x^2 + 70x + 41	\( -\,29^{18}\cdot 41^{3}\cdot 3671\cdot 3769^{2} \)	21T123	Trivial (GRH)
21.9.2128052128770141235151849578843227099906048.1	x^21 + 18x^19 - 12x^18 + 27x^17 - 36x^16 - 879x^15 + 1782x^14 - 5157x^13 + 10848x^12 - 11070x^11 + 6324x^10 + 8720x^9 - 45216x^8 + 75093x^7 - 58850x^6 + 14148x^5 + 13464x^4 - 14096x^3 + 6048x^2 - 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 29^{18}\cdot 59 \)	21T123	Trivial (GRH)
21.9.6889117908391474168033953721339938577661952.1	x^21 - 21x^19 - 18x^18 + 189x^17 + 324x^16 - 1237x^15 - 2430x^14 + 7215x^13 + 8552x^12 - 31383x^11 - 7854x^10 + 83367x^9 - 36828x^8 - 115263x^7 + 119134x^6 + 55404x^5 - 131280x^4 + 28608x^3 + 55008x^2 - 39168x + 7552	\( 2^{14}\cdot 3^{21}\cdot 29^{18}\cdot 191 \)	21T123	Trivial (GRH)
21.13.10423848562958827406082788615011739523268608.1	x^21 - 24x^19 - 16x^18 + 135x^17 + 180x^16 + 519x^15 + 918x^14 - 4653x^13 - 13904x^12 - 7236x^11 + 16440x^10 + 49612x^9 + 101808x^8 + 105621x^7 - 51646x^6 - 286524x^5 - 369432x^4 - 255248x^3 - 102816x^2 - 22848x - 2176	\( 2^{14}\cdot 3^{21}\cdot 17^{2}\cdot 29^{18} \)	21T123	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)
21.17.1030734672607869933507362803637337302271442944.1	x^21 - 45x^19 - 30x^18 + 756x^17 + 1008x^16 - 5415x^15 - 11502x^14 + 9504x^13 + 44088x^12 + 54054x^11 + 47892x^10 - 77257x^9 - 444996x^8 - 684633x^7 - 275986x^6 + 489132x^5 + 837144x^4 + 609616x^3 + 247968x^2 + 55104x + 5248	\( 2^{14}\cdot 3^{21}\cdot 17\cdot 29^{18}\cdot 41^{2} \)	21T123	Trivial (GRH)
21.15.3181220474533863069678902335333881959645528064.1	x^21 - 42x^19 - 28x^18 + 567x^17 + 756x^16 - 2205x^15 - 4914x^14 - 4977x^13 - 5264x^12 + 12474x^11 + 54684x^10 + 75264x^9 + 50400x^8 + 14613x^7 - 7966x^6 - 20412x^5 - 22680x^4 - 15120x^3 - 6048x^2 - 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 7^{37} \)	21T123	Trivial (GRH)
21.7.3419995858430775529141866755724737853735124992.1	x^21 + 39x^19 - 26x^18 + 486x^17 - 648x^16 + 2241x^15 - 4050x^14 + 2538x^13 - 168x^12 - 11124x^11 + 35832x^10 - 59945x^9 + 81252x^8 - 95367x^7 + 85054x^6 - 57132x^5 + 32472x^4 - 16208x^3 + 6048x^2 - 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 43^{18}\cdot 79 \)	21T123	Trivial (GRH)
21.13.14848842777743746917666586040678292200394276864.1	x^21 + 36x^19 - 24x^18 - 108x^17 + 144x^16 - 7608x^15 + 15120x^14 + 6768x^13 - 42688x^12 + 402624x^11 - 1212288x^10 - 86528x^9 + 5658624x^8 - 8884608x^7 + 761600x^6 + 13312512x^5 - 18994176x^4 + 13400064x^3 - 5419008x^2 + 1204224x - 114688	\( 2^{14}\cdot 3^{21}\cdot 7^{3}\cdot 43^{18} \)	21T123	Trivial (GRH)
21.15.727593296109443598965662715993236317819319566336.1	x^21 - 3x^19 - 2x^18 - 162x^17 - 216x^16 + 873x^15 + 1890x^14 + 4338x^13 + 8488x^12 - 17064x^11 - 80592x^10 - 106609x^9 - 54468x^8 + 116223x^7 + 527006x^6 + 1015308x^5 + 1115352x^4 + 741328x^3 + 296352x^2 + 65856x + 6272	\( -\,2^{14}\cdot 3^{21}\cdot 7^{5}\cdot 43^{18} \)	21T123	Trivial (GRH)
21.11.5085862618644065944682370862103067572913300652032.1	x^21 + 21x^19 - 14x^18 - 2457x^15 + 4914x^14 - 16884x^13 + 37016x^12 - 19278x^11 - 40572x^10 + 241311x^9 - 723996x^8 + 1097907x^7 - 806246x^6 + 111132x^5 + 297864x^4 - 272496x^3 + 114912x^2 - 25536x + 2432	\( -\,2^{14}\cdot 3^{21}\cdot 7^{36}\cdot 19^{2}\cdot 31 \)	21T123	Trivial (GRH)
21.15.5093153072766105192759639011952654224735236964352.1	x^21 - 24x^19 - 16x^18 + 81x^17 + 108x^16 + 2061x^15 + 4050x^14 - 15687x^13 - 48432x^12 - 15984x^11 + 88368x^10 + 224896x^9 + 424512x^8 + 469797x^7 - 11902x^6 - 758268x^5 - 1046808x^4 - 733712x^3 - 296352x^2 - 65856x - 6272	\( -\,2^{14}\cdot 3^{21}\cdot 7^{6}\cdot 43^{18} \)	21T123	Trivial (GRH)
21.7.10010511695891821022949387798060679015952437886976.1	x^21 + 60x^19 - 40x^18 + 1431x^17 - 1908x^16 + 17835x^15 - 34398x^14 + 130419x^13 - 291728x^12 + 593784x^11 - 1151232x^10 + 1535068x^9 - 1504944x^8 + 662757x^7 + 2027806x^6 - 5458428x^5 + 6437016x^4 - 4356624x^3 + 1747872x^2 - 388416x + 36992	\( -\,2^{14}\cdot 3^{21}\cdot 17^{4}\cdot 29^{18}\cdot 3323 \)	21T123	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)
21.15.28145346243034236618000959151522201107893866240000000.1	x^21 - 45x^19 - 30x^18 + 594x^17 + 792x^16 - 897x^15 - 2322x^14 - 17910x^13 - 43976x^12 - 10098x^11 + 92388x^10 + 258803x^9 + 551340x^8 + 841095x^7 + 929166x^6 + 845100x^5 + 656280x^4 + 387920x^3 + 151200x^2 + 33600x + 3200	\( -\,2^{14}\cdot 3^{21}\cdot 5^{7}\cdot 71^{18} \)	21T123	Trivial (GRH)
21.13.2240383313285621648550590602803486470004158142680478857.1	x^21 - x^20 - 144x^19 + 378x^18 + 8278x^17 - 35490x^16 - 221869x^15 + 1501757x^14 + 1838931x^13 - 32357739x^12 + 41883236x^11 + 324873323x^10 - 1145395041x^9 - 404084435x^8 + 9148701429x^7 - 16963827940x^6 - 7849718366x^5 + 80178499093x^4 - 144336599294x^3 + 129703535043x^2 - 59636222162x + 10937301223	\( 17^{3}\cdot 29^{18}\cdot 307^{2}\cdot 4794766099^{2} \)	21T123	$[3]$ (GRH)
21.21.483509712157573278109148029130668665453659848723054473746235392.1	x^21 - x^20 - 278x^19 + 211x^18 + 32317x^17 - 11281x^16 - 2039432x^15 - 467981x^14 + 75279887x^13 + 73572952x^12 - 1596987413x^11 - 3083325600x^10 + 16530810553x^9 + 56124016529x^8 - 18817408458x^7 - 347856148950x^6 - 730940435110x^5 - 788186980737x^4 - 503882066680x^3 - 193054422458x^2 - 41100543009x - 3748629959	\( 2^{14}\cdot 29^{18}\cdot 3323\cdot 17923^{2}\cdot 102139^{2}\cdot 112213^{2} \)	21T123	$[3]$ (GRH)
21.21.4750515842525774314075603960650823606111677688716139449933283328.1	x^21 - 6x^20 - 300x^19 + 1927x^18 + 36842x^17 - 264617x^16 - 2308644x^15 + 19971897x^14 + 70201991x^13 - 880321458x^12 - 313927359x^11 + 21760800986x^10 - 42451631619x^9 - 237011113971x^8 + 1113186887432x^7 - 554971101499x^6 - 7187885452232x^5 + 23873107738441x^4 - 37359130697657x^3 + 33010416695533x^2 - 15899761516876x + 3264801335137	\( 2^{14}\cdot 29^{18}\cdot 3323\cdot 11354851^{2}\cdot 56706367^{2} \)	21T123	$[3]$ (GRH)