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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.13.25192291127470187521040280871398560021.1	x^21 - 2x^20 - 15x^19 + 58x^18 + 22x^17 - 451x^16 + 666x^15 + 864x^14 - 3424x^13 + 1655x^12 + 5377x^11 - 4629x^10 - 8530x^9 + 10138x^8 + 6523x^7 - 9568x^6 - 4336x^5 + 6971x^4 - 397x^3 - 845x^2 - 78x - 1	\( 29^{19}\cdot 41^{2}\cdot 1567^{2} \)	21T112	Trivial (GRH)
21.21.8766456641448373848515625225224872939068899328.1	x^21 - 87x^19 - 58x^18 + 3132x^17 + 4176x^16 - 58899x^15 - 120582x^14 + 586728x^13 + 1761112x^12 - 2435130x^11 - 13256364x^10 - 4665665x^9 + 43241436x^8 + 70388133x^7 - 3531910x^6 - 129793212x^5 - 179073144x^4 - 125497616x^3 - 50688288x^2 - 11264064x - 1072768	\( 2^{14}\cdot 3^{21}\cdot 17^{2}\cdot 29^{20} \)	21T112	Trivial (GRH)
21.7.93977273942858186518781596986652804327823677210624.1	x^21 - 2x^20 - 76x^19 + 66x^18 + 2617x^17 + 569x^16 - 50629x^15 - 61336x^14 + 556684x^13 + 1235397x^12 - 2937995x^11 - 11189080x^10 + 104799x^9 + 39726191x^8 + 57810175x^7 + 35427809x^6 - 35767659x^5 - 294130577x^4 - 660000851x^3 - 873114494x^2 - 1007548599x - 696833749	\( -\,2^{14}\cdot 29^{18}\cdot 331^{2}\cdot 15772171^{2} \)	21T112	$[3]$ (GRH)
21.21.3242965296276187008239641241713030829835123165216768.1	x^21 - 108x^19 - 72x^18 + 4887x^17 + 6516x^16 - 117789x^15 - 239922x^14 + 1562355x^13 + 4557264x^12 - 9837504x^11 - 46059792x^10 + 1346012x^9 + 217805616x^8 + 298243653x^7 - 184162654x^6 - 943551612x^5 - 1211376024x^4 - 836177936x^3 - 336758688x^2 - 74835264x - 7127168	\( 2^{14}\cdot 3^{21}\cdot 29^{19}\cdot 55681^{2} \)	21T112	Trivial (GRH)
21.13.5805853122246764931899778242573785764324687217345781.1	x^21 - 9x^20 - 97x^19 + 833x^18 + 4984x^17 - 31715x^16 - 175533x^15 + 562585x^14 + 4094879x^13 - 1859808x^12 - 53998064x^11 - 94535203x^10 + 237316339x^9 + 1298499408x^8 + 2093062163x^7 - 1378228052x^6 - 15222593937x^5 - 40842190694x^4 - 67054672118x^3 - 73764878089x^2 - 50695704981x - 16324734619	\( 29^{19}\cdot 126151^{2}\cdot 7731457^{2} \)	21T112	$[3]$ (GRH)
21.15.199590046918721268199019961542607044275952072765726408704.1	x^21 - 6x^20 - 203x^19 + 838x^18 + 14852x^17 - 59663x^16 - 530509x^15 + 2576288x^14 + 9166942x^13 - 66398244x^12 - 28436177x^11 + 936461376x^10 - 1582339958x^9 - 5167321863x^8 + 23210975798x^7 - 20434819891x^6 - 69789330828x^5 + 247971929908x^4 - 375341626400x^3 + 321030524262x^2 - 151939714933x + 31214514281	\( -\,2^{14}\cdot 29^{18}\cdot 7608122372761^{2} \)	21T112	$[3]$ (GRH)
21.7.301774308463597940020774144983778249139309451403045912576.1	x^21 - 5x^20 - 162x^19 + 1164x^18 + 9298x^17 - 103335x^16 - 121449x^15 + 4484709x^14 - 10039699x^13 - 91309246x^12 + 508027928x^11 + 248421674x^10 - 9128617007x^9 + 23259829893x^8 + 41621122062x^7 - 352710251075x^6 + 637129534424x^5 + 698222785081x^4 - 5446453497276x^3 + 11279843000465x^2 - 11486117124675x + 4938448359709	\( -\,2^{14}\cdot 29^{18}\cdot 853^{2}\cdot 10967310769^{2} \)	21T112	$[3]$ (GRH)
21.15.1312348190467104151476370758095143331434441717851465322827.1	x^21 - 2x^20 - 278x^19 + 1209x^18 + 28609x^17 - 188663x^16 - 1265361x^15 + 12878599x^14 + 13360899x^13 - 429530466x^12 + 780621370x^11 + 6395176809x^10 - 27439148621x^9 - 14072788600x^8 + 293371856110x^7 - 536805970235x^6 - 490924632667x^5 + 3155238661458x^4 - 4701437594680x^3 + 2873237146615x^2 - 294214513112x - 270275728417	\( -\,3^{7}\cdot 29^{18}\cdot 157^{2}\cdot 3307^{2}\cdot 3943^{2}\cdot 26083^{2} \)	21T112	$[3]$ (GRH)