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 6 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.13.79356206645831716224655747338287777368449179467776.1	x^21 - 30x^19 - 20x^18 - 621x^17 - 828x^16 + 17247x^15 + 35046x^14 + 66051x^13 + 119024x^12 - 1844262x^11 - 6476388x^10 - 4483504x^9 + 11041056x^8 + 23943879x^7 + 14457846x^6 - 7997076x^5 - 19421064x^4 - 14795696x^3 - 6066144x^2 - 1348032x - 128384	\( 2^{14}\cdot 3^{28}\cdot 17^{2}\cdot 29^{18}\cdot 59^{2} \)	21T120	Trivial (GRH)
21.13.10017279497047013285784312521273620782624202478075904.1	x^21 + 33x^19 - 22x^18 - 540x^17 + 720x^16 - 21597x^15 + 42714x^14 - 65736x^13 + 105688x^12 + 1371762x^11 - 4859580x^10 + 9685343x^9 - 16976412x^8 - 2163123x^7 + 96125046x^6 - 220676508x^5 + 253088568x^4 - 170110352x^3 + 68154912x^2 - 15145536x + 1442432	\( 2^{14}\cdot 3^{28}\cdot 29^{18}\cdot 59^{2}\cdot 191^{2} \)	21T120	Trivial (GRH)
21.9.148644694877567190405834966748762728825589403667677184.1	x^21 + 96x^19 - 64x^18 + 2457x^17 - 3276x^16 + 5007x^15 - 7830x^14 - 330687x^13 + 894592x^12 - 1467288x^11 + 2303232x^10 - 705280x^9 - 5911488x^8 + 14850711x^7 - 23979414x^6 + 31209516x^5 - 29920248x^4 + 19112272x^3 - 7578144x^2 + 1684032x - 160384	\( 2^{14}\cdot 3^{28}\cdot 7^{2}\cdot 43^{18}\cdot 179^{2} \)	21T120	Trivial (GRH)
21.9.365733978997947732510665000581452096461458495283189161.1	x^21 - 8x^20 - 103x^19 + 746x^18 + 4832x^17 - 26062x^16 - 141694x^15 + 408022x^14 + 2611992x^13 - 1563121x^12 - 26772274x^11 - 33304253x^10 + 100887793x^9 + 374558971x^8 + 379783904x^7 - 477643726x^6 - 2363188741x^5 - 4691718180x^4 - 6210392913x^3 - 5943695836x^2 - 3952581284x - 1568656069	\( 17^{4}\cdot 29^{18}\cdot 354439^{2}\cdot 406969^{2} \)	21T120	$[3]$ (GRH)
21.17.2712192105373922519664024881359850830750751437537163927329.1	x^21 - 2x^20 - 247x^19 + 374x^18 + 21338x^17 - 46630x^16 - 894666x^15 + 2940618x^14 + 18770143x^13 - 94465370x^12 - 136594601x^11 + 1533079457x^10 - 1602281931x^9 - 10196324980x^8 + 32974204263x^7 - 12323502724x^6 - 123064374241x^5 + 311864589974x^4 - 357944054578x^3 + 206217600578x^2 - 42463522216x - 5081287879	\( 17^{4}\cdot 29^{18}\cdot 1486813^{2}\cdot 8354569^{2} \)	21T120	$[3]$ (GRH)
21.17.3926566176958448757359587989819452371300355828605456367281.1	x^21 - 8x^20 - 348x^19 + 3024x^18 + 40305x^17 - 440536x^16 - 1679481x^15 + 30563454x^14 - 13469087x^13 - 1062422296x^12 + 3376643844x^11 + 15621844277x^10 - 107528391994x^9 + 48609973691x^8 + 1236692996796x^7 - 3838480636743x^6 + 106835860626x^5 + 24805429178070x^4 - 67245831255093x^3 + 87778802366986x^2 - 59670215937464x + 16989857262797	\( 17^{6}\cdot 29^{18}\cdot 157^{2}\cdot 5599871521^{2} \)	21T120	$[3]$ (GRH)