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
21.3.3960879820606443846053527.1	x^21 - 5x^20 + 11x^19 - 20x^18 + 37x^17 - 68x^16 + 120x^15 - 168x^14 + 237x^13 - 331x^12 + 362x^11 - 431x^10 + 452x^9 - 381x^8 + 350x^7 - 238x^6 + 169x^5 - 90x^4 + 43x^3 + 6x^2 + 27	\( -\,13^{2}\cdot 1801^{2}\cdot 193327^{3} \)	21T139	Trivial (GRH)
21.3.930871627030827422699634607.1	x^21 - 5x^20 + 36x^18 - 35x^17 - 108x^16 + 155x^15 + 176x^14 - 338x^13 - 129x^12 + 413x^11 - 50x^10 - 234x^9 + 162x^8 - 66x^7 - 51x^6 + 196x^5 - 92x^4 - 98x^3 + 71x^2 - 10x - 25	\( -\,151^{2}\cdot 2377^{2}\cdot 193327^{3} \)	21T139	Trivial (GRH)
21.9.18453551447289410297167049873.1	x^21 - 2x^20 - 2x^19 + 12x^18 - 25x^17 + x^16 + 48x^15 - 91x^14 + 103x^13 - 12x^12 - 110x^11 + 272x^10 - 277x^9 - 78x^8 + 278x^7 - 46x^6 + 11x^5 - 114x^4 + 3x^3 + 93x^2 - 19x - 23	\( 71^{3}\cdot 8623^{3}\cdot 283573^{2} \)	21T139	Trivial (GRH)
21.9.77814973866654515283350056553.1	x^21 - 8x^20 + 15x^19 + 42x^18 - 181x^17 + 43x^16 + 664x^15 - 785x^14 - 999x^13 + 2386x^12 - 12x^11 - 3337x^10 + 2186x^9 + 1818x^8 - 2845x^7 + 445x^6 + 1349x^5 - 754x^4 - 347x^3 + 279x^2 + 76x + 1	\( 71^{3}\cdot 157^{2}\cdot 3709^{2}\cdot 8623^{3} \)	21T139	Trivial (GRH)
21.15.30334115052100547879498687424199.1	x^21 - 7x^20 + 4x^19 + 78x^18 - 172x^17 - 227x^16 + 1027x^15 - 237x^14 - 2424x^13 + 2147x^12 + 2451x^11 - 3882x^10 - 561x^9 + 3295x^8 - 1120x^7 - 1109x^6 + 907x^5 - 79x^4 - 154x^3 + 74x^2 - 14x + 1	\( -\,107^{3}\cdot 313^{2}\cdot 5023^{2}\cdot 21557^{3} \)	21T139	Trivial (GRH)
21.15.38320240821952780061354303199559.1	x^21 - 7x^20 + 4x^19 + 76x^18 - 158x^17 - 247x^16 + 951x^15 + 33x^14 - 2574x^13 + 1625x^12 + 3365x^11 - 4136x^10 - 1183x^9 + 3929x^8 - 1250x^7 - 1233x^6 + 995x^5 - 101x^4 - 152x^3 + 74x^2 - 14x + 1	\( -\,107^{3}\cdot 21557^{3}\cdot 1767079^{2} \)	21T139	Trivial (GRH)
21.21.84034131400742875647626644438054873.1	x^21 - 8x^20 + 8x^19 + 94x^18 - 269x^17 - 195x^16 + 1577x^15 - 1066x^14 - 3297x^13 + 4973x^12 + 1604x^11 - 7061x^10 + 2541x^9 + 3722x^8 - 3133x^7 - 183x^6 + 1045x^5 - 344x^4 - 56x^3 + 58x^2 - 13x + 1	\( 71^{3}\cdot 109^{2}\cdot 29437^{2}\cdot 283583^{3} \)	21T139	Trivial (GRH)
21.21.123701082051105541760811365981795257.1	x^21 - 6x^20 - 6x^19 + 102x^18 - 113x^17 - 557x^16 + 1235x^15 + 876x^14 - 4391x^13 + 1595x^12 + 6346x^11 - 6325x^10 - 2479x^9 + 6202x^8 - 1793x^7 - 1829x^6 + 1407x^5 - 158x^4 - 178x^3 + 84x^2 - 15x + 1	\( 71^{3}\cdot 283583^{3}\cdot 3892951^{2} \)	21T139	Trivial (GRH)