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
21.15.62777025856649436362941930381175751.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 3x^14 + 2940x^13 + 42x^12 - 5733x^11 - 231x^10 + 7007x^9 + 630x^8 - 5145x^7 - 882x^6 + 2058x^5 + 588x^4 - 343x^3 - 147x^2 + 3	\( -\,3^{28}\cdot 7^{21}\cdot 17^{3} \)	21T70	Trivial (GRH)
21.15.274900661946440887644863785621377875.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 2x^14 + 2940x^13 + 28x^12 - 5733x^11 - 154x^10 + 7007x^9 + 420x^8 - 5148x^7 - 588x^6 + 2079x^5 + 392x^4 - 385x^3 - 98x^2 + 21x + 5	\( -\,5^{3}\cdot 7^{21}\cdot 13^{14} \)	21T70	Trivial (GRH)
21.9.1694979698129534781799432120291745277.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 6x^14 + 2940x^13 + 84x^12 - 5733x^11 - 462x^10 + 7007x^9 + 1260x^8 - 5136x^7 - 1764x^6 + 1995x^5 + 1176x^4 - 217x^3 - 294x^2 - 63x - 1	\( 3^{31}\cdot 7^{21}\cdot 17^{3} \)	21T70	Trivial (GRH)
21.9.17475230337747878140135688009187415737.1	x^21 - 21x^19 + 189x^17 - 952x^15 - 9x^14 + 2940x^13 + 126x^12 - 5733x^11 - 693x^10 + 7007x^9 + 1890x^8 - 5121x^7 - 2646x^6 + 1890x^5 + 1764x^4 - 7x^3 - 441x^2 - 168x - 19	\( 3^{31}\cdot 7^{21}\cdot 37^{3} \)	21T70	Trivial (GRH)
21.3.97690571647614384537849467759845470171.1	x^21 + 21x^19 + 189x^17 + 952x^15 + 2940x^13 + 5733x^11 + 7007x^9 + 5142x^7 + 2037x^5 + 301x^3 - 21x - 1	\( -\,3^{28}\cdot 7^{21}\cdot 197^{3} \)	21T70	Trivial (GRH)
21.3.161629911646340812419073232001227463999.1	x^21 + 21x^19 + 189x^17 + 952x^15 - 3x^14 + 2940x^13 - 42x^12 + 5733x^11 - 231x^10 + 7007x^9 - 630x^8 + 5145x^7 - 882x^6 + 2058x^5 - 588x^4 + 343x^3 - 147x^2 + 1	\( -\,3^{28}\cdot 7^{21}\cdot 233^{3} \)	21T70	Trivial (GRH)
21.21.23775269732638142813384381192164997335278189777532971313088692224.1	x^21 - 3x^20 - 126x^19 + 590x^18 + 4959x^17 - 34101x^16 - 40871x^15 + 707025x^14 - 962760x^13 - 4547872x^12 + 12890748x^11 + 5372634x^10 - 51667790x^9 + 36692820x^8 + 68540517x^7 - 110714509x^6 + 17089548x^5 + 69115944x^4 - 62120671x^3 + 23606859x^2 - 4317927x + 310897	\( 2^{18}\cdot 3^{28}\cdot 7^{15}\cdot 71^{3}\cdot 1326319793^{3} \)	21T70	Trivial (GRH)
21.21.1455017556485777831827718837684258199501571708701991598100360439005184.1	x^21 - 3x^20 - 154x^19 + 702x^18 + 7675x^17 - 48437x^16 - 121539x^15 + 1311181x^14 - 604724x^13 - 13780424x^12 + 24227654x^11 + 53854396x^10 - 155785132x^9 - 44499970x^8 + 349494407x^7 - 72022779x^6 - 299417524x^5 + 81644768x^4 + 75064083x^3 - 21679907x^2 - 4245015x + 1188557	\( 2^{18}\cdot 7^{14}\cdot 11^{6}\cdot 19^{14}\cdot 37^{6}\cdot 1311031^{3} \)	21T70	Trivial (GRH)