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
18.6.270283659433679895481.1	x^18 - 6x^17 + 13x^16 - 5x^15 - 50x^14 + 186x^13 - 408x^12 + 671x^11 - 888x^10 + 973x^9 - 888x^8 + 671x^7 - 408x^6 + 186x^5 - 50x^4 - 5x^3 + 13x^2 - 6x + 1	\( 37^{4}\cdot 229^{6} \)	18T203	Trivial
18.6.3221287037577650765824.1	x^18 - 5x^16 + 11x^14 - 25x^12 + 51x^10 - 65x^8 + 59x^6 - 40x^4 + 13x^2 - 1	\( 2^{18}\cdot 31^{6}\cdot 61^{4} \)	18T203	Trivial
18.6.3435531027183254634496.1	x^18 - 7x^16 + 26x^14 - 68x^12 + 122x^10 - 137x^8 + 86x^6 - 26x^4 + 5x^2 - 1	\( 2^{18}\cdot 23^{6}\cdot 97^{4} \)	18T203	Trivial
18.6.123704507881117580682321.1	x^18 - 9x^17 + 40x^16 - 116x^15 + 226x^14 - 266x^13 + 44x^12 + 568x^11 - 1371x^10 + 1839x^9 - 1517x^8 + 528x^7 + 458x^6 - 864x^5 + 686x^4 - 326x^3 + 94x^2 - 15x + 1	\( 3^{6}\cdot 7^{4}\cdot 643^{6} \)	18T203	Trivial
18.18.70853239618582582520971264.1	x^18 - 17x^16 + 115x^14 - 404x^12 + 802x^10 - 911x^8 + 568x^6 - 176x^4 + 24x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T203	Trivial (GRH)
18.18.32428394513987687070386356224.1	x^18 - 27x^16 + 293x^14 - 1668x^12 + 5427x^10 - 10303x^8 + 11189x^6 - 6448x^4 + 1584x^2 - 49	\( 2^{18}\cdot 3^{6}\cdot 7^{4}\cdot 643^{6} \)	18T203	Trivial (GRH)