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
18.6.394876295174073378555289.1	x^18 - 7x^17 + 21x^16 - 21x^15 - 38x^14 + 149x^13 - 180x^12 + 7x^11 + 241x^10 - 270x^9 + 54x^8 + 111x^7 - 89x^6 + 20x^5 - 3x^3 - 8x^2 + 14x - 1	\( 19^{16}\cdot 37^{2} \)	18T177	Trivial
18.10.3683108409844954690118689.1	x^18 - 5x^17 + 5x^16 + 23x^15 - 103x^14 + 149x^13 + 84x^12 - 583x^11 + 624x^10 - 141x^9 - 309x^8 + 764x^7 - 692x^6 + 138x^5 + 151x^4 - 110x^3 + 21x^2 + 3x - 1	\( 19^{16}\cdot 113^{2} \)	18T177	Trivial
18.14.6576752670755330244294481.1	x^18 - 3x^17 - 14x^16 + 47x^15 + 79x^14 - 321x^13 - 234x^12 + 1356x^11 + 76x^10 - 3435x^9 + 1672x^8 + 4094x^7 - 3619x^6 - 1450x^5 + 2070x^4 - 70x^3 - 260x^2 + 11x + 1	\( 19^{16}\cdot 151^{2} \)	18T177	Trivial (GRH)
18.6.10522631208360387818170561.1	x^18 - 6x^17 + 12x^16 + 7x^15 - 79x^14 + 151x^13 - 64x^12 - 230x^11 + 499x^10 - 357x^9 - 17x^8 + 499x^7 - 373x^6 + 445x^5 + 78x^4 - 12x^3 - 56x^2 + 15x - 1	\( 19^{16}\cdot 191^{2} \)	18T177	Trivial
18.10.75613185918270483380568064.1	x^18 - x^16 - 27x^14 + 7x^12 + 173x^10 + 4x^8 - 229x^6 + 124x^4 - 14x^2 - 1	\( 2^{18}\cdot 19^{16} \)	18T177	Trivial (GRH)
18.14.75613185918270483380568064.1	x^18 - 7x^16 + 7x^14 + 45x^12 - 100x^10 - 13x^8 + 170x^6 - 139x^4 + 36x^2 - 1	\( 2^{18}\cdot 19^{16} \)	18T177	Trivial (GRH)
18.18.103514451522112291747997679616.1	x^18 - 25x^16 + 263x^14 - 1528x^12 + 5404x^10 - 12064x^8 + 16994x^6 - 14559x^4 + 6882x^2 - 1369	\( 2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T177	Trivial (GRH)
18.18.141711284133771727403008823394304.1	x^18 - 80x^16 + 2399x^14 - 35671x^12 + 294157x^10 - 1411309x^8 + 3984308x^6 - 6446621x^4 + 5470524x^2 - 1874161	\( 2^{18}\cdot 19^{16}\cdot 37^{4} \)	18T177	Trivial (GRH)