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
12.4.3696640000000000.1	x^12 - 2x^11 - 2x^10 + 6x^9 + 15x^8 - 44x^7 - 12x^6 + 28x^5 + 51x^4 - 10x^3 - 10x^2 - 10x + 5	\( 2^{20}\cdot 5^{10}\cdot 19^{2} \)	12T215	Trivial
12.8.4364666806640625.1	x^12 - 6x^11 + 12x^10 + 3x^9 - 57x^8 + 63x^7 + 83x^6 - 132x^5 - 57x^4 + 93x^3 + 12x^2 - 21x + 1	\( 3^{12}\cdot 5^{10}\cdot 29^{2} \)	12T215	Trivial
12.4.17213440000000000.1	x^12 - 2x^11 + 4x^10 - 8x^9 + x^8 + 10x^7 - 10x^6 - 40x^5 + 5x^4 + 90x^3 + 50x^2 - 20x - 20	\( 2^{20}\cdot 5^{10}\cdot 41^{2} \)	12T215	Trivial
12.8.34050628916015625.1	x^12 - 12x^10 - 7x^9 + 54x^8 + 63x^7 - 99x^6 - 189x^5 + 27x^4 + 206x^3 + 81x^2 - 51x - 29	\( 3^{20}\cdot 5^{10} \)	12T215	Trivial
12.12.1964546058240000000000.1	x^12 - 42x^10 - 28x^9 + 594x^8 + 792x^7 - 3084x^6 - 6696x^5 + 1692x^4 + 15424x^3 + 16416x^2 + 7296x + 1216	\( 2^{20}\cdot 3^{12}\cdot 5^{10}\cdot 19^{2} \)	12T215	Trivial (GRH)
12.12.159128230717440000000000.1	x^12 - 108x^10 - 136x^9 + 4284x^8 + 10416x^7 - 68656x^6 - 258912x^5 + 231312x^4 + 2075392x^3 + 2582784x^2 - 58368x - 1147904	\( 2^{20}\cdot 3^{16}\cdot 5^{10}\cdot 19^{2} \)	12T215	Trivial (GRH)