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
12.4.12457785357953028025.1	x^12 - x^11 - 15x^10 + 18x^9 + 18x^8 - 368x^7 + 72x^6 + 2283x^5 + 974x^4 - 3374x^3 + 10x^2 + 3166x - 961	\( 5^{2}\cdot 163^{8} \)	$C_2\times C_4^2:C_3$ (as 12T55)	$[2]$
12.4.12457785357953028025.2	x^12 - x^11 - 5x^10 - 25x^9 + 111x^8 - 124x^7 - 26x^6 - 571x^5 + 2612x^4 - 3609x^3 + 1838x^2 + 131x - 331	\( 5^{2}\cdot 163^{8} \)	$C_2\times C_4^2:C_3$ (as 12T55)	$[2]$
12.0.213838914125824000000.1	x^12 + 30x^10 + 323x^8 + 1460x^6 + 2420x^4 + 1200x^2 + 25	\( 2^{24}\cdot 5^{6}\cdot 13^{8} \)	$C_2\times C_4^2:C_3$ (as 12T55)	$[2, 34]$
12.12.213838914125824000000.1	x^12 - 24x^10 + 202x^8 - 750x^6 + 1215x^4 - 700x^2 + 25	\( 2^{24}\cdot 5^{6}\cdot 13^{8} \)	$C_2\times C_4^2:C_3$ (as 12T55)	Trivial
12.8.213838914125824000000.1	x^12 - 2x^10 - 97x^8 + 360x^6 - 345x^4 + 50x^2 + 25	\( 2^{24}\cdot 5^{6}\cdot 13^{8} \)	$C_2\times C_4^2:C_3$ (as 12T55)	Trivial
12.0.213838914125824000000.2	x^12 + 30x^10 + 352x^8 + 2040x^6 + 6045x^4 + 8450x^2 + 4225	\( 2^{24}\cdot 5^{6}\cdot 13^{8} \)	$C_2\times C_4^2:C_3$ (as 12T55)	$[2, 34]$
12.8.213838914125824000000.2	x^12 - 22x^10 + 93x^8 + 500x^6 - 2140x^4 - 2250x^2 + 625	\( 2^{24}\cdot 5^{6}\cdot 13^{8} \)	$C_2\times C_4^2:C_3$ (as 12T55)	Trivial
12.12.213838914125824000000.3	x^12 - 30x^10 + 352x^8 - 2040x^6 + 6045x^4 - 8450x^2 + 4225	\( 2^{24}\cdot 5^{6}\cdot 13^{8} \)	$C_2\times C_4^2:C_3$ (as 12T55)	Trivial (GRH)