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
12.0.851162814333.1	x^12 - x^9 + 2x^6 - 2x^3 + 1	\( 3^{18}\cdot 13^{3} \)	$C_3\times S_3\wr C_2$ (as 12T121)	Trivial
12.0.2180445558813.1	x^12 + 4x^6 - 3x^3 + 1	\( 3^{16}\cdot 37^{3} \)	$C_3\times S_3\wr C_2$ (as 12T121)	Trivial
12.6.25345511310483.1	x^12 - x^11 - x^10 + 9x^9 - 5x^8 - 23x^7 + 8x^6 + 25x^5 - 5x^4 - 17x^3 + 2x^2 + 5x - 1	\( -\,3^{7}\cdot 7^{4}\cdot 13^{6} \)	$C_3\times S_3\wr C_2$ (as 12T121)	Trivial
12.6.85280185546875.1	x^12 - 4x^11 + x^10 + 20x^9 - 40x^8 + x^7 + 86x^6 - 99x^5 + 90x^3 - 54x^2 + 36x - 9	\( -\,3^{8}\cdot 5^{10}\cdot 11^{3} \)	$C_3\times S_3\wr C_2$ (as 12T121)	Trivial
12.0.57027502543638528.1	x^12 - 12x^10 - 12x^9 + 54x^8 + 108x^7 - 51x^6 - 324x^5 - 261x^4 + 204x^3 + 513x^2 + 360x + 96	\( 2^{12}\cdot 3^{21}\cdot 11^{3} \)	$C_3\times S_3\wr C_2$ (as 12T121)	$[2]$
12.0.1185993841962232512.1	x^12 + 12x^10 - 3x^9 + 54x^8 - 27x^7 + 111x^6 - 81x^5 + 99x^4 - 78x^3 + 27x^2 + 9x + 12	\( 2^{6}\cdot 3^{21}\cdot 11^{6} \)	$C_3\times S_3\wr C_2$ (as 12T121)	$[2]$
12.12.10252602328798828125.1	x^12 - 30x^10 - 15x^9 + 315x^8 + 315x^7 - 1310x^6 - 2025x^5 + 1350x^4 + 4050x^3 + 2250x^2 + 225x - 25	\( 3^{16}\cdot 5^{10}\cdot 29^{3} \)	$C_3\times S_3\wr C_2$ (as 12T121)	Trivial (GRH)
12.12.2000405745576596953125.1	x^12 - 42x^10 - 21x^9 + 531x^8 + 531x^7 - 1966x^6 - 2835x^5 + 1620x^4 + 4320x^3 + 1800x^2 - 225x - 175	\( 3^{16}\cdot 5^{7}\cdot 29^{6} \)	$C_3\times S_3\wr C_2$ (as 12T121)	Trivial (GRH)