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
12.4.248155780267521.1	x^12 - 5x^9 + 9x^8 - 9x^7 + 9x^6 + 9x^5 - 36x^4 + 55x^3 - 54x^2 + 27x - 5	\( 3^{16}\cdot 7^{8} \)	$PSU(3,2):C_2$ (as 12T84)	Trivial
12.4.722204136308736.1	x^12 - 6x^11 + 12x^10 + 2x^9 - 39x^8 + 36x^7 + 24x^6 - 24x^5 - 48x^4 + 32x^3 + 24x^2 - 8	\( 2^{24}\cdot 3^{16} \)	$PSU(3,2):C_2$ (as 12T84)	Trivial
12.4.3143861048180736.1	x^12 - 8x^10 - 8x^9 + 9x^8 + 12x^7 + 10x^6 + 24x^5 + 10x^4 - 4x^3 - 8x - 2	\( 2^{24}\cdot 3^{8}\cdot 13^{4} \)	$PSU(3,2):C_2$ (as 12T84)	Trivial
12.4.4057816381784064.1	x^12 - 4x^11 + 4x^10 + 8x^9 - 23x^8 + 8x^7 + 28x^6 - 40x^5 + x^4 + 36x^3 - 24x^2 + 9	\( 2^{36}\cdot 3^{10} \)	$PSU(3,2):C_2$ (as 12T84)	Trivial
12.12.18591282024274722816.1	x^12 - 24x^10 - 4x^9 + 207x^8 + 72x^7 - 780x^6 - 360x^5 + 1215x^4 + 488x^3 - 684x^2 - 84x + 97	\( 2^{28}\cdot 3^{12}\cdot 19^{4} \)	$PSU(3,2):C_2$ (as 12T84)	Trivial
12.12.30047698576998400000000.1	x^12 - 4x^11 - 24x^10 + 120x^9 + 98x^8 - 1088x^7 + 984x^6 + 2496x^5 - 5578x^4 + 3992x^3 - 1064x^2 + 64x + 4	\( 2^{38}\cdot 5^{8}\cdot 23^{4} \)	$PSU(3,2):C_2$ (as 12T84)	$[2]$ (GRH)