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 9 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.32293067924601.1	x^12 - x^11 - x^10 + 3x^8 - 4x^6 - x^5 + 4x^4 + x^3 - 2x^2 + 1	\( 3^{4}\cdot 11^{2}\cdot 61^{2}\cdot 941^{2} \)	$A_{12}$ (as 12T300)	Trivial
12.0.327636933353536.1	x^12 - 2x^11 + 2x^10 - 3x^9 + 4x^8 - 5x^7 + 5x^6 - 4x^5 + 6x^4 - 3x^3 + x^2 - 2x + 1	\( 2^{6}\cdot 2262593^{2} \)	$A_{12}$ (as 12T300)	Trivial
12.4.584769075636001.1	x^12 - 5x^11 + 10x^10 - 7x^9 - 9x^8 + 28x^7 - 32x^6 + 11x^5 + 15x^4 - 26x^3 + 19x^2 - 7x + 1	\( 24181999^{2} \)	$A_{12}$ (as 12T300)	Trivial
12.4.37295073688455625.1	x^12 - 4x^11 + 6x^10 - 6x^9 + 5x^8 + x^7 - 9x^6 + 11x^5 - 7x^4 + x^3 + 4x^2 - 5x + 1	\( 5^{4}\cdot 7^{2}\cdot 19^{2}\cdot 241^{4} \)	$A_{12}$ (as 12T300)	Trivial
12.8.94768777961133151657570669707264.1	x^12 - 2x^11 + 43x^10 + 30x^9 - 480x^8 + 384x^7 + 2604x^6 + 48x^5 - 3840x^4 - 2170x^3 + 191x^2 + 254x + 21	\( 2^{14}\cdot 3^{16}\cdot 11591846801^{2} \)	$A_{12}$ (as 12T300)	Trivial (GRH)
12.8.1983953888340397738015626127097856.1	x^12 - 138x^10 - 1000x^9 - 345x^8 + 14880x^7 + 33012x^6 - 36720x^5 - 121905x^4 + 7200x^3 + 83862x^2 + 5400x - 5751	\( 2^{14}\cdot 3^{10}\cdot 7^{8}\cdot 596427121^{2} \)	$A_{12}$ (as 12T300)	Trivial (GRH)
12.12.12030640053495428917361789703369140625.1	x^12 - 864x^10 - 16920x^9 - 138510x^8 - 527796x^7 - 561330x^6 + 2519424x^5 + 10235160x^4 + 15943230x^3 + 11868849x^2 + 3542940x + 59049	\( 3^{28}\cdot 5^{18}\cdot 13^{10} \)	$A_{12}$ (as 12T300)	Trivial (GRH)
12.12.80395305020560195610021041260875524780564497501562500000000.1	x^12 - 64290x^10 - 1521160x^9 + 1413391275x^8 + 55149567840x^7 - 11816325894450x^6 - 551549392646400x^5 + 24196102698409425x^4 + 906390235169823000x^3 + 9912416687818565400x^2 + 43526001864084588000x + 64178007246927738000	\( 2^{8}\cdot 3^{16}\cdot 5^{14}\cdot 7^{8}\cdot 137^{6}\cdot 5599914953^{2} \)	$A_{12}$ (as 12T300)	$[2, 4]$ (GRH)
12.12.124220674037581049430090394518362216959104955545802500000000.1	x^12 - 43095x^10 - 150220x^9 + 579490200x^8 - 466244190x^7 - 3123608892765x^6 + 7515402970950x^5 + 7206776378221275x^4 - 9062974515513700x^3 - 5991420705430217400x^2 - 10416503841795589200x + 11016133065262452400	\( 2^{8}\cdot 3^{20}\cdot 5^{10}\cdot 31^{6}\cdot 43^{6}\cdot 347^{2}\cdot 145242751^{2} \)	$A_{12}$ (as 12T300)	$[2, 4]$ (GRH)