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
12.0.406239826673664.1	x^12 - 6x^11 + 18x^10 - 32x^9 + 27x^8 - 18x^6 + 45x^4 - 38x^3 + 12x^2 + 1	\( 2^{20}\cdot 3^{18} \)	$S_3\times A_4$ (as 12T43)	Trivial
12.0.489631389843456.1	x^12 + 4x^10 - 6x^9 + x^8 - 16x^7 + 22x^6 - 12x^5 + 27x^4 + 12x^3 + 14x^2 + 2x + 1	\( 2^{20}\cdot 3^{4}\cdot 7^{8} \)	$S_3\times A_4$ (as 12T43)	$[3]$
12.4.41753392563387961.1	x^12 - 4x^11 + 6x^10 - 11x^9 + 5x^8 - 19x^7 - 4x^6 - 27x^5 + 90x^4 + 92x^3 - 129x^2 + 101x - 29	\( 19^{6}\cdot 31^{6} \)	$S_3\times A_4$ (as 12T43)	Trivial
12.4.223580268118933504.1	x^12 - 4x^11 - 2x^10 + 40x^9 - 118x^8 + 222x^7 - 322x^6 + 456x^5 - 620x^4 + 436x^3 + 299x^2 - 738x + 353	\( 2^{18}\cdot 31^{8} \)	$S_3\times A_4$ (as 12T43)	Trivial
12.0.231203843592945664.1	x^12 + 8x^10 - 14x^9 + 32x^8 - 20x^7 + 26x^6 + 28x^4 + 4x^3 + 4x^2 - 4x + 2	\( 2^{20}\cdot 7^{6}\cdot 37^{4} \)	$S_3\times A_4$ (as 12T43)	Trivial
12.0.349064245382494464.1	x^12 + 5x^10 - 15x^9 + 45x^8 - 50x^7 + 108x^6 - 123x^5 + 143x^4 - 61x^3 + 36x^2 + 8x + 10	\( 2^{8}\cdot 3^{12}\cdot 37^{6} \)	$S_3\times A_4$ (as 12T43)	$[2]$
12.12.20706359771987105161.1	x^12 - 4x^11 - 17x^10 + 82x^9 + 19x^8 - 414x^7 + 336x^6 + 516x^5 - 645x^4 - 172x^3 + 344x^2 - 43	\( 11^{6}\cdot 43^{8} \)	$S_3\times A_4$ (as 12T43)	Trivial
12.12.1592978333150141614336.1	x^12 - 2x^11 - 43x^10 + 41x^9 + 601x^8 - 128x^7 - 3194x^6 - 489x^5 + 6471x^4 + 2179x^3 - 3462x^2 - 884x + 278	\( 2^{8}\cdot 11^{6}\cdot 37^{8} \)	$S_3\times A_4$ (as 12T43)	Trivial (GRH)