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
12.4.6306188441142951936.1	x^12 - 12x^10 - 8x^9 + 21x^8 + 36x^7 + 192x^6 + 240x^5 - 84x^4 - 68x^3 - 72x^2 - 48x + 5	\( 2^{24}\cdot 3^{12}\cdot 29^{4} \)	$M_{12}$ (as 12T295)	Trivial
12.4.6306188441142951936.2	x^12 - 16x^10 - 36x^9 + 111x^8 + 372x^7 - 204x^6 - 1500x^5 - 384x^4 + 2200x^3 + 1404x^2 - 688x + 21	\( 2^{24}\cdot 3^{12}\cdot 29^{4} \)	$M_{12}$ (as 12T295)	Trivial
12.0.9440732714731831296.1	x^12 - 4x^11 + 4x^10 + 12x^9 - 72x^8 + 168x^7 - 132x^6 - 324x^5 + 1197x^4 - 1752x^3 + 1500x^2 - 672x + 207	\( 2^{24}\cdot 3^{14}\cdot 7^{6} \)	$M_{12}$ (as 12T295)	Trivial (GRH)
12.0.84966594432586481664.1	x^12 + 18x^10 - 12x^9 + 189x^8 - 288x^7 + 1458x^6 - 2796x^5 + 7092x^4 - 11988x^3 + 17010x^2 - 19404x + 10185	\( 2^{24}\cdot 3^{16}\cdot 7^{6} \)	$M_{12}$ (as 12T295)	$[2]$ (GRH)
12.12.111534324540107369492059712937081339641856.1	x^12 - 968x^10 + 346060x^8 - 56221440x^6 + 4128059232x^4 - 247374336x^3 - 114286943232x^2 + 19295198208x + 632319724608	\( 2^{24}\cdot 3^{8}\cdot 11^{20}\cdot 197^{4} \)	$M_{12}$ (as 12T295)	Trivial (GRH)
12.12.1003808920860966325428537416433732056776704.1	x^12 - 4x^11 - 3036x^10 + 16940x^9 + 3435883x^8 - 21476268x^7 - 1841908992x^6 + 11122519452x^5 + 490521018900x^4 - 2361270759804x^3 - 62489273434236x^2 + 167503033069380x + 3005497215363897	\( 2^{24}\cdot 3^{10}\cdot 11^{20}\cdot 197^{4} \)	$M_{12}$ (as 12T295)	Trivial (GRH)