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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator
3.1.972.1	$x^{3} - 12$	$3$	[1,1]	$-\,2^{2}\cdot 3^{5}$	$2$	$9.90578174668$	$11.896219369500566$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$5.10583548555$
3.1.972.2	$x^{3} - 6$	$3$	[1,1]	$-\,2^{2}\cdot 3^{5}$	$2$	$9.90578174668$	$11.896219369500566$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$5.78993214232$

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