Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (unique match)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
6.0.706...744.1	$x^{6} - 84462 x^{4} - 28154 x^{3} + 1809682812 x^{2} - 2430140664 x + 125057534140$	$6$	[0,3]	$-\,2^{4}\cdot 3^{8}\cdot 7^{5}\cdot 23^{3}\cdot 2011^{5}$	$5$	$94363.494095689$	$94363.494095689$			?	$S_3\times C_3$ (as 6T5)	$[3, 3, 3, 6, 270412464]$	$2$	$2$	$289.12955934891767$
6.0.157...992.1	$x^{6} - 77226 x^{4} - 25742 x^{3} + 1513899891 x^{2} - 2033592258 x + 100075410073$	$6$	[0,3]	$-\,2^{9}\cdot 3^{8}\cdot 11^{3}\cdot 61^{5}\cdot 211^{5}$	$5$	$107914.52851802012$	$107914.52851802012$			?	$S_3\times C_3$ (as 6T5)	$[3, 6, 6, 138560940]$	$2$	$2$	$285.1255178139885$
6.0.676...728.1	$x^{6} - 660102 x^{4} - 220034 x^{3} + 109503990729 x^{2} - 146383559418 x + 21036679850881$	$6$	[0,3]	$-\,2^{6}\cdot 3^{8}\cdot 110017^{5}$	$3$	$137533.3961044407$	$137533.3961044407$			?	$S_3\times C_3$ (as 6T5)	$[3, 5369285196]$	$2$	$2$	$388.8415933157587$
6.0.115...000.1	$x^{6} + 9042250$	$6$	[0,3]	$-\,2^{11}\cdot 3^{6}\cdot 5^{3}\cdot 7^{5}\cdot 5167^{5}$	$5$	$150351.6967514922$	$180562.90890228277$			?	$D_{6}$ (as 6T3)	$[2, 2, 6, 12, 36, 5313384]$	$2$	$2$	$376.84541505563385$