Number field search results

Results (displaying both matches)

 

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
19.5.896...328.1	$x^{19} - 2 x^{18} - 3 x^{17} + 9 x^{16} + x^{15} - 16 x^{14} + 5 x^{13} + 17 x^{12} - 10 x^{11} - 12 x^{10} + 10 x^{9} + x^{8} + 3 x^{6} - 9 x^{5} + 2 x^{4} + 6 x^{3} - 5 x^{2} - x + 1$	$19$	[5,7]	$-\,2^{4}\cdot 3947\cdot 1431584761\cdot 99216821342546749$	$4$	$42.5690720688$				✓	$S_{19}$ (as 19T8)	trivial	$2$	$11$	$363184844.905$
19.5.239...200.1	$x^{19} - x^{18} - 6 x^{17} + 7 x^{16} + 13 x^{15} - 21 x^{14} - 16 x^{13} + 41 x^{12} + 10 x^{11} - 51 x^{10} + 5 x^{9} + 43 x^{8} - 19 x^{7} - 24 x^{6} + 18 x^{5} + 5 x^{4} - 11 x^{3} + 2 x^{2} + 3 x - 1$	$19$	[5,7]	$-\,2^{3}\cdot 5^{2}\cdot 430709\cdot 19005923\cdot 14610723851226353$	$5$	$44.824396879$				✓	$S_{19}$ (as 19T8)	trivial	$2$	$11$	$840306267.085$