Number field search results

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

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
19.7.105...804.1	$x^{19} - 3 x^{18} - x^{17} + 15 x^{16} - 22 x^{15} - 6 x^{14} + 59 x^{13} - 70 x^{12} - 6 x^{11} + 106 x^{10} - 107 x^{9} + 92 x^{7} - 73 x^{6} - x^{5} + 35 x^{4} - 19 x^{3} - x^{2} + 4 x - 1$	$19$	[7,6]	$2^{2}\cdot 131\cdot 149\cdot 397\cdot 20117\cdot 218819\cdot 773146117559$	$7$	$33.6928527152$	$324794707032692.7$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$12$	$52861133.6694$
19.7.832...904.1	$x^{19} - 3 x^{18} - x^{17} + 15 x^{16} - 22 x^{15} - 6 x^{14} + 59 x^{13} - 70 x^{12} - 6 x^{11} + 106 x^{10} - 107 x^{9} - x^{8} + 92 x^{7} - 72 x^{6} - x^{5} + 35 x^{4} - 19 x^{3} - x^{2} + 4 x - 1$	$19$	[7,6]	$2^{10}\cdot 2746819\cdot 2958679616604904629509$	$3$	$42.4014216337$	$254981683825377.03$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$12$	$409832342.529$