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
19.15.576...912.1	$x^{19} - 4 x^{18} - 9 x^{17} + 54 x^{16} + 4 x^{15} - 273 x^{14} + 190 x^{13} + 657 x^{12} - 794 x^{11} - 749 x^{10} + 1408 x^{9} + 239 x^{8} - 1230 x^{7} + 266 x^{6} + 485 x^{5} - 243 x^{4} - 42 x^{3} + 54 x^{2} - 13 x + 1$	$19$	[15,2]	$2^{3}\cdot 5783\cdot 631751\cdot 4586531\cdot 15400183\cdot 279342423421$	$6$	$76.2350234722$				?	$S_{19}$ (as 19T8)	trivial	$2$	$16$	$548628216242$
19.15.136...521.1	$x^{19} - 4 x^{18} - 12 x^{17} + 58 x^{16} + 55 x^{15} - 343 x^{14} - 118 x^{13} + 1061 x^{12} + 109 x^{11} - 1835 x^{10} - 10 x^{9} + 1773 x^{8} - 31 x^{7} - 924 x^{6} - 9 x^{5} + 247 x^{4} + 14 x^{3} - 29 x^{2} - 2 x + 1$	$19$	[15,2]	$37\cdot 12871711399\cdot 28730995145192693176301867$	$3$	$90.0608925355$	$3.69908527550456e+18$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$16$	$3037570713740$