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
19.17.162...036.1	$x^{19} - 4 x^{18} - 12 x^{17} + 60 x^{16} + 46 x^{15} - 352 x^{14} - 35 x^{13} + 1037 x^{12} - 167 x^{11} - 1652 x^{10} + 409 x^{9} + 1450 x^{8} - 351 x^{7} - 696 x^{6} + 130 x^{5} + 178 x^{4} - 20 x^{3} - 22 x^{2} + x + 1$	$19$	[17,1]	$-\,2^{2}\cdot 29^{2}\cdot 48\!\cdots\!49$	$3$	$80.4941590978$				✓	$S_{19}$ (as 19T8)	trivial	$2$	$17$	$1717453570520$
19.17.830...243.1	$x^{19} - 5 x^{18} - 8 x^{17} + 71 x^{16} - 9 x^{15} - 391 x^{14} + 254 x^{13} + 1082 x^{12} - 915 x^{11} - 1650 x^{10} + 1444 x^{9} + 1428 x^{8} - 1109 x^{7} - 691 x^{6} + 400 x^{5} + 177 x^{4} - 62 x^{3} - 22 x^{2} + 3 x + 1$	$19$	[17,1]	$-\,541\cdot 919\cdot 1097\cdot 225221\cdot 232073\cdot 291356817597358517$	$6$	$87.7253606866$	$2.8819672670924815e+18$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$17$	$1494743224830$