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
19.13.801...664.1	$x^{19} - 2 x^{18} - 18 x^{17} + 32 x^{16} + 132 x^{15} - 202 x^{14} - 502 x^{13} + 645 x^{12} + 1045 x^{11} - 1122 x^{10} - 1176 x^{9} + 1078 x^{8} + 700 x^{7} - 557 x^{6} - 220 x^{5} + 151 x^{4} + 34 x^{3} - 20 x^{2} - 2 x + 1$	$19$	[13,3]	$-\,2^{3}\cdot 13^{2}\cdot 17\cdot 3229\cdot 34365587\cdot 85132367\cdot 3692009831$	$7$	$53.9247520599$	$1.2041290670651694e+16$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$15$	$23798894722.8$
19.13.610...484.1	$x^{19} - 3 x^{18} - 12 x^{17} + 40 x^{16} + 52 x^{15} - 216 x^{14} - 88 x^{13} + 614 x^{12} + 8 x^{11} - 987 x^{10} + 143 x^{9} + 904 x^{8} - 163 x^{7} - 461 x^{6} + 72 x^{5} + 128 x^{4} - 14 x^{3} - 18 x^{2} + x + 1$	$19$	[13,3]	$-\,2^{2}\cdot 90313\cdot 16881409121807\cdot 1000636759045331$	$4$	$60.0045203941$	$7.811738632783035e+16$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$15$	$61782008553.5$