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
19.9.159...156.1	$x^{19} - 3 x^{18} - 8 x^{17} + 30 x^{16} + 16 x^{15} - 115 x^{14} + 31 x^{13} + 208 x^{12} - 175 x^{11} - 165 x^{10} + 280 x^{9} + 5 x^{8} - 206 x^{7} + 82 x^{6} + 75 x^{5} - 54 x^{4} - 13 x^{3} + 13 x^{2} + x - 1$	$19$	[9,5]	$-\,2^{2}\cdot 937\cdot 971\cdot 4676220259\cdot 93910895860973$	$5$	$38.8744917393$				✓	$S_{19}$ (as 19T8)	trivial	$2$	$13$	$222480440.47$
19.9.138...476.1	$x^{19} - 2 x^{18} - 14 x^{17} + 23 x^{16} + 83 x^{15} - 104 x^{14} - 274 x^{13} + 234 x^{12} + 555 x^{11} - 274 x^{10} - 708 x^{9} + 162 x^{8} + 554 x^{7} - 50 x^{6} - 246 x^{5} + 17 x^{4} + 56 x^{3} - 7 x^{2} - 5 x + 1$	$19$	[9,5]	$-\,2^{2}\cdot 34\!\cdots\!19$	$2$	$55.505833971$	$2.9571521810644656e+16$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$13$	$8259829376.29$