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
27.27.274...441.1	$x^{27} - 9 x^{26} - 45 x^{25} + 558 x^{24} + 564 x^{23} - 14325 x^{22} + 3278 x^{21} + 200187 x^{20} - 152250 x^{19} - 1689790 x^{18} + 1662003 x^{17} + 9058716 x^{16} - 9244050 x^{15} - 31587348 x^{14} + 28970679 x^{13} + 71864499 x^{12} - 50585529 x^{11} - 103930188 x^{10} + 44676536 x^{9} + 88142967 x^{8} - 15697422 x^{7} - 37059379 x^{6} + 2104236 x^{5} + 7157724 x^{4} - 134797 x^{3} - 528300 x^{2} + 16716 x + 7064$	$27$	[27,0]	$3^{36}\cdot 7^{18}\cdot 13^{18}$	$3$	$87.5365180904$	$87.5365180904025$		✓		$C_3^3$ (as 27T4)	trivial	$2$	$26$	$1149187264584812300$
27.27.254...689.1	$x^{27} - 9 x^{26} - 63 x^{25} + 774 x^{24} + 834 x^{23} - 26013 x^{22} + 24482 x^{21} + 438771 x^{20} - 917742 x^{19} - 3954764 x^{18} + 12493773 x^{17} + 17637390 x^{16} - 89943576 x^{15} - 16499340 x^{14} + 367102377 x^{13} - 183437513 x^{12} - 838172511 x^{11} + 827108970 x^{10} + 967374964 x^{9} - 1484013339 x^{8} - 364627638 x^{7} + 1223353523 x^{6} - 171844968 x^{5} - 419177382 x^{4} + 123185675 x^{3} + 52146132 x^{2} - 17057376 x - 1145024$	$27$	[27,0]	$3^{36}\cdot 7^{18}\cdot 19^{18}$	$3$	$112.736037753$	$112.7360377530179$		✓		$C_3^3$ (as 27T4)	$[2, 2]$	$2$	$26$	$8214137232374256000$