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
23.19.211...793.1	$x^{23} - 2 x^{22} - 21 x^{21} + 41 x^{20} + 186 x^{19} - 354 x^{18} - 905 x^{17} + 1679 x^{16} + 2640 x^{15} - 4790 x^{14} - 4721 x^{13} + 8478 x^{12} + 5041 x^{11} - 9294 x^{10} - 2890 x^{9} + 6142 x^{8} + 560 x^{7} - 2310 x^{6} + 194 x^{5} + 432 x^{4} - 99 x^{3} - 26 x^{2} + 11 x - 1$	$23$	[19,2]	$3^{2}\cdot 31\cdot 61\cdot 12200617224119\cdot 101917126957405185189830413$	$5$	$76.5103398382$	$2.65595601828885e+21$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$20$	$288525695460000$
23.19.143...772.1	$x^{23} - 2 x^{22} - 21 x^{21} + 37 x^{20} + 191 x^{19} - 284 x^{18} - 982 x^{17} + 1173 x^{16} + 3122 x^{15} - 2833 x^{14} - 6321 x^{13} + 4080 x^{12} + 8142 x^{11} - 3423 x^{10} - 6534 x^{9} + 1539 x^{8} + 3140 x^{7} - 283 x^{6} - 847 x^{5} - 17 x^{4} + 115 x^{3} + 12 x^{2} - 6 x - 1$	$23$	[19,2]	$2^{2}\cdot 35\!\cdots\!93$	$2$	$101.591150149$	$9.516982163844924e+22$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$20$	$9532691492330000$