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
23.7.484...792.1	$x^{23} - 3 x^{21} - 6 x^{20} + x^{19} + 17 x^{18} + 18 x^{17} - 10 x^{16} - 43 x^{15} - 25 x^{14} + 33 x^{13} + 60 x^{12} + 11 x^{11} - 54 x^{10} - 48 x^{9} + 12 x^{8} + 44 x^{7} + 17 x^{6} - 17 x^{5} - 16 x^{4} + 6 x^{2} + x - 1$	$23$	[7,8]	$2^{3}\cdot 3^{2}\cdot 4231\cdot 4210631\cdot 3775042239237949162501$	$5$	$29.1452075964$	$4.017553168705311e+16$			✓	$S_{23}$ (as 23T7)	trivial	$2$	$14$	$179256140.602$
23.7.437...528.1	$x^{23} - 3 x^{22} + 4 x^{20} + 5 x^{19} - 5 x^{18} - 14 x^{17} + 4 x^{16} + 15 x^{15} + 10 x^{14} - 22 x^{13} - 13 x^{12} + 16 x^{11} + 18 x^{10} - 3 x^{9} - 23 x^{8} + x^{7} + 13 x^{6} + 4 x^{5} - 7 x^{4} - 4 x^{3} + 5 x^{2} + x - 1$	$23$	[7,8]	$2^{4}\cdot 17\cdot 241\cdot 1709\cdot 3877\cdot 111868093\cdot 346250347\cdot 25983511363$	$8$	$47.8659710754$				✓	$S_{23}$ (as 23T7)	trivial	$2$	$14$	$78508567076.1$