Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (10 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
13.5.28261626739249.1	$x^{13} - 3 x^{12} + 3 x^{11} + 3 x^{10} - 13 x^{9} + 14 x^{8} + 2 x^{7} - 20 x^{6} + 18 x^{5} + x^{4} - 11 x^{3} + 6 x^{2} + x - 1$	$13$	[5,4]	$2161\cdot 13078031809$	$2$	$10.8319706242$	$5316166.545477013$			?	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$33.0726626498$
13.5.28318356165577.1	$x^{13} - 3 x^{11} - 4 x^{10} + 2 x^{9} + 9 x^{8} + 6 x^{7} - 4 x^{6} - 10 x^{5} - 3 x^{4} + 4 x^{3} + 4 x^{2} - 1$	$13$	[5,4]	$1721\cdot 16454593937$	$2$	$10.8336416122$	$5321499.428316891$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$33.1184429974$
13.5.132939170094109.1	$x^{13} - x^{12} - x^{11} - 3 x^{10} + x^{9} + 5 x^{8} + 5 x^{7} + 3 x^{6} - 7 x^{5} - 7 x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1$	$13$	[5,4]	$132939170094109$	$1$	$12.2021074028$	$11529924.982154436$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$84.1149437602$
13.5.197683647463424.1	$x^{13} - 2 x^{12} + x^{11} - 3 x^{10} - 5 x^{9} + 7 x^{8} + 2 x^{7} + 6 x^{6} + 4 x^{5} - 6 x^{4} - 8 x^{3} + 6 x - 2$	$13$	[5,4]	$2^{14}\cdot 12065652311$	$2$	$12.5802727589$	$549595.2837715879$			?	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$173.327894786$
13.5.1204994394291500.1	$x^{13} - 3 x^{12} + 2 x^{10} + 6 x^{9} - 9 x^{7} - 3 x^{6} + x^{5} + 4 x^{4} - 8 x^{3} - 3 x^{2} + 3 x + 1$	$13$	[5,4]	$2^{2}\cdot 5^{3}\cdot 83\cdot 11171\cdot 2599231$	$5$	$14.4569197834$	$10381617.17294946$			?	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$546.676164956$
13.5.5020153876560896.1	$x^{13} - 4 x^{12} + 13 x^{10} + 6 x^{9} - 39 x^{8} - 16 x^{7} + 54 x^{6} + 45 x^{5} - 47 x^{4} - 48 x^{3} + 9 x^{2} + 24 x + 4$	$13$	[5,4]	$2^{10}\cdot 83\cdot 173\cdot 341423081$	$4$	$16.1342010261$	$8856630.528664047$			?	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$1981.72650066$
13.5.5749519947196921.1	$x^{13} - 2 x^{12} - 3 x^{11} + 7 x^{10} + 5 x^{9} - 16 x^{8} - 6 x^{7} + 18 x^{6} + 2 x^{5} - 16 x^{4} - 4 x^{3} + 7 x^{2} + x - 1$	$13$	[5,4]	$7^{4}\cdot 241^{2}\cdot 6421^{2}$	$3$	$16.3034438732$	$27143.05132536518$			?	$A_{13}$ (as 13T8)	trivial	$2$	$8$	$838.358604129$
13.5.274918279650903001.1	$x^{13} - 3 x^{11} - 2 x^{10} + 2 x^{9} + 4 x^{8} - 2 x^{7} - 3 x^{6} - x^{5} + 3 x^{4} - 4 x^{2} + 1$	$13$	[5,4]	$47^{2}\cdot 89^{2}\cdot 163^{2}\cdot 769^{2}$	$4$	$21.9521570645$	$101667.42283652654$			?	$A_{13}$ (as 13T8)	trivial	$2$	$8$	$12272.0363797$
13.5.842...704.1	$x^{13} - x^{12} - 3 x^{11} - 7 x^{10} + 37 x^{9} - 9 x^{8} - 168 x^{7} + 24 x^{6} + 396 x^{5} + 20 x^{4} - 128 x^{3} + 192 x^{2} - 176 x - 16$	$13$	[5,4]	$2^{28}\cdot 3^{22}$	$2$	$28.563292541$	$90.51754317479573$				$\PSL(3,3)$ (as 13T7)	trivial	$2$	$8$	$185892.213477$
13.5.842...704.2	$x^{13} - 2 x^{12} - 8 x^{10} + 55 x^{9} - 90 x^{8} - 108 x^{7} + 684 x^{6} - 1341 x^{5} + 1526 x^{4} - 1090 x^{3} + 468 x^{2} - 100 x + 8$	$13$	[5,4]	$2^{28}\cdot 3^{22}$	$2$	$28.563292541$	$90.51754317479573$				$\PSL(3,3)$ (as 13T7)	trivial	$2$	$8$	$185892.213477$