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
9.3.714...803.1	$x^{9} - 1083 x^{6} - 34901267010 x^{3} - 47045881$	$9$	[3,3]	$-\,3^{13}\cdot 7^{6}\cdot 13^{6}\cdot 19^{6}\cdot 109^{6}$	$5$	$16069.023030079186$	$17080.328125914075$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 9, 45, 1311570]$	$2$	$5$	$624601.983318254$
9.3.129...128.1	$x^{9} - 1290 x^{6} - 693384 x^{3} - 79507000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 37^{6}\cdot 937^{6}$	$4$	$17162.09055848005$	$18242.18793617888$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 18, 2106, 4212]$	$2$	$5$	$1018216.3548909103$
9.3.256...112.1	$x^{9} - 22953 x^{7} - 772751 x^{6} + 176761053 x^{5} + 11940931002 x^{4} - 254776280136 x^{3} - 46438330222305 x^{2} - 1576314861611553 x - 17864614168714621$	$9$	[3,3]	$-\,2^{6}\cdot 3^{12}\cdot 7^{7}\cdot 17^{3}\cdot 1093^{7}$	$5$	$18521.13894581099$	$48809.53074800336$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 311317038]$	$2$	$5$	$500611.7956937643$
9.3.354...523.1	$x^{9} - 55125 x^{6} - 1266200964 x^{3} - 6204146484375$	$9$	[3,3]	$-\,3^{19}\cdot 7^{6}\cdot 11719^{6}$	$3$	$19197.663648155085$	$20405.86996157946$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 18, 108, 418068]$	$2$	$5$	$670673.5113762561$
9.3.428...107.1	$x^{9} - 56007 x^{6} - 1307041974 x^{3} - 6506735712309$	$9$	[3,3]	$-\,3^{19}\cdot 7^{6}\cdot 12097^{6}$	$3$	$19608.29336818753$	$20842.342691955022$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 27, 27, 213462]$	$2$	$5$	$676965.492731745$
9.3.100...232.1	$x^{9} - 294 x^{6} - 5423916624 x^{3} - 941192$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 7^{6}\cdot 13^{6}\cdot 1609^{6}$	$5$	$21557.25374687955$	$22913.96102930838$			?	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 234, 1027026]$	$2$	$5$	$841839.7155778112$
9.3.115...688.1	$x^{9} - 294 x^{6} - 5554607856 x^{3} - 941192$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 7^{6}\cdot 31^{6}\cdot 691^{6}$	$5$	$21902.162507048793$	$23280.576646584264$			?	$S_3\times C_3$ (as 9T4)	$[6, 6, 18, 36, 859068]$	$2$	$5$	$847493.9055073519$
9.3.413...232.1	$x^{9} - 10332 x^{6} - 44479584 x^{3} - 40849752384$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 163^{6}\cdot 379^{6}$	$4$	$25224.76848150728$	$26812.29106199348$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 21, 126, 208278]$	$2$	$5$	$1254920.5203087274$
9.3.449...808.1	$x^{9} - 10404 x^{6} - 45101664 x^{3} - 41709719232$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 37^{6}\cdot 1693^{6}$	$4$	$25459.41580639492$	$27061.705932794695$			?	$S_3\times C_3$ (as 9T4)	$[2, 6, 6, 6, 6, 18, 54, 8694]$	$2$	$5$	$1259454.4509814582$
9.3.165...747.1	$x^{9} - 1587 x^{6} - 106360847916 x^{3} - 148035889$	$9$	[3,3]	$-\,3^{15}\cdot 7^{6}\cdot 23^{6}\cdot 2011^{6}$	$4$	$29423.48128223111$	$31275.250148466665$			?	$S_3\times C_3$ (as 9T4)	$[6, 6, 18, 90029340]$	$2$	$5$	$721493.8747397298$