Number field search results

Results (1-50 of 353093 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.1.29510281.1	$ x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{5} + 7 x^{4} - 8 x^{3} + 6 x^{2} + \cdots + 1 $	$9$	[1,4]	$101\cdot 292181$	$2$	$6.76078364853$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.680531134278$
9.1.30073129.1	$ x^{9} - 2 x^{8} + 2 x^{7} - x^{5} + x^{3} + x^{2} - 2 x + 1 $	$9$	[1,4]	$353\cdot 85193$	$2$	$6.77499119692$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.688991454074$
9.1.30450401.1	$ x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 2 x^{4} + x^{3} - 1 $	$9$	[1,4]	$31\cdot 982271$	$2$	$6.784382654590378$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.6943689096630966$
9.1.30453593.1	$ x^{9} - x^{7} - x^{6} + x^{4} - x^{3} + x + 1 $	$9$	[1,4]	$137\cdot 222289$	$2$	$6.7844616710304475$			not computed	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.6951489854299296$
9.1.30544313.1	$ x^{9} - x^{8} + x^{6} - 3 x^{5} + 2 x^{4} - 2 x^{2} + 2 x - 1 $	$9$	[1,4]	$47\cdot 649879$	$2$	$6.786704329211214$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.6960773498170069$
9.1.30626693.1	$ x^{9} - x^{6} - 2 x^{5} - x^{4} + 2 x^{2} + x + 1 $	$9$	[1,4]	$30626693$	$1$	$6.78873569358$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.697791262451$
9.1.30861161.1	$ x^{9} - 3 x^{8} + 5 x^{7} - 5 x^{6} + 5 x^{5} - 5 x^{4} + 5 x^{3} + \cdots - 1 $	$9$	[1,4]	$30861161$	$1$	$6.794490845023192$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.700663986552305$
9.1.31042889.1	$ x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + 2 x^{5} - 2 x^{4} + 3 x^{3} + \cdots - 1 $	$9$	[1,4]	$37\cdot 47\cdot 17851$	$3$	$6.798924787991613$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7037123132761675$
9.1.31508353.1	$ x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 2 x^{4} + 2 x^{3} - x + 1 $	$9$	[1,4]	$359\cdot 87767$	$2$	$6.8101771847288655$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7109245176713707$
9.1.31638601.1	$ x^{9} - x^{8} - 2 x^{7} + 3 x^{6} + x^{5} - 2 x^{4} + 1 $	$9$	[1,4]	$31638601$	$1$	$6.813299413387336$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7125137165211469$
9.1.31759433.1	$ x^{9} - 3 x^{5} + 2 x - 1 $	$9$	[1,4]	$179\cdot 177427$	$2$	$6.81618572777313$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7139714909872039$
9.1.32029433.1	$ x^{9} - 2 x^{8} + 3 x^{6} - x^{5} - 3 x^{4} + 3 x^{3} + x^{2} - 2 x + 1 $	$9$	[1,4]	$32029433$	$1$	$6.82260010718$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7178935503824918$
9.1.32031161.1	$ x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 5 x^{3} + \cdots - 1 $	$9$	[1,4]	$61\cdot 525101$	$2$	$6.822641004182137$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7178415555973245$
9.1.32058553.1	$ x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + x^{5} - x^{4} + x^{3} - 2 x^{2} + \cdots - 1 $	$9$	[1,4]	$32058553$	$1$	$6.823289035606978$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7183654917840255$
9.1.32206049.1	$ x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 6 x^{5} - 6 x^{4} + 5 x^{3} + \cdots - 1 $	$9$	[1,4]	$23^{3}\cdot 2647$	$2$	$6.82677001293$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.720252095298$
9.1.32344469.1	$ x^{9} - x^{7} - x^{6} + 2 x^{5} + 2 x^{4} - x^{3} - 2 x^{2} + 1 $	$9$	[1,4]	$53\cdot 89\cdot 6857$	$3$	$6.83002392654$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.722703704685$
9.1.32652713.1	$ x^{9} - 2 x^{8} + 4 x^{6} - 3 x^{5} - 2 x^{4} + 4 x^{3} - 2 x + 1 $	$9$	[1,4]	$32652713$	$1$	$6.837225741156748$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7271831373870599$
9.1.32768213.1	$ x^{9} - 2 x^{7} - x^{6} + x^{5} + 2 x^{2} + x - 1 $	$9$	[1,4]	$3413\cdot 9601$	$2$	$6.839908726808573$			not computed	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7287627479094403$
9.1.32855993.1	$ x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 3 x^{5} + x^{4} + x^{3} - x^{2} + \cdots - 1 $	$9$	[1,4]	$113\cdot 290761$	$2$	$6.841942179695031$			not computed	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.729608042282312$
9.1.32894473.1	$ x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 3 x^{4} + x^{3} + \cdots + 1 $	$9$	[1,4]	$17\cdot 1934969$	$2$	$6.842832059610452$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7304523946359703$
9.1.32923873.1	$ x^{9} - x^{8} + 3 x^{7} - 4 x^{6} + 5 x^{5} - 5 x^{4} + 5 x^{3} + \cdots - 1 $	$9$	[1,4]	$809\cdot 40697$	$2$	$6.843511334119867$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7306149370217431$
9.1.32987233.1	$ x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{6} + x^{4} - 2 x^{3} + 2 x^{2} + \cdots + 1 $	$9$	[1,4]	$32987233$	$1$	$6.844973408840747$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7315932692727032$
9.1.33121433.1	$ x^{9} + x^{7} - x^{6} - 2 x^{5} - x^{3} + x^{2} + x - 1 $	$9$	[1,4]	$1321\cdot 25073$	$2$	$6.848061939602068$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7356771671046255$
9.1.33445561.1	$ x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{4} + 5 x^{3} - 2 x^{2} - x + 1 $	$9$	[1,4]	$449\cdot 74489$	$2$	$6.855475915810484$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7400598322062453$
9.1.33571261.1	$ x^{9} - x^{8} + x^{6} + x^{5} - 2 x^{4} - 2 x^{3} + 3 x^{2} + x - 1 $	$9$	[1,4]	$43\cdot 857\cdot 911$	$3$	$6.858333950961397$			not computed	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7412699877661832$
9.1.33626161.1	$ x^{9} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 12 x^{5} - 12 x^{4} + \cdots - 1 $	$9$	[1,4]	$23\cdot 67\cdot 21821$	$3$	$6.859579226245459$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7431092993530156$
9.1.33860761.1	$ x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{5} + 2 x^{4} - x + 1 $	$9$	[1,4]	$11^{2}\cdot 23^{4}$	$2$	$6.8648802879$			✓	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T30)	trivial	$2$	$4$	$0.744153660637$
9.1.33984793.1	$ x^{9} - x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 3 x^{4} + 2 x^{2} + \cdots - 1 $	$9$	[1,4]	$33984793$	$1$	$6.867669756729682$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.74673838323778$
9.1.34090153.1	$ x^{9} - 2 x^{8} + 3 x^{7} - 2 x^{6} - x^{5} + 5 x^{4} - 6 x^{3} + \cdots + 1 $	$9$	[1,4]	$71\cdot 480143$	$2$	$6.8700321945101726$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7498544128110662$
9.1.34349041.1	$ x^{9} - x^{8} - x^{7} + 2 x^{6} - 2 x^{4} + x^{2} - 1 $	$9$	[1,4]	$34349041$	$1$	$6.8758096673688$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7514041293660256$
9.1.34405373.1	$ x^{9} - x^{8} + x^{6} - 2 x^{5} - x^{4} + 3 x^{3} + x^{2} - 2 x - 1 $	$9$	[1,4]	$34405373$	$1$	$6.87706167089583$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7526295068317561$
9.1.34573709.1	$ x^{9} - x^{8} - x^{7} + 2 x^{6} - 2 x^{4} + 2 x^{3} - x + 1 $	$9$	[1,4]	$34573709$	$1$	$6.880792184488982$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7549654984195712$
9.1.34590113.1	$ x^{9} - x^{8} + x^{7} + x^{6} - x^{4} + 2 x^{3} - 3 x^{2} + 2 x - 1 $	$9$	[1,4]	$509\cdot 67957$	$2$	$6.881154851586754$			not computed	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7592380312557747$
9.1.34628113.1	$ x^{9} - x^{6} - x^{5} + x^{4} + x^{3} + x^{2} - 1 $	$9$	[1,4]	$13\cdot 2663701$	$2$	$6.881994385964947$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7566233443489708$
9.1.35028793.1	$ x^{9} - 2 x^{8} + 4 x^{7} - 7 x^{6} + 10 x^{5} - 11 x^{4} + \cdots - 1 $	$9$	[1,4]	$23^{3}\cdot 2879$	$2$	$6.89079712201$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$4$	$0.760652964324$
9.1.35050633.1	$ x^{9} - x^{8} + x^{7} - 3 x^{6} + 3 x^{5} - 2 x^{4} + 4 x^{3} - 2 x^{2} + \cdots - 1 $	$9$	[1,4]	$43\cdot 311\cdot 2621$	$3$	$6.891274359$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7613732494747866$
9.1.35051893.1	$ x^{9} - x^{8} + 3 x^{7} - 3 x^{6} + 5 x^{5} - 5 x^{4} + 4 x^{3} + \cdots - 1 $	$9$	[1,4]	$109\cdot 321577$	$2$	$6.891301883842185$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7612088480089704$
9.1.35234033.1	$ x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 4 x^{4} + 3 x^{3} + \cdots - 1 $	$9$	[1,4]	$59\cdot 347\cdot 1721$	$3$	$6.895271529570494$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7650177657725251$
9.1.35357129.1	$ x^{9} + x^{7} - 3 x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - x^{2} + 2 x - 1 $	$9$	[1,4]	$41\cdot 862369$	$2$	$6.897944025537414$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7655906869400728$
9.1.35607973.1	$ x^{9} - 2 x^{7} + 4 x^{5} - 4 x^{3} - x^{2} + 2 x + 1 $	$9$	[1,4]	$5501\cdot 6473$	$2$	$6.903364514047256$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7698346623635847$
9.1.35666053.1	$ x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 2 x + 1 $	$9$	[1,4]	$787\cdot 45319$	$2$	$6.9046147242172875$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7697638265558684$
9.1.35678113.1	$ x^{9} - x^{8} + 3 x^{6} - 3 x^{5} + 3 x^{3} - 2 x^{2} - x + 1 $	$9$	[1,4]	$199\cdot 179287$	$2$	$6.904874096724272$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7740357851599975$
9.1.35686793.1	$ x^{9} - 2 x^{7} - 2 x^{6} + 2 x^{5} + 4 x^{4} + 2 x^{3} - 2 x^{2} + \cdots - 1 $	$9$	[1,4]	$35686793$	$1$	$6.905060727881392$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7717632848146379$
9.1.35935321.1	$ x^{9} - 2 x^{7} - x^{6} + x^{5} + 2 x^{4} - x^{2} - 1 $	$9$	[1,4]	$29\cdot 337\cdot 3677$	$3$	$6.910387355992345$			not computed	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7750794614336419$
9.1.36055441.1	$ x^{9} - x^{8} - x^{7} + x^{6} + x^{5} + x^{4} - x^{3} - 2 x^{2} + x + 1 $	$9$	[1,4]	$41\cdot 879401$	$2$	$6.912950124346879$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7771849288158317$
9.1.36155633.1	$ x^{9} - x^{8} + x^{7} - x^{6} - x^{3} + x^{2} + 1 $	$9$	[1,4]	$36155633$	$1$	$6.915081928897711$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7789574842919698$
9.1.36722413.1	$ x^{9} - x^{8} + x^{6} - x^{4} + x^{3} + x^{2} - 2 x + 1 $	$9$	[1,4]	$7^{2}\cdot 13\cdot 57649$	$3$	$6.927043458364813$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7869155967978311$
9.1.36743849.1	$ x^{9} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 13 x^{5} - 14 x^{4} + \cdots - 1 $	$9$	[1,4]	$37\cdot 71^{2}\cdot 197$	$3$	$6.927492622732046$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7848509470291687$
9.1.37009129.1	$ x^{9} - 2 x^{8} + x^{7} - x^{6} + x^{5} + x^{4} + x^{2} - 2 x + 1 $	$9$	[1,4]	$839\cdot 44111$	$2$	$6.933032038439399$			not computed	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7903392925308504$
9.1.37065113.1	$ x^{9} - x^{8} - x^{6} + x^{5} + 3 x^{4} - 2 x^{3} - 2 x^{2} + x + 1 $	$9$	[1,4]	$5849\cdot 6337$	$2$	$6.934196550406416$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7932015302763461$