Number field search results

Results (1-50 of 3544 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
9.1.29510281.1	$x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{5} + 7 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$	$9$	[1,4]	$101\cdot 292181$	$2$	$6.76078364853$	$5432.3366059183045$			✓	$S_9$ (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]	$353\cdot 85193$	$2$	$6.77499119692$	$5483.897245572714$			✓	$S_9$ (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]	$31\cdot 982271$	$2$	$6.784382654590378$	$5518.188199037797$			✓	$S_9$ (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]	$137\cdot 222289$	$2$	$6.7844616710304475$	$5518.477416824318$			?	$S_9$ (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]	$47\cdot 649879$	$2$	$6.786704329211214$	$5526.690962954234$			✓	$S_9$ (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]	$30626693$	$1$	$6.78873569358$	$5534.138867068661$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.697791262451$
9.1.30861161.1	$x^{9} - 3 x^{8} + 5 x^{7} - 5 x^{6} + 5 x^{5} - 5 x^{4} + 5 x^{3} - 4 x^{2} + 3 x - 1$	$9$	[1,4]	$30861161$	$1$	$6.794490845023192$	$5555.282261055689$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.700663986552305$
9.1.31042889.1	$x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + 2 x^{5} - 2 x^{4} + 3 x^{3} - 3 x^{2} + 3 x - 1$	$9$	[1,4]	$37\cdot 47\cdot 17851$	$3$	$6.798924787991613$	$5571.614577481109$			✓	$S_9$ (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]	$359\cdot 87767$	$2$	$6.8101771847288655$	$5613.230175219968$			✓	$S_9$ (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]	$31638601$	$1$	$6.813299413387336$	$5624.82008601164$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7125137165211469$
9.1.31759433.1	$x^{9} - 3 x^{5} + 2 x - 1$	$9$	[1,4]	$179\cdot 177427$	$2$	$6.81618572777313$	$5635.5508160249965$			✓	$S_9$ (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]	$32029433$	$1$	$6.82260010718$	$5659.455185793064$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7178935503824918$
9.1.32031161.1	$x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 5 x^{3} - 5 x^{2} + 3 x - 1$	$9$	[1,4]	$61\cdot 525101$	$2$	$6.822641004182137$	$5659.607848605767$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7178415555973245$
9.1.32058553.1	$x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + x^{5} - x^{4} + x^{3} - 2 x^{2} + 2 x - 1$	$9$	[1,4]	$32058553$	$1$	$6.823289035606978$	$5662.027287111923$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7183654917840255$
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]	$53\cdot 89\cdot 6857$	$3$	$6.83002392654$	$5687.219795295413$			✓	$S_9$ (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]	$32652713$	$1$	$6.837225741156748$	$5714.255244561622$			✓	$S_9$ (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]	$3413\cdot 9601$	$2$	$6.839908726808573$	$5724.352627153572$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7287627479094403$
9.1.32855993.1	$x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 3 x^{5} + x^{4} + x^{3} - x^{2} - 1$	$9$	[1,4]	$113\cdot 290761$	$2$	$6.841942179695031$	$5732.014741781462$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.729608042282312$
9.1.32894473.1	$x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 3 x^{4} + x^{3} + x^{2} - 2 x + 1$	$9$	[1,4]	$17\cdot 1934969$	$2$	$6.842832059610452$	$5735.370345496444$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7304523946359703$
9.1.32923873.1	$x^{9} - x^{8} + 3 x^{7} - 4 x^{6} + 5 x^{5} - 5 x^{4} + 5 x^{3} - 4 x^{2} + 2 x - 1$	$9$	[1,4]	$809\cdot 40697$	$2$	$6.843511334119867$	$5737.932815918987$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7306149370217431$
9.1.32987233.1	$x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{6} + x^{4} - 2 x^{3} + 2 x^{2} + 1$	$9$	[1,4]	$32987233$	$1$	$6.844973408840747$	$5743.4513143231225$			✓	$S_9$ (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]	$1321\cdot 25073$	$2$	$6.848061939602068$	$5755.122327109998$			✓	$S_9$ (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]	$449\cdot 74489$	$2$	$6.855475915810484$	$5783.213725948575$			✓	$S_9$ (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]	$43\cdot 857\cdot 911$	$3$	$6.858333950961397$	$5794.071193901573$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7412699877661832$
9.1.33626161.1	$x^{9} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 12 x^{5} - 12 x^{4} + 11 x^{3} - 8 x^{2} + 4 x - 1$	$9$	[1,4]	$23\cdot 67\cdot 21821$	$3$	$6.859579226245459$	$5798.80686003595$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7431092993530156$
9.1.33984793.1	$x^{9} - x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 3 x^{4} + 2 x^{2} - x - 1$	$9$	[1,4]	$33984793$	$1$	$6.867669756729682$	$5829.647759513434$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.74673838323778$
9.1.34090153.1	$x^{9} - 2 x^{8} + 3 x^{7} - 2 x^{6} - x^{5} + 5 x^{4} - 6 x^{3} + 5 x^{2} - 3 x + 1$	$9$	[1,4]	$71\cdot 480143$	$2$	$6.8700321945101726$	$5838.677333095227$			✓	$S_9$ (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]	$34349041$	$1$	$6.8758096673688$	$5860.805490715418$			✓	$S_9$ (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]	$34405373$	$1$	$6.87706167089583$	$5865.609346010012$			✓	$S_9$ (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]	$34573709$	$1$	$6.880792184488982$	$5879.941241203011$			✓	$S_9$ (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]	$509\cdot 67957$	$2$	$6.881154851586754$	$5881.33598768171$			?	$S_9$ (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]	$13\cdot 2663701$	$2$	$6.881994385964947$	$5884.565659417864$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7566233443489708$
9.1.35050633.1	$x^{9} - x^{8} + x^{7} - 3 x^{6} + 3 x^{5} - 2 x^{4} + 4 x^{3} - 2 x^{2} + x - 1$	$9$	[1,4]	$43\cdot 311\cdot 2621$	$3$	$6.891274359$	$5920.357506097077$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7613732494747866$
9.1.35051893.1	$x^{9} - x^{8} + 3 x^{7} - 3 x^{6} + 5 x^{5} - 5 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$	$9$	[1,4]	$109\cdot 321577$	$2$	$6.891301883842185$	$5920.463917633482$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7612088480089704$
9.1.35234033.1	$x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 4 x^{4} + 3 x^{3} - 2 x^{2} + 2 x - 1$	$9$	[1,4]	$59\cdot 347\cdot 1721$	$3$	$6.895271529570494$	$5935.826227240821$			✓	$S_9$ (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]	$41\cdot 862369$	$2$	$6.897944025537414$	$5946.186088578123$			✓	$S_9$ (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]	$5501\cdot 6473$	$2$	$6.903364514047256$	$5967.2416575835105$			✓	$S_9$ (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]	$787\cdot 45319$	$2$	$6.9046147242172875$	$5972.1062448687235$			✓	$S_9$ (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]	$199\cdot 179287$	$2$	$6.904874096724272$	$5973.115853555831$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7740357851599975$
9.1.35686793.1	$x^{9} - 2 x^{7} - 2 x^{6} + 2 x^{5} + 4 x^{4} + 2 x^{3} - 2 x^{2} - 3 x - 1$	$9$	[1,4]	$35686793$	$1$	$6.905060727881392$	$5973.842398322875$			✓	$S_9$ (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]	$29\cdot 337\cdot 3677$	$3$	$6.910387355992345$	$5994.607660222644$			?	$S_9$ (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]	$41\cdot 879401$	$2$	$6.912950124346879$	$6004.618305937523$			✓	$S_9$ (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]	$36155633$	$1$	$6.915081928897711$	$6012.955429736695$			✓	$S_9$ (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]	$7^{2}\cdot 13\cdot 57649$	$3$	$6.927043458364813$	$2290.4276893191804$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7869155967978311$
9.1.36743849.1	$x^{9} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 13 x^{5} - 14 x^{4} + 12 x^{3} - 8 x^{2} + 4 x - 1$	$9$	[1,4]	$37\cdot 71^{2}\cdot 197$	$3$	$6.927492622732046$	$1463.8824614235823$			✓	$S_9$ (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]	$839\cdot 44111$	$2$	$6.933032038439399$	$6083.512883195038$			?	$S_9$ (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]	$5849\cdot 6337$	$2$	$6.934196550406416$	$6088.112433258768$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7932015302763461$
9.1.37086373.1	$x^{9} + x^{7} - x^{3} - x - 1$	$9$	[1,4]	$23\cdot 1612451$	$2$	$6.934638365839786$	$6089.858208529982$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7901849778796387$
9.1.37232393.1	$x^{9} - x^{8} - x^{7} + 3 x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 2 x + 1$	$9$	[1,4]	$11\cdot 157\cdot 21559$	$3$	$6.937666816699602$	$6101.835215736328$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7952303640831712$
9.1.37354501.1	$x^{9} - x^{8} - x^{6} - x^{5} + 2 x^{4} + x^{2} + x - 1$	$9$	[1,4]	$37354501$	$1$	$6.940191238433723$	$6111.83286747928$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7956561087675897$