Number field search results

Results (1-50 of 737 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
9.1.775511104.1	$x^{9} - 3 x^{8} + 4 x^{7} - 5 x^{6} + 6 x^{5} - x^{4} - 5 x^{3} + 4 x^{2} - 2$	$9$	[1,4]	$2^{6}\cdot 59^{4}$	$2$	$9.72147138751$	$12.19305884048769$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$9.32338475716$
9.1.1568239201.1	$x^{9} - x^{8} - 3 x^{6} + 3 x^{3} + 3 x^{2} + 5 x + 1$	$9$	[1,4]	$199^{4}$	$1$	$10.5126566038$	$14.106735979665885$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$10.6542252322$
9.1.3037332544.1	$x^{9} - x^{8} - 2 x^{7} - 3 x^{6} + 2 x^{5} + 5 x^{4} + 5 x^{3} + 6 x^{2} + 4 x + 2$	$9$	[1,4]	$2^{6}\cdot 83^{4}$	$2$	$11.3138459323$	$14.461911847420069$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$22.5632318214$
9.1.4372515625.1	$x^{9} - x^{8} - x^{7} - 6 x^{6} + 6 x^{5} + 4 x^{4} + 4 x^{3} - 5 x^{2} + 10 x + 5$	$9$	[1,4]	$5^{6}\cdot 23^{4}$	$2$	$11.781277197$	$14.023096443646823$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$14.5533485703$
9.1.8389094464.2	$x^{9} - 5 x^{7} - 2 x^{6} + 9 x^{5} + 2 x^{4} - 3 x^{3} + 6 x^{2} + 10 x + 2$	$9$	[1,4]	$2^{6}\cdot 107^{4}$	$2$	$12.6658695104$	$16.420204160652293$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$42.1577837072$
9.1.12594450625.1	$x^{9} - 3 x^{8} + x^{7} + 4 x^{6} - 2 x^{5} - 6 x^{4} - 2 x^{3} + 7 x^{2} - 5$	$9$	[1,4]	$5^{4}\cdot 67^{4}$	$2$	$13.2508011419$	$18.303005217723125$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$40.2615035438$
9.1.18141126721.1	$x^{9} - x^{8} - 3 x^{7} - x^{6} + 6 x^{5} - x^{4} + 6 x^{3} - 7 x^{2} + 2 x - 3$	$9$	[1,4]	$367^{4}$	$1$	$13.7991261239$	$19.157244060668017$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$49.309063828$
9.1.23891266624.1	$x^{9} - 4 x^{8} + 5 x^{7} + 4 x^{6} - 13 x^{5} + 4 x^{4} + 11 x^{3} - 8 x^{2} - 8 x - 4$	$9$	[1,4]	$2^{6}\cdot 139^{4}$	$2$	$14.2277978518$	$18.715182389460562$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$100.3350364$
9.1.30821664721.1	$x^{9} - 2 x^{7} - 4 x^{6} + 4 x^{5} + 10 x^{4} - x^{3} - 8 x^{2} + 8 x + 8$	$9$	[1,4]	$419^{4}$	$1$	$14.6362040196$	$20.46948949045872$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$126.721959977$
9.1.41764235769.1	$x^{9} - 3 x^{8} + 6 x^{7} - 14 x^{6} + 9 x^{5} - 21 x^{4} + 6 x^{3} - 12 x^{2} - 3$	$9$	[1,4]	$3^{10}\cdot 29^{4}$	$2$	$15.1387282506$	$19.401730279803232$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$80.7481763691$
9.1.58120048561.1	$x^{9} - 2 x^{8} - 2 x^{7} + 8 x^{5} + 6 x^{4} - 5 x^{3} - 2 x^{2} + 4 x + 8$	$9$	[1,4]	$491^{4}$	$1$	$15.7049377285$	$22.15851980616034$				$D_{9}$ (as 9T3)	$[2]$	$2$	$4$	$93.8005460851$
9.1.72555348321.1	$x^{9} - 3 x^{8} + 5 x^{7} - 9 x^{6} - 3 x^{5} - 3 x^{4} - 13 x^{3} + x - 3$	$9$	[1,4]	$3^{4}\cdot 173^{4}$	$2$	$16.096855592$	$22.781571499789035$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$248.51662192$
9.1.77133397441.1	$x^{9} - 3 x^{8} + 5 x^{7} - 11 x^{6} + 14 x^{5} - 19 x^{4} + 22 x^{3} - 19 x^{2} + 14 x - 5$	$9$	[1,4]	$17^{4}\cdot 31^{4}$	$2$	$16.2066631952$	$22.956480566497994$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$73.1002819824$
9.1.100469346961.1	$x^{9} - 3 x^{8} + x^{7} + 2 x^{6} + 4 x^{5} - 16 x^{4} + 35 x^{3} - 53 x^{2} + 43 x - 10$	$9$	[1,4]	$563^{4}$	$1$	$16.6896863672$	$23.727621035409346$				$D_{9}$ (as 9T3)	$[2]$	$2$	$4$	$136.739370058$
9.1.108651322129.1	$x^{9} - 2 x^{8} - 4 x^{7} + x^{6} + 14 x^{5} + 19 x^{4} - x^{3} - 41 x^{2} - 59 x - 27$	$9$	[1,4]	$7^{6}\cdot 31^{4}$	$2$	$16.8355036336$	$20.37415192496631$				$D_{9}$ (as 9T3)	$[3]$	$2$	$4$	$37.5174330624$
9.1.126855644224.1	$x^{9} - 4 x^{8} + 9 x^{7} - 22 x^{6} + 33 x^{5} - 46 x^{4} + 51 x^{3} - 46 x^{2} + 26 x - 6$	$9$	[1,4]	$2^{6}\cdot 211^{4}$	$2$	$17.1277804883$	$23.05833218287126$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$274.666117044$
9.1.148718980881.2	$x^{9} - 6 x^{7} - 5 x^{6} + 27 x^{5} - 3 x^{4} - 11 x^{3} - 45 x^{2} + 60 x - 37$	$9$	[1,4]	$3^{12}\cdot 23^{4}$	$2$	$17.4330768446$	$20.75035786129348$			?	$D_{9}$ (as 9T3)	$[3]$	$2$	$4$	$33.411581888$
9.1.212558803681.1	$x^{9} + 2 x^{7} - 7 x^{6} + 3 x^{5} - 7 x^{4} + 16 x^{3} + 7 x^{2} - 13 x + 7$	$9$	[1,4]	$7^{4}\cdot 97^{4}$	$2$	$18.1388098697$	$26.057628441590765$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$231.516251145$
9.1.242137805625.3	$x^{9} - 6 x^{6} + 27 x^{5} - 27 x^{4} - 12 x^{3} + 54 x^{2} - 45 x + 15$	$9$	[1,4]	$3^{18}\cdot 5^{4}$	$2$	$18.403305886$	$21.391155657968785$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$305.853114994$
9.1.410511866944.1	$x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 17 x^{5} + 16 x^{4} - 21 x^{3} + 14 x^{2} + 116 x + 62$	$9$	[1,4]	$2^{6}\cdot 283^{4}$	$2$	$19.5150435147$	$26.704219034461545$				$D_{9}$ (as 9T3)	$[2]$	$2$	$4$	$288.115635624$
9.1.458774574241.1	$x^{9} - 3 x^{8} + 12 x^{7} - 27 x^{6} + 47 x^{5} - 67 x^{4} + 71 x^{3} - 59 x^{2} + 35 x - 25$	$9$	[1,4]	$823^{4}$	$1$	$19.7575577531$	$28.687976575562104$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$323.838092813$
9.1.490796923761.1	$x^{9} + 6 x^{7} - 11 x^{6} + 9 x^{5} - 48 x^{4} + 12 x^{3} - 99 x^{2} + 54 x - 53$	$9$	[1,4]	$3^{12}\cdot 31^{4}$	$2$	$19.906233427$	$24.090317279593503$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$177.196344776$
9.1.495755401801.1	$x^{9} - 4 x^{8} + 4 x^{7} - x^{6} + 5 x^{5} + 40 x^{4} - 17 x^{3} - 82 x^{2} - 38 x - 23$	$9$	[1,4]	$11^{6}\cdot 23^{4}$	$2$	$19.9284793824$	$23.72060207739333$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$182.493109815$
9.1.768231214144.1	$x^{9} - 3 x^{8} + 3 x^{7} - 3 x^{6} + 22 x^{5} + 6 x^{4} - 48 x^{3} + 12 x^{2} + 40 x - 12$	$9$	[1,4]	$2^{6}\cdot 331^{4}$	$2$	$20.9223381315$	$28.880230868717202$				$D_{9}$ (as 9T3)	$[2]$	$2$	$4$	$387.155535418$
9.1.845813141761.1	$x^{9} - 3 x^{8} + 3 x^{7} - 2 x^{6} - 11 x^{5} + 7 x^{4} + 30 x^{3} - 3 x^{2} + 26 x + 1$	$9$	[1,4]	$7^{4}\cdot 137^{4}$	$2$	$21.1471922891$	$30.967725134404045$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$270.687621284$
9.1.895152515625.1	$x^{9} - x^{8} + 4 x^{7} - 11 x^{6} + 11 x^{5} - 41 x^{4} + 24 x^{3} - 60 x^{2} + 45 x - 45$	$9$	[1,4]	$3^{4}\cdot 5^{6}\cdot 29^{4}$	$3$	$21.2808298628$	$27.27342180226682$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1085.49841916$
9.1.933714431521.1	$x^{9} - 3 x^{8} + 5 x^{7} + 7 x^{6} - 15 x^{5} + 8 x^{4} + 39 x^{3} - 40 x^{2} + 6 x + 5$	$9$	[1,4]	$983^{4}$	$1$	$21.3807918591$	$31.352830813181765$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$207.44385427$
9.1.1238824650625.1	$x^{9} - 2 x^{8} + 11 x^{7} - 10 x^{6} + 30 x^{5} - 28 x^{4} + 31 x^{3} - 58 x^{2} - 40$	$9$	[1,4]	$5^{4}\cdot 211^{4}$	$2$	$22.0631623051$	$32.48076353782343$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$586.348341222$
9.1.1320495160384.1	$x^{9} - 4 x^{8} + 4 x^{7} + 15 x^{6} - 32 x^{5} - 46 x^{4} + 163 x^{3} - 108 x^{2} - 18 x + 27$	$9$	[1,4]	$2^{6}\cdot 379^{4}$	$2$	$22.2202292271$	$30.90340039251852$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1049.83879169$
9.1.1350739057369.1	$x^{9} - 4 x^{8} + 12 x^{7} - 26 x^{6} + 32 x^{5} - 59 x^{4} - 3 x^{3} - 176 x^{2} - 89 x - 125$	$9$	[1,4]	$13^{6}\cdot 23^{4}$	$2$	$22.2762084473$	$26.515072536738543$			?	$D_{9}$ (as 9T3)	$[3]$	$2$	$4$	$108.048594222$
9.1.1396105301761.1	$x^{9} - x^{8} + 5 x^{6} - 7 x^{4} + 39 x^{3} - 58 x^{2} + 47 x - 27$	$9$	[1,4]	$1087^{4}$	$1$	$22.3581236124$	$32.96968304366907$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$603.283315079$
9.1.1586874322944.5	$x^{9} + 9 x^{7} - 6 x^{6} + 27 x^{5} - 36 x^{4} + 27 x^{3} - 54 x^{2} - 32$	$9$	[1,4]	$2^{12}\cdot 3^{18}$	$2$	$22.6785788981$	$27.05790946495165$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$6828.74347748$
9.9.1624709678881.1	$x^{9} - 3 x^{8} - 10 x^{7} + 38 x^{6} + 5 x^{5} - 107 x^{4} + 58 x^{3} + 78 x^{2} - 60 x - 1$	$9$	[9,0]	$1129^{4}$	$1$	$22.7380314624$	$33.60059523282288$			?	$D_{9}$ (as 9T3)	trivial	$2$	$8$	$1134.93352883$
9.1.1636073786281.1	$x^{9} - 2 x^{8} - 10 x^{7} + 29 x^{6} + 19 x^{5} - 98 x^{4} - 115 x^{3} + 611 x^{2} - 705 x + 279$	$9$	[1,4]	$11^{6}\cdot 31^{4}$	$2$	$22.755648126$	$27.538649401961177$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$449.223111039$
9.1.1659523650625.1	$x^{9} - x^{8} - 3 x^{7} + 16 x^{5} - 12 x^{4} - 10 x^{3} - 13 x^{2} + 60 x - 45$	$9$	[1,4]	$5^{4}\cdot 227^{4}$	$2$	$22.791658996$	$33.689761055846034$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1049.80181138$
9.1.1826195471424.1	$x^{9} - x^{8} + 5 x^{6} + 22 x^{5} + 33 x^{4} + 43 x^{3} + 32 x^{2} + 24 x - 6$	$9$	[1,4]	$2^{6}\cdot 3^{4}\cdot 137^{4}$	$3$	$23.0353141889$	$32.181595718882335$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$3089.69538974$
9.1.1886733005056.1	$x^{9} - x^{8} - 6 x^{7} - 8 x^{6} + 21 x^{5} + 55 x^{4} - 24 x^{3} - 38 x^{2} - 24 x - 104$	$9$	[1,4]	$2^{8}\cdot 293^{4}$	$2$	$23.1189351849$	$34.23448553724738$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$6371.30222198$
9.1.1985193642961.1	$x^{9} - 2 x^{8} - 2 x^{7} + 16 x^{6} - 6 x^{5} + 2 x^{4} + 35 x^{3} - 36 x^{2} + 36 x - 16$	$9$	[1,4]	$1187^{4}$	$1$	$23.2499777579$	$34.45286635390443$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1585.91282831$
9.1.2048118765625.1	$x^{9} - 4 x^{8} + 3 x^{7} + 9 x^{6} - 6 x^{5} + 15 x^{4} - 18 x^{3} - 96 x^{2} + 56 x - 16$	$9$	[1,4]	$5^{6}\cdot 107^{4}$	$2$	$23.330731117$	$30.24627467097449$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1483.38231675$
9.1.2075751918009.1	$x^{9} - 3 x^{7} - 8 x^{6} - 15 x^{5} - 30 x^{4} - 12 x^{3} - 39 x^{2} - 21$	$9$	[1,4]	$3^{10}\cdot 7^{4}\cdot 11^{4}$	$3$	$23.3654984294$	$31.61453703951766$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1085.28844439$
9.1.2122409008801.1	$x^{9} - 2 x^{7} - 3 x^{6} - 8 x^{5} - 12 x^{4} + 25 x^{3} + 30 x^{2} + 27 x + 27$	$9$	[1,4]	$17^{4}\cdot 71^{4}$	$2$	$23.4232781469$	$34.741905532080416$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$692.185552204$
9.1.2296318960321.1	$x^{9} - 4 x^{8} + 4 x^{7} + 3 x^{6} + 21 x^{5} - 24 x^{4} + 25 x^{3} + 17 x^{2} + 7 x - 33$	$9$	[1,4]	$1231^{4}$	$1$	$23.6291458801$	$35.08560958569767$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$808.509418378$
9.1.2541865828329.1	$x^{9} - 9 x^{6} + 27 x^{3} - 3$	$9$	[1,4]	$3^{26}$	$1$	$23.8973801059$	$25.401363405535825$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$2341.49334808$
9.1.2647805875264.1	$x^{9} - 3 x^{8} + 7 x^{7} - 13 x^{6} + 16 x^{5} - 42 x^{4} + 40 x^{3} - 40 x^{2} + 48 x - 36$	$9$	[1,4]	$2^{6}\cdot 11^{4}\cdot 41^{4}$	$3$	$24.0060486774$	$33.71125608762117$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1587.53224367$
9.1.2777825555761.1	$x^{9} - 4 x^{8} + 5 x^{7} - 13 x^{6} + 38 x^{5} - 55 x^{4} + 32 x^{3} - 28 x^{2} + 64 x - 48$	$9$	[1,4]	$1291^{4}$	$1$	$24.134254351$	$35.93048844644336$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$2550.15009294$
9.1.2812412850625.1	$x^{9} - 4 x^{8} + x^{7} + 3 x^{6} + 6 x^{5} + 25 x^{4} + 2 x^{3} + 6 x^{2} - 10 x + 5$	$9$	[1,4]	$5^{4}\cdot 7^{4}\cdot 37^{4}$	$3$	$24.1674599849$	$35.98610843089316$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1205.00704049$
9.1.3026768337121.1	$x^{9} - 4 x^{8} + 6 x^{7} - 9 x^{6} + 10 x^{5} - 11 x^{4} + 41 x^{3} - 6 x^{2} + 26 x + 17$	$9$	[1,4]	$1319^{4}$	$1$	$24.365507675$	$36.318039594669756$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$339.627531057$
9.1.3082394705625.1	$x^{9} + 6 x^{7} - 16 x^{6} + 15 x^{5} - 18 x^{4} + 23 x^{3} + 9 x^{2} - 5$	$9$	[1,4]	$3^{10}\cdot 5^{4}\cdot 17^{4}$	$3$	$24.4148606586$	$33.21627494595334$			?	$D_{9}$ (as 9T3)	trivial	$2$	$4$	$1609.00301131$
9.1.3658379210721.1	$x^{9} - 4 x^{8} - 2 x^{7} + 38 x^{6} - 110 x^{5} + 221 x^{4} - 312 x^{3} + 258 x^{2} - 126 x + 45$	$9$	[1,4]	$3^{4}\cdot 461^{4}$	$2$	$24.8840444782$	$37.1887079635741$				$D_{9}$ (as 9T3)	trivial	$2$	$4$	$2674.42202727$
9.1.3830635754401.1	$x^{9} - 3 x^{8} + 3 x^{7} + 13 x^{6} - 21 x^{5} - 4 x^{4} + 65 x^{3} - 56 x^{2} + 10 x - 9$	$9$	[1,4]	$1399^{4}$	$1$	$25.0115845578$	$37.403208418530085$				$D_{9}$ (as 9T3)	$[2]$	$2$	$4$	$343.585284507$