Number field search results

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Results (1-50 of 63973 matches)

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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
3.1.524.1	$x^{3} - x^{2} + 3 x - 5$	$3$	[1,1]	$-\,2^{2}\cdot 131$	$2$	$8.06201797891$	$18.168635476349255$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$3.42237427955$
3.1.655.1	$x^{3} - x^{2} + 5$	$3$	[1,1]	$-\,5\cdot 131$	$2$	$8.68454560272$	$25.592967784139454$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$2.9056198052$
3.1.1048.1	$x^{3} - x^{2} + 8 x - 12$	$3$	[1,1]	$-\,2^{3}\cdot 131$	$2$	$10.1575061563$	$32.37282811247729$				$S_3$ (as 3T2)	trivial	$2$	$1$	$8.94988598617$
3.1.1572.1	$x^{3} - x^{2} + x + 15$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 131$	$3$	$11.6274419659$	$39.64845520319802$				$S_3$ (as 3T2)	$[5]$	$2$	$1$	$2.85678470938$
3.1.2227.1	$x^{3} - x^{2} + 3 x + 8$	$3$	[1,1]	$-\,17\cdot 131$	$2$	$13.0589042933$	$47.19110085598767$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$10.1629239804$
3.3.3144.1	$x^{3} - x^{2} - 16 x - 8$	$3$	[3,0]	$2^{3}\cdot 3\cdot 131$	$3$	$14.6496588893$	$56.07138307550475$				$S_3$ (as 3T2)	trivial	$2$	$2$	$24.8641443621$
3.1.5240.1	$x^{3} - x^{2} + 9 x - 29$	$3$	[1,1]	$-\,2^{3}\cdot 5\cdot 131$	$3$	$17.3690912054$	$72.38784428341543$				$S_3$ (as 3T2)	trivial	$2$	$1$	$18.8878385339$
3.1.5371.1	$x^{3} - x^{2} - 15 x - 22$	$3$	[1,1]	$-\,41\cdot 131$	$2$	$17.5126439237$	$73.287106642301$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$7.37403019552$
3.1.6419.1	$x^{3} - x^{2} - 9 x + 22$	$3$	[1,1]	$-\,7^{2}\cdot 131$	$2$	$18.5847101386$	$41.88266818867061$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$4.21821079135$
3.3.6681.1	$x^{3} - x^{2} - 14 x - 9$	$3$	[3,0]	$3\cdot 17\cdot 131$	$3$	$18.8341991057$	$81.73738434767778$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$15.5588337497$
3.1.6943.1	$x^{3} - x^{2} - 4 x - 15$	$3$	[1,1]	$-\,53\cdot 131$	$2$	$19.0772478366$	$83.32466621595313$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$8.64681297757$
3.1.7336.1	$x^{3} - x^{2} + 16 x - 28$	$3$	[1,1]	$-\,2^{3}\cdot 7\cdot 131$	$3$	$19.4306102655$	$85.65045242145543$				$S_3$ (as 3T2)	trivial	$2$	$1$	$26.1506781912$
3.3.9301.1	$x^{3} - x^{2} - 21 x - 26$	$3$	[3,0]	$71\cdot 131$	$2$	$21.0301908909$	$96.44169222903547$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$2$	$9.22988697106$
3.1.9563.1	$x^{3} - 16 x - 31$	$3$	[1,1]	$-\,73\cdot 131$	$2$	$21.2258318082$	$97.79059259458448$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$14.8770936504$
3.1.10611.1	$x^{3} + 6 x - 19$	$3$	[1,1]	$-\,3^{4}\cdot 131$	$2$	$21.9744883339$	$49.521902501602206$			✓	$S_3$ (as 3T2)	$[6]$	$2$	$1$	$2.87150161037$
3.1.12183.1	$x^{3} - x^{2} - 2 x - 63$	$3$	[1,1]	$-\,3\cdot 31\cdot 131$	$3$	$23.0100774994$	$110.37662796081425$				$S_3$ (as 3T2)	trivial	$2$	$1$	$18.8534917027$
3.1.13231.1	$x^{3} - x^{2} - 4 x - 21$	$3$	[1,1]	$-\,101\cdot 131$	$2$	$23.6518013727$	$115.02608399836969$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$8.41272762742$
3.1.14279.1	$x^{3} - x - 23$	$3$	[1,1]	$-\,109\cdot 131$	$2$	$24.2604730332$	$119.49476976001921$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$3.24456897397$
3.1.17292.1	$x^{3} - x^{2} - 11 x + 33$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 11\cdot 131$	$4$	$25.8591994364$	$104.3708646960016$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$33.7361707351$
3.3.17685.1	$x^{3} - 33 x - 52$	$3$	[3,0]	$3^{3}\cdot 5\cdot 131$	$3$	$26.0536368082$	$92.2066224138059$				$S_3$ (as 3T2)	trivial	$2$	$2$	$49.2108075157$
3.1.18340.1	$x^{3} + 37 x - 58$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 7\cdot 131$	$4$	$26.371395403$	$135.4252561378416$				$S_3$ (as 3T2)	trivial	$2$	$1$	$58.3791598601$
3.1.19912.1	$x^{3} - x^{2} - 19 x - 57$	$3$	[1,1]	$-\,2^{3}\cdot 19\cdot 131$	$3$	$27.1043061743$	$141.10988625890107$				$S_3$ (as 3T2)	trivial	$2$	$1$	$51.8575865087$
3.3.20436.1	$x^{3} - 36 x - 10$	$3$	[3,0]	$2^{2}\cdot 3\cdot 13\cdot 131$	$4$	$27.3400076239$	$113.46309218343123$				$S_3$ (as 3T2)	trivial	$2$	$2$	$64.6800286882$
3.3.20829.1	$x^{3} - x^{2} - 17 x + 6$	$3$	[3,0]	$3\cdot 53\cdot 131$	$3$	$27.514152495$	$144.32255540974876$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$61.6698214886$
3.3.21877.1	$x^{3} - x^{2} - 37 x - 8$	$3$	[3,0]	$131\cdot 167$	$2$	$27.9680758605$	$147.9087556569928$				$S_3$ (as 3T2)	trivial	$2$	$2$	$76.7437505818$
3.1.22008.1	$x^{3} - x^{2} + 6 x - 30$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 7\cdot 131$	$4$	$28.0237893063$	$148.35093528522157$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$69.4162933773$
3.1.22139.1	$x^{3} - x^{2} - 4 x + 116$	$3$	[1,1]	$-\,13^{2}\cdot 131$	$2$	$28.0792821033$	$63.27972007830352$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$7.48995029976$
3.3.24104.1	$x^{3} - x^{2} - 31 x - 21$	$3$	[3,0]	$2^{3}\cdot 23\cdot 131$	$3$	$28.8865963554$	$155.2546295606028$				$S_3$ (as 3T2)	trivial	$2$	$2$	$65.1087326112$
3.1.24628.1	$x^{3} - x^{2} + 29 x + 3$	$3$	[1,1]	$-\,2^{2}\cdot 47\cdot 131$	$3$	$29.0944207409$	$156.93310676845724$				$S_3$ (as 3T2)	trivial	$2$	$1$	$53.473671185$
3.1.24759.1	$x^{3} - 33 x - 79$	$3$	[1,1]	$-\,3^{3}\cdot 7\cdot 131$	$3$	$29.1459153983$	$109.1003469460434$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$11.7548358552$
3.1.25283.1	$x^{3} + 2 x - 153$	$3$	[1,1]	$-\,131\cdot 193$	$2$	$29.3500965938$	$159.00628918379297$				$S_3$ (as 3T2)	trivial	$2$	$1$	$64.3555243938$
3.1.25676.1	$x^{3} - x^{2} + 5 x + 29$	$3$	[1,1]	$-\,2^{2}\cdot 7^{2}\cdot 131$	$3$	$29.5013884245$	$66.48459154193077$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$5.54100206504$
3.1.25676.2	$x^{3} - 28 x - 84$	$3$	[1,1]	$-\,2^{2}\cdot 7^{2}\cdot 131$	$3$	$29.5013884245$	$66.48459154193077$				$S_3$ (as 3T2)	$[6]$	$2$	$1$	$8.53679583639$
3.1.25807.1	$x^{3} - x^{2} + 10 x - 64$	$3$	[1,1]	$-\,131\cdot 197$	$2$	$29.5514757676$	$160.6455726125062$				$S_3$ (as 3T2)	trivial	$2$	$1$	$93.8322963538$
3.1.26855.1	$x^{3} - x^{2} - 30 x - 80$	$3$	[1,1]	$-\,5\cdot 41\cdot 131$	$3$	$29.9461998722$	$163.8749523264614$				$S_3$ (as 3T2)	trivial	$2$	$1$	$84.2646968691$
3.1.27903.1	$x^{3} - 15 x - 99$	$3$	[1,1]	$-\,3\cdot 71\cdot 131$	$3$	$30.3307837758$	$167.04191090861$				$S_3$ (as 3T2)	$[2]$	$2$	$1$	$13.46717786$
3.3.28165.1	$x^{3} - 28 x - 47$	$3$	[3,0]	$5\cdot 43\cdot 131$	$3$	$30.4254202199$	$167.82431289893606$			✓	$S_3$ (as 3T2)	$[5]$	$2$	$2$	$7.93507888285$
3.1.28296.1	$x^{3} - 9 x - 34$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 131$	$3$	$30.4725184688$	$116.63317687150375$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$24.8945848469$
3.1.28427.1	$x^{3} - x^{2} + 9 x + 28$	$3$	[1,1]	$-\,7\cdot 31\cdot 131$	$3$	$30.5194715761$	$168.6030841948035$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$27.2896655694$
3.1.28951.1	$x^{3} - x^{2} - 14 x - 64$	$3$	[1,1]	$-\,13\cdot 17\cdot 131$	$3$	$30.7058546485$	$170.1499338818561$				$S_3$ (as 3T2)	trivial	$2$	$1$	$98.1856762584$
3.1.29868.1	$x^{3} - x^{2} + x + 33$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 19\cdot 131$	$4$	$31.0266853122$	$137.17018976122338$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$21.7802202273$
3.1.29999.1	$x^{3} - x^{2} + 6 x + 31$	$3$	[1,1]	$-\,131\cdot 229$	$2$	$31.0719798076$	$173.20219398148512$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$9.55058998008$
3.1.30392.1	$x^{3} + 14 x - 64$	$3$	[1,1]	$-\,2^{3}\cdot 29\cdot 131$	$3$	$31.2070770709$	$174.33301465872722$				$S_3$ (as 3T2)	trivial	$2$	$1$	$47.8071815954$
3.3.30392.1	$x^{3} - x^{2} - 31 x + 3$	$3$	[3,0]	$2^{3}\cdot 29\cdot 131$	$3$	$31.2070770709$	$174.33301465872722$				$S_3$ (as 3T2)	trivial	$2$	$2$	$86.9570658943$
3.1.30523.1	$x^{3} - x^{2} - 2 x + 68$	$3$	[1,1]	$-\,131\cdot 233$	$2$	$31.2518505571$	$174.7083283647348$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$38.5892454847$
3.3.30785.1	$x^{3} - x^{2} - 20 x + 17$	$3$	[3,0]	$5\cdot 47\cdot 131$	$3$	$31.3410146652$	$175.45654732725137$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$35.9501130975$
3.1.31571.1	$x^{3} - x^{2} - 20 x + 148$	$3$	[1,1]	$-\,131\cdot 241$	$2$	$31.6055083064$	$177.68230075052494$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$18.8017022055$
3.3.31833.1	$x^{3} - 45 x - 111$	$3$	[3,0]	$3^{5}\cdot 131$	$2$	$31.6926963573$	$85.77445122024731$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$21.0962388836$
3.3.33929.1	$x^{3} - 41 x - 72$	$3$	[3,0]	$7\cdot 37\cdot 131$	$3$	$32.3735520588$	$184.1982627496796$				$S_3$ (as 3T2)	trivial	$2$	$2$	$146.675277025$
3.1.34060.1	$x^{3} - x^{2} + 19 x + 11$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 13\cdot 131$	$4$	$32.415163354$	$146.4802221452087$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$35.3788859527$

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