Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 142758 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
3.3.316.1	$x^{3} - x^{2} - 4 x + 2$	$3$	[3,0]	$2^{2}\cdot 79$	$2$	$6.81128460769$	$17.776388834631177$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$3.91345849211$
3.1.948.1	$x^{3} - x^{2} + 6$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 79$	$3$	$9.82357229868$	$30.789608636681304$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$10.0586517309$
3.1.1580.1	$x^{3} - x^{2} + 5 x + 5$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 79$	$3$	$11.6471328451$	$31.548971923296484$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$5.26336081191$
3.1.2291.1	$x^{3} + 8 x - 3$	$3$	[1,1]	$-\,29\cdot 79$	$2$	$13.1828212403$	$47.86439177509728$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$14.8651832713$
3.1.2923.1	$x^{3} - x^{2} + 14 x - 12$	$3$	[1,1]	$-\,37\cdot 79$	$2$	$14.2980322329$	$54.064775963653084$				$S_3$ (as 3T2)	trivial	$2$	$1$	$11.587160601$
3.1.4108.1	$x^{3} + 10 x - 2$	$3$	[1,1]	$-\,2^{2}\cdot 13\cdot 79$	$3$	$16.015609766$	$50.871188667890095$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$5.53334267878$
3.3.4345.1	$x^{3} - x^{2} - 10 x + 5$	$3$	[3,0]	$5\cdot 11\cdot 79$	$3$	$16.3178621607$	$65.91661399070799$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$9.1586897766$
3.1.4424.1	$x^{3} - x^{2} + 16 x + 4$	$3$	[1,1]	$-\,2^{3}\cdot 7\cdot 79$	$3$	$16.4161649063$	$66.51315659326356$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$20.5935511662$
3.1.4503.1	$x^{3} - x^{2} + 10 x - 9$	$3$	[1,1]	$-\,3\cdot 19\cdot 79$	$3$	$16.5133042375$	$67.10439627923047$			✓	$S_3$ (as 3T2)	$[4]$	$2$	$1$	$2.38174344715$
3.1.4819.1	$x^{3} + 4 x - 13$	$3$	[1,1]	$-\,61\cdot 79$	$2$	$16.8908812541$	$69.41901756723442$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$12.8994197988$
3.1.5767.1	$x^{3} - x^{2} + 12 x - 45$	$3$	[1,1]	$-\,73\cdot 79$	$2$	$17.9328775821$	$75.94076639065476$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$7.75919344984$
3.3.5925.1	$x^{3} - x^{2} - 18 x + 12$	$3$	[3,0]	$3\cdot 5^{2}\cdot 79$	$3$	$18.0951748888$	$45.0146809031441$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$29.500625439$
3.1.6004.1	$x^{3} - 14 x - 36$	$3$	[1,1]	$-\,2^{2}\cdot 19\cdot 79$	$3$	$18.1752430771$	$77.48548251124207$				$S_3$ (as 3T2)	trivial	$2$	$1$	$26.654634949$
3.1.6083.1	$x^{3} - x^{2} - 5 x - 14$	$3$	[1,1]	$-\,7\cdot 11\cdot 79$	$3$	$18.2546119576$	$77.99358948016176$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$13.9898898263$
3.1.6399.1	$x^{3} + 9 x - 45$	$3$	[1,1]	$-\,3^{4}\cdot 79$	$2$	$18.5653882864$	$38.456983737546345$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$6.15496627162$
3.3.6557.1	$x^{3} - x^{2} - 13 x - 6$	$3$	[3,0]	$79\cdot 83$	$2$	$18.7169491826$	$80.97530487747484$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$25.1112994658$
3.1.6636.1	$x^{3} - x^{2} - 15 x + 33$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 7\cdot 79$	$4$	$18.7918177764$	$64.65615240293215$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$18.7777388655$
3.1.6715.1	$x^{3} - x^{2} - 21 x - 34$	$3$	[1,1]	$-\,5\cdot 17\cdot 79$	$3$	$18.866094508$	$81.94510357550352$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$21.7106721865$
3.1.7031.1	$x^{3} - x^{2} + 18 x - 45$	$3$	[1,1]	$-\,79\cdot 89$	$2$	$19.1575087525$	$83.85105843100611$				$S_3$ (as 3T2)	trivial	$2$	$1$	$19.7096002661$
3.1.8216.1	$x^{3} - x^{2} + 6 x - 54$	$3$	[1,1]	$-\,2^{3}\cdot 13\cdot 79$	$3$	$20.1784038711$	$90.64215354899729$				$S_3$ (as 3T2)	trivial	$2$	$1$	$42.9961824885$
3.1.8532.1	$x^{3} + 18 x - 20$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 79$	$3$	$20.4338538231$	$64.04496684325997$				$S_3$ (as 3T2)	$[9]$	$2$	$1$	$3.05136186131$
3.1.8532.2	$x^{3} + 9 x - 34$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 79$	$3$	$20.4338538231$	$64.04496684325997$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$9.84992794273$
3.1.8532.3	$x^{3} - 15 x - 42$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 79$	$3$	$20.4338538231$	$64.04496684325997$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$11.0278163632$
3.3.8532.1	$x^{3} - 24 x - 28$	$3$	[3,0]	$2^{2}\cdot 3^{3}\cdot 79$	$3$	$20.4338538231$	$50.83252387012967$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$23.6274318195$
3.3.8769.1	$x^{3} - x^{2} - 22 x - 29$	$3$	[3,0]	$3\cdot 37\cdot 79$	$3$	$20.6213308441$	$93.64293886887575$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$17.0338433739$
3.1.9480.1	$x^{3} - x^{2} + 10 x - 18$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 5\cdot 79$	$4$	$21.1642449403$	$97.36529155710468$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$46.9162278851$
3.1.10191.1	$x^{3} + 21 x - 45$	$3$	[1,1]	$-\,3\cdot 43\cdot 79$	$3$	$21.6806484376$	$100.9504829111778$				$S_3$ (as 3T2)	trivial	$2$	$1$	$17.2060048318$
3.3.11060.1	$x^{3} - x^{2} - 21 x - 25$	$3$	[3,0]	$2^{2}\cdot 5\cdot 7\cdot 79$	$4$	$22.2801636093$	$83.47073382880163$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$33.6300966297$
3.1.11139.1	$x^{3} - 12 x - 63$	$3$	[1,1]	$-\,3\cdot 47\cdot 79$	$3$	$22.333085812$	$105.54146104730596$				$S_3$ (as 3T2)	trivial	$2$	$1$	$26.3958891085$
3.1.11771.1	$x^{3} - x^{2} - 15 x + 112$	$3$	[1,1]	$-\,79\cdot 149$	$2$	$22.7477154249$	$108.49423947841655$				$S_3$ (as 3T2)	trivial	$2$	$1$	$23.3639719983$
3.1.12324.1	$x^{3} - x^{2} - 7 x - 41$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 13\cdot 79$	$4$	$23.0985063032$	$111.01351269102334$				$S_3$ (as 3T2)	trivial	$2$	$1$	$44.8130950722$
3.1.12719.1	$x^{3} - x^{2} + 6 x - 23$	$3$	[1,1]	$-\,7\cdot 23\cdot 79$	$3$	$23.3426946564$	$112.7785440586994$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$6.82768087927$
3.1.13035.1	$x^{3} - x^{2} + 14 x - 44$	$3$	[1,1]	$-\,3\cdot 5\cdot 11\cdot 79$	$4$	$23.5344296896$	$114.17092449481173$				$S_3$ (as 3T2)	trivial	$2$	$1$	$39.5779239155$
3.1.13351.1	$x^{3} + 13 x - 13$	$3$	[1,1]	$-\,13^{2}\cdot 79$	$2$	$23.7230904825$	$49.14082543353559$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.7609143894$
3.1.13983.1	$x^{3} - x^{2} - 6 x + 48$	$3$	[1,1]	$-\,3\cdot 59\cdot 79$	$3$	$24.0916633528$	$118.24973572909158$				$S_3$ (as 3T2)	trivial	$2$	$1$	$87.0898151629$
3.3.14141.1	$x^{3} - x^{2} - 17 x - 10$	$3$	[3,0]	$79\cdot 179$	$2$	$24.1820644375$	$118.91593669479293$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$46.4017288084$
3.3.14457.1	$x^{3} - x^{2} - 32 x - 3$	$3$	[3,0]	$3\cdot 61\cdot 79$	$3$	$24.3608662309$	$120.23726543796644$				$S_3$ (as 3T2)	trivial	$2$	$2$	$29.1247947375$
3.1.14536.1	$x^{3} + 22 x - 24$	$3$	[1,1]	$-\,2^{3}\cdot 23\cdot 79$	$3$	$24.4051588125$	$120.56533498481228$				$S_3$ (as 3T2)	$[11]$	$2$	$1$	$3.22370441202$
3.1.14931.1	$x^{3} - 24 x - 51$	$3$	[1,1]	$-\,3^{3}\cdot 7\cdot 79$	$3$	$24.6242473595$	$84.72352749632165$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$25.0973466461$
3.3.15089.1	$x^{3} - 17 x - 13$	$3$	[3,0]	$79\cdot 191$	$2$	$24.7108007859$	$122.83729075488436$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$16.532821232$
3.1.15800.1	$x^{3} - x^{2} - 8 x + 52$	$3$	[1,1]	$-\,2^{3}\cdot 5^{2}\cdot 79$	$3$	$25.0929870409$	$73.50866609793951$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$30.174581502$
3.3.16116.1	$x^{3} - x^{2} - 25 x + 13$	$3$	[3,0]	$2^{2}\cdot 3\cdot 17\cdot 79$	$4$	$25.2591706061$	$100.75933614337129$				$S_3$ (as 3T2)	trivial	$2$	$2$	$41.2668916545$
3.1.16511.1	$x^{3} - x^{2} + 14 x + 67$	$3$	[1,1]	$-\,11\cdot 19\cdot 79$	$3$	$25.4638729731$	$128.49513609471762$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$22.3472344762$
3.1.16748.1	$x^{3} + 20 x - 36$	$3$	[1,1]	$-\,2^{2}\cdot 53\cdot 79$	$3$	$25.5851313398$	$102.71601078614603$				$S_3$ (as 3T2)	trivial	$2$	$1$	$41.8900296428$
3.1.16827.1	$x^{3} - x^{2} - 3 x - 24$	$3$	[1,1]	$-\,3\cdot 71\cdot 79$	$3$	$25.6252964471$	$129.71892691508052$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$17.4778075586$
3.1.17064.1	$x^{3} + 21 x - 34$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 79$	$3$	$25.7450425622$	$90.57326071147344$				$S_3$ (as 3T2)	$[2]$	$2$	$1$	$23.7108623765$
3.1.17380.1	$x^{3} - x^{2} + 12 x + 122$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 11\cdot 79$	$4$	$25.9029915598$	$131.83322798141597$				$S_3$ (as 3T2)	trivial	$2$	$1$	$48.6483415147$
3.1.17459.1	$x^{3} + 23 x - 28$	$3$	[1,1]	$-\,13\cdot 17\cdot 79$	$3$	$25.9421792013$	$132.1325092473461$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$17.034717448$
3.1.18091.1	$x^{3} - x^{2} + 5 x + 24$	$3$	[1,1]	$-\,79\cdot 229$	$2$	$26.251504071$	$134.50278807519194$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$23.7505940266$
3.1.18407.1	$x^{3} - x^{2} - 4 x - 77$	$3$	[1,1]	$-\,79\cdot 233$	$2$	$26.4034698531$	$135.67239955127204$				$S_3$ (as 3T2)	$[2]$	$2$	$1$	$13.08517021$