Number field search results

Results (1-50 of 119940 matches)

  Download displayed columns for results to

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
3.3.169.1	$x^{3} - x^{2} - 4 x - 1$	$3$	[3,0]	$13^{2}$	$1$	$5.52877481368$	$5.528774813678872$		✓	✓	$C_3$ (as 3T1)	trivial	$2$	$2$	$1.36504986759$
3.1.4563.1	$x^{3} - 13$	$3$	[1,1]	$-\,3^{3}\cdot 13^{2}$	$2$	$16.586324441$	$19.919129971779828$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$5.6420579792$
3.3.8281.1	$x^{3} - x^{2} - 30 x + 64$	$3$	[3,0]	$7^{2}\cdot 13^{2}$	$2$	$20.2314772451$	$20.23147724512629$		✓		$C_3$ (as 3T1)	$[3]$	$2$	$2$	$15.6222994475$
3.3.8281.2	$x^{3} - x^{2} - 30 x - 27$	$3$	[3,0]	$7^{2}\cdot 13^{2}$	$2$	$20.2314772451$	$20.23147724512629$		✓		$C_3$ (as 3T1)	$[3]$	$2$	$2$	$7.94957796855$
3.1.8619.1	$x^{3} - x^{2} + 9 x + 12$	$3$	[1,1]	$-\,3\cdot 13^{2}\cdot 17$	$3$	$20.5030731066$	$39.483349629417994$			✓	$S_3$ (as 3T2)	$[9]$	$2$	$1$	$2.65920416875$
3.1.11492.1	$x^{3} - x^{2} - 4 x - 40$	$3$	[1,1]	$-\,2^{2}\cdot 13^{2}\cdot 17$	$3$	$22.5665519256$	$45.59144507410518$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$8.45168933011$
3.1.12675.1	$x^{3} - x^{2} + 22 x + 12$	$3$	[1,1]	$-\,3\cdot 5^{2}\cdot 13^{2}$	$3$	$23.3157463848$	$28.000741470983698$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$10.4511172909$
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)	$[3]$	$2$	$1$	$2.7609143894$
3.1.14703.3	$x^{3} - x^{2} - 4 x - 92$	$3$	[1,1]	$-\,3\cdot 13^{2}\cdot 29$	$3$	$24.498264489$	$51.56897838635333$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$28.3557998473$
3.1.14872.1	$x^{3} - x^{2} + 22 x - 66$	$3$	[1,1]	$-\,2^{3}\cdot 11\cdot 13^{2}$	$3$	$24.5917702217$	$51.86450503718846$				$S_3$ (as 3T2)	$[9]$	$2$	$1$	$4.89164726552$
3.3.19604.1	$x^{3} - x^{2} - 17 x - 1$	$3$	[3,0]	$2^{2}\cdot 13^{2}\cdot 29$	$3$	$26.9638290223$	$47.26226862497353$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$2$	$13.4761273974$
3.1.20280.1	$x^{3} - x^{2} + 9 x + 51$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 5\cdot 13^{2}$	$4$	$27.2702624035$	$60.5646936163668$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$24.3758575064$
3.1.23660.1	$x^{3} - x^{2} + 35 x - 53$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 7\cdot 13^{2}$	$4$	$28.7081306105$	$51.92178177076271$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$21.2416680138$
3.1.26871.1	$x^{3} + 39 x - 13$	$3$	[1,1]	$-\,3\cdot 13^{2}\cdot 53$	$3$	$29.9521459291$	$69.7151977657584$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$5.86927299534$
3.1.29068.2	$x^{3} - x^{2} - 17 x + 77$	$3$	[1,1]	$-\,2^{2}\cdot 13^{2}\cdot 43$	$3$	$30.7471630229$	$57.550591695302664$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$12.8762403139$
3.1.35659.2	$x^{3} - x^{2} + 35 x + 64$	$3$	[1,1]	$-\,13^{2}\cdot 211$	$2$	$32.9146862737$	$80.31009306692427$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$13.9587334614$
3.1.35828.1	$x^{3} - x^{2} - 4 x + 220$	$3$	[1,1]	$-\,2^{2}\cdot 13^{2}\cdot 53$	$3$	$32.9666022687$	$80.50017639333723$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$38.8838223005$
3.1.39715.1	$x^{3} - x^{2} + 9 x - 40$	$3$	[1,1]	$-\,5\cdot 13^{2}\cdot 47$	$3$	$34.1181014022$	$84.75451298300825$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$19.1529531475$
3.1.41912.1	$x^{3} - x^{2} + 22 x - 14$	$3$	[1,1]	$-\,2^{3}\cdot 13^{2}\cdot 31$	$3$	$34.7359724622$	$87.06723283309124$			✓	$S_3$ (as 3T2)	$[6]$	$2$	$1$	$9.98566593579$
3.1.43771.1	$x^{3} - 26 x - 65$	$3$	[1,1]	$-\,7\cdot 13^{2}\cdot 37$	$3$	$35.2421305975$	$88.9772099672483$			✓	$S_3$ (as 3T2)	$[9]$	$2$	$1$	$7.92948134015$
3.1.44447.1	$x^{3} - x^{2} + 22 x + 64$	$3$	[1,1]	$-\,13^{2}\cdot 263$	$2$	$35.4226312138$	$89.66166013027681$				$S_3$ (as 3T2)	$[9]$	$2$	$1$	$9.61253307701$
3.3.44616.1	$x^{3} - x^{2} - 56 x + 12$	$3$	[3,0]	$2^{3}\cdot 3\cdot 11\cdot 13^{2}$	$4$	$35.4674700354$	$89.83195783382237$				$S_3$ (as 3T2)	$[3]$	$2$	$2$	$41.3273038491$
3.3.46644.1	$x^{3} - x^{2} - 69 x - 183$	$3$	[3,0]	$2^{2}\cdot 3\cdot 13^{2}\cdot 23$	$4$	$35.9969133156$	$72.90211208684438$				$S_3$ (as 3T2)	$[3]$	$2$	$2$	$21.2997378031$
3.1.47827.2	$x^{3} - x^{2} - 30 x + 116$	$3$	[1,1]	$-\,13^{2}\cdot 283$	$2$	$36.2986979273$	$93.00838841805972$				$S_3$ (as 3T2)	$[9]$	$2$	$1$	$6.18190557627$
3.1.54756.1	$x^{3} - 39 x - 104$	$3$	[1,1]	$-\,2^{2}\cdot 3^{4}\cdot 13^{2}$	$3$	$37.9732036385$	$47.84323859612865$			✓	$S_3$ (as 3T2)	$[6]$	$2$	$1$	$11.7301072347$
3.1.55432.1	$x^{3} - 26 x - 104$	$3$	[1,1]	$-\,2^{3}\cdot 13^{2}\cdot 41$	$3$	$38.1288332614$	$100.13037055979224$				$S_3$ (as 3T2)	$[6]$	$2$	$1$	$12.8575094098$
3.3.64220.1	$x^{3} - x^{2} - 56 x + 90$	$3$	[3,0]	$2^{2}\cdot 5\cdot 13^{2}\cdot 19$	$4$	$40.045780916$	$107.77566217537493$				$S_3$ (as 3T2)	$[3]$	$2$	$2$	$48.0417795491$
3.3.65741.1	$x^{3} - 26 x - 13$	$3$	[3,0]	$13^{2}\cdot 389$	$2$	$40.3594682213$	$109.04448411452947$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$2$	$21.9487032955$
3.1.66079.1	$x^{3} - x^{2} - 4 x + 51$	$3$	[1,1]	$-\,13^{2}\cdot 17\cdot 23$	$3$	$40.4285179166$	$109.32444473988701$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$6.52058642487$
3.1.70135.1	$x^{3} - x^{2} + 74 x + 51$	$3$	[1,1]	$-\,5\cdot 13^{2}\cdot 83$	$3$	$41.2393299614$	$112.6297058517578$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$10.9909547031$
3.1.70811.1	$x^{3} - 13 x - 104$	$3$	[1,1]	$-\,13^{2}\cdot 419$	$2$	$41.3714023761$	$113.17119794371254$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$11.825624507$
3.1.72332.3	$x^{3} - x^{2} - 17 x - 53$	$3$	[1,1]	$-\,2^{2}\cdot 13^{2}\cdot 107$	$3$	$41.6655217463$	$90.78361119887941$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$11.7053210629$
3.1.74867.1	$x^{3} + 26 x - 13$	$3$	[1,1]	$-\,13^{2}\cdot 443$	$2$	$42.1466903943$	$116.36724825561461$			✓	$S_3$ (as 3T2)	$[9]$	$2$	$1$	$4.67256751695$
3.1.76388.1	$x^{3} - x^{2} + 9 x + 103$	$3$	[1,1]	$-\,2^{2}\cdot 13^{2}\cdot 113$	$3$	$42.4301968348$	$117.54336487036251$				$S_3$ (as 3T2)	$[9]$	$2$	$1$	$7.26753662843$
3.1.81796.2	$x^{3} - x^{2} + 48 x + 90$	$3$	[1,1]	$-\,2^{2}\cdot 11^{2}\cdot 13^{2}$	$3$	$43.4087575325$	$54.69160736497349$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$47.983113794$
3.1.86359.1	$x^{3} - x^{2} - 30 x - 391$	$3$	[1,1]	$-\,7\cdot 13^{2}\cdot 73$	$3$	$44.2013840397$	$124.97966366785035$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$10.7154839551$
3.1.88556.1	$x^{3} - x^{2} - 17 x - 339$	$3$	[1,1]	$-\,2^{2}\cdot 13^{2}\cdot 131$	$3$	$44.5730819492$	$100.45029422055221$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$23.8327184713$
3.1.89908.1	$x^{3} - x^{2} - 56 x + 350$	$3$	[1,1]	$-\,2^{2}\cdot 7\cdot 13^{2}\cdot 19$	$4$	$44.7987722878$	$127.52188322118192$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$42.1280597099$
3.3.89908.1	$x^{3} - x^{2} - 43 x - 79$	$3$	[3,0]	$2^{2}\cdot 7\cdot 13^{2}\cdot 19$	$4$	$44.7987722878$	$101.21418578713504$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$2$	$22.1245211384$
3.1.90584.1	$x^{3} + 26 x - 104$	$3$	[1,1]	$-\,2^{3}\cdot 13^{2}\cdot 67$	$3$	$44.9107696846$	$128.0003910308021$				$S_3$ (as 3T2)	$[18]$	$2$	$1$	$3.96707922147$
3.1.93964.3	$x^{3} - x^{2} - 69 x - 261$	$3$	[1,1]	$-\,2^{2}\cdot 13^{2}\cdot 139$	$3$	$45.4625542252$	$103.47202902825593$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$28.3822115736$
3.3.95992.2	$x^{3} - 91 x - 234$	$3$	[3,0]	$2^{3}\cdot 13^{2}\cdot 71$	$3$	$45.7872977621$	$131.7659111232115$				$S_3$ (as 3T2)	$[6]$	$2$	$2$	$43.9083835272$
3.1.96499.1	$x^{3} - x^{2} + 35 x - 300$	$3$	[1,1]	$-\,13^{2}\cdot 571$	$2$	$45.8677676952$	$132.1134262175922$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$33.3618316235$
3.1.97175.2	$x^{3} - x^{2} + 22 x - 183$	$3$	[1,1]	$-\,5^{2}\cdot 13^{2}\cdot 23$	$3$	$45.9746236847$	$77.53054242742431$				$S_3$ (as 3T2)	$[9]$	$2$	$1$	$7.26749231215$
3.1.99372.1	$x^{3} - x^{2} + 61 x - 27$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 7^{2}\cdot 13^{2}$	$4$	$46.3185203008$	$55.6256227382759$				$S_3$ (as 3T2)	$[3, 3]$	$2$	$1$	$8.50045374333$
3.1.105287.1	$x^{3} - 13 x - 65$	$3$	[1,1]	$-\,7\cdot 13^{2}\cdot 89$	$3$	$47.2198841339$	$137.9980421449899$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$9.92073777311$
3.3.109681.1	$x^{3} - x^{2} - 56 x - 131$	$3$	[3,0]	$11\cdot 13^{2}\cdot 59$	$3$	$47.8678366666$	$140.8481833759315$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$2$	$10.0757283984$
3.1.110019.1	$x^{3} - x^{2} + 9 x - 66$	$3$	[1,1]	$-\,3\cdot 7\cdot 13^{2}\cdot 31$	$4$	$47.9169571081$	$141.06503982979189$			✓	$S_3$ (as 3T2)	$[9]$	$2$	$1$	$12.609635958$
3.3.110357.1	$x^{3} - 65 x - 156$	$3$	[3,0]	$13^{2}\cdot 653$	$2$	$47.9659770472$	$141.28156342588198$				$S_3$ (as 3T2)	$[3]$	$2$	$2$	$41.4242694222$
3.1.114075.1	$x^{3} - 65$	$3$	[1,1]	$-\,3^{3}\cdot 5^{2}\cdot 13^{2}$	$3$	$48.4987068773$	$58.24388936725177$			✓	$S_3$ (as 3T2)	$[3, 6]$	$2$	$1$	$3.87637797602$

  Download displayed columns for results to