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.

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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
3.1.107.1	$x^{3} - x^{2} + 3 x - 2$	$3$	[1,1]	$-\,107$	$1$	$4.74745939852$	$10.344080432788601$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$1.25605672147$
3.3.321.1	$x^{3} - x^{2} - 4 x + 1$	$3$	[3,0]	$3\cdot 107$	$2$	$6.84702127757$	$17.916472867168917$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$2.56925968013$
3.1.856.1	$x^{3} - x^{2} + x + 11$	$3$	[1,1]	$-\,2^{3}\cdot 107$	$2$	$9.49491879705$	$29.257477676655586$				$S_3$ (as 3T2)	trivial	$2$	$1$	$7.58223464414$
3.1.4280.1	$x^{3} - 13 x - 22$	$3$	[1,1]	$-\,2^{3}\cdot 5\cdot 107$	$3$	$16.2360827586$	$65.4217089351845$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$16.1208547412$
3.1.4708.1	$x^{3} - x^{2} + 17 x - 9$	$3$	[1,1]	$-\,2^{2}\cdot 11\cdot 107$	$3$	$16.7601853846$	$68.61486719363377$				$S_3$ (as 3T2)	trivial	$2$	$1$	$23.0050158947$
3.3.6420.1	$x^{3} - x^{2} - 21 x - 15$	$3$	[3,0]	$2^{2}\cdot 3\cdot 5\cdot 107$	$4$	$18.585675177$	$63.595177255532064$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$28.3108005433$
3.1.6955.1	$x^{3} - x^{2} + 25 x - 18$	$3$	[1,1]	$-\,5\cdot 13\cdot 107$	$3$	$19.0882322915$	$83.3966426182733$				$S_3$ (as 3T2)	trivial	$2$	$1$	$22.3991146785$
3.1.7276.1	$x^{3} - 14 x - 26$	$3$	[1,1]	$-\,2^{2}\cdot 17\cdot 107$	$3$	$19.3774918751$	$67.70223614857598$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$12.864398026$
3.1.7811.1	$x^{3} - x^{2} + 3 x + 16$	$3$	[1,1]	$-\,73\cdot 107$	$2$	$19.8412431475$	$88.37986195961159$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$9.47968037272$
3.1.8667.1	$x^{3} + 18 x - 45$	$3$	[1,1]	$-\,3^{4}\cdot 107$	$2$	$20.5410638327$	$44.75623667824389$				$S_3$ (as 3T2)	$[6]$	$2$	$1$	$3.40783442259$
3.1.8667.2	$x^{3} + 6 x - 17$	$3$	[1,1]	$-\,3^{4}\cdot 107$	$2$	$20.5410638327$	$44.75623667824389$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$6.29722122909$
3.1.8667.3	$x^{3} + 15 x - 28$	$3$	[1,1]	$-\,3^{4}\cdot 107$	$2$	$20.5410638327$	$44.75623667824389$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$7.37528639852$
3.1.9523.1	$x^{3} - x^{2} - 3 x + 20$	$3$	[1,1]	$-\,89\cdot 107$	$2$	$21.196196066$	$97.58585963140357$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$26.257594399$
3.1.9844.1	$x^{3} - x^{2} - 4 x - 18$	$3$	[1,1]	$-\,2^{2}\cdot 23\cdot 107$	$3$	$21.4317286353$	$99.2169340384997$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$30.5055042801$
3.1.10700.1	$x^{3} + 20 x - 20$	$3$	[1,1]	$-\,2^{2}\cdot 5^{2}\cdot 107$	$3$	$22.0357545322$	$48.01296823082401$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$3.12985835632$
3.1.10700.2	$x^{3} - x^{2} + 7 x + 37$	$3$	[1,1]	$-\,2^{2}\cdot 5^{2}\cdot 107$	$3$	$22.0357545322$	$48.01296823082401$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$4.63538906601$
3.1.10700.3	$x^{3} - x^{2} - 13 x + 67$	$3$	[1,1]	$-\,2^{2}\cdot 5^{2}\cdot 107$	$3$	$22.0357545322$	$48.01296823082401$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$11.8249074177$
3.1.10807.1	$x^{3} - x^{2} - 6 x + 23$	$3$	[1,1]	$-\,101\cdot 107$	$2$	$22.1089635568$	$103.95672176439578$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$9.40384762418$
3.1.11235.1	$x^{3} - x^{2} - x - 20$	$3$	[1,1]	$-\,3\cdot 5\cdot 7\cdot 107$	$4$	$22.3970606262$	$105.99528291391084$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$38.007974938$
3.1.11556.1	$x^{3} + 21 x - 74$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 107$	$3$	$22.6083661302$	$74.53553075429286$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$26.6067804471$
3.3.13589.1	$x^{3} - 29 x - 40$	$3$	[3,0]	$107\cdot 127$	$2$	$23.8632266541$	$116.57186624567696$				$S_3$ (as 3T2)	trivial	$2$	$2$	$44.0788661477$
3.1.14124.1	$x^{3} + 18 x - 62$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 11\cdot 107$	$4$	$24.1723701692$	$94.32689146981149$				$S_3$ (as 3T2)	trivial	$2$	$1$	$23.1700243756$
3.1.14552.1	$x^{3} - 10 x - 48$	$3$	[1,1]	$-\,2^{3}\cdot 17\cdot 107$	$3$	$24.4141099076$	$120.63167080000177$				$S_3$ (as 3T2)	trivial	$2$	$1$	$65.879543194$
3.1.14980.1	$x^{3} - x^{2} + 9 x - 49$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 7\cdot 107$	$4$	$24.6511549256$	$122.39281024635393$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$51.0303771496$
3.1.15087.1	$x^{3} - x^{2} - 12 x + 33$	$3$	[1,1]	$-\,3\cdot 47\cdot 107$	$3$	$24.7097089578$	$122.82914963476708$			✓	$S_3$ (as 3T2)	$[5]$	$2$	$1$	$3.7908492988$
3.1.15943.1	$x^{3} - x^{2} + 2 x + 48$	$3$	[1,1]	$-\,107\cdot 149$	$2$	$25.1684622688$	$126.2655930964568$				$S_3$ (as 3T2)	trivial	$2$	$1$	$77.7055752135$
3.1.16264.1	$x^{3} - x^{2} - 16 x - 96$	$3$	[1,1]	$-\,2^{3}\cdot 19\cdot 107$	$3$	$25.3362569725$	$127.53038853543887$				$S_3$ (as 3T2)	trivial	$2$	$1$	$43.4096226414$
3.3.16585.1	$x^{3} - x^{2} - 16 x + 11$	$3$	[3,0]	$5\cdot 31\cdot 107$	$3$	$25.5018581242$	$128.78276282173792$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$15.0394968634$
3.1.17548.1	$x^{3} - x^{2} - 33 x + 101$	$3$	[1,1]	$-\,2^{2}\cdot 41\cdot 107$	$3$	$25.9861859557$	$105.1406072446684$				$S_3$ (as 3T2)	trivial	$2$	$1$	$23.4428656678$
3.1.17976.1	$x^{3} - x^{2} - 26 x + 102$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 7\cdot 107$	$4$	$26.1957610219$	$134.07460609675496$				$S_3$ (as 3T2)	$[5]$	$2$	$1$	$10.9526469878$
3.1.18511.1	$x^{3} - x^{2} + 26 x - 24$	$3$	[1,1]	$-\,107\cdot 173$	$2$	$26.4531032435$	$136.05513588247965$				$S_3$ (as 3T2)	trivial	$2$	$1$	$71.9532396864$
3.1.19367.1	$x^{3} - 25 x - 72$	$3$	[1,1]	$-\,107\cdot 181$	$2$	$26.8547296221$	$139.16536925542934$				$S_3$ (as 3T2)	trivial	$2$	$1$	$127.476784693$
3.1.20223.1	$x^{3} + 15 x - 79$	$3$	[1,1]	$-\,3^{3}\cdot 7\cdot 107$	$3$	$27.2446893671$	$98.60123910703273$				$S_3$ (as 3T2)	trivial	$2$	$1$	$16.6808851402$
3.1.20651.1	$x^{3} - x^{2} + 20 x - 112$	$3$	[1,1]	$-\,107\cdot 193$	$2$	$27.4355515573$	$143.7045580348793$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$20.7682881823$
3.3.20865.1	$x^{3} - x^{2} - 20 x - 15$	$3$	[3,0]	$3\cdot 5\cdot 13\cdot 107$	$4$	$27.5299948203$	$144.44722219551335$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$35.3205278294$
3.3.21293.1	$x^{3} - 41 x - 84$	$3$	[3,0]	$107\cdot 199$	$2$	$27.7169614652$	$145.9212116177768$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$48.9950911176$
3.1.21507.1	$x^{3} - x^{2} + 13 x + 18$	$3$	[1,1]	$-\,3\cdot 67\cdot 107$	$3$	$27.8095062636$	$146.65265084545862$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$40.4235406033$
3.3.23005.1	$x^{3} - 37 x - 64$	$3$	[3,0]	$5\cdot 43\cdot 107$	$3$	$28.4407304224$	$151.67399249706588$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$39.3753966504$
3.1.23112.1	$x^{3} - 42 x - 120$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 107$	$3$	$28.4847563911$	$105.40915847139789$				$S_3$ (as 3T2)	trivial	$2$	$1$	$60.0958021534$
3.3.23112.1	$x^{3} - 30 x - 24$	$3$	[3,0]	$2^{3}\cdot 3^{3}\cdot 107$	$3$	$28.4847563911$	$105.40915847139789$				$S_3$ (as 3T2)	trivial	$2$	$2$	$69.7328483775$
3.1.23219.1	$x^{3} - x^{2} + 35 x + 28$	$3$	[1,1]	$-\,7\cdot 31\cdot 107$	$3$	$28.5286466861$	$152.3778199082793$				$S_3$ (as 3T2)	$[2]$	$2$	$1$	$30.0159655158$
3.1.23540.1	$x^{3} + 17 x - 12$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 11\cdot 107$	$4$	$28.6595138695$	$153.42750731208534$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$99.2494473352$
3.1.23647.1	$x^{3} - 29 x - 67$	$3$	[1,1]	$-\,13\cdot 17\cdot 107$	$3$	$28.7028717478$	$153.7758108416275$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$8.89343402726$
3.1.24396.1	$x^{3} + 6 x - 90$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 19\cdot 107$	$4$	$29.0027742094$	$123.96982280626871$				$S_3$ (as 3T2)	$[5]$	$2$	$1$	$10.6051235323$
3.1.25252.1	$x^{3} - 35 x - 146$	$3$	[1,1]	$-\,2^{2}\cdot 59\cdot 107$	$3$	$29.3380961045$	$158.90877886385007$				$S_3$ (as 3T2)	trivial	$2$	$1$	$64.5623983372$
3.1.25359.1	$x^{3} - x^{2} + 20 x + 79$	$3$	[1,1]	$-\,3\cdot 79\cdot 107$	$3$	$29.3794757025$	$159.245094115957$				$S_3$ (as 3T2)	trivial	$2$	$1$	$15.6500433967$
3.1.25787.1	$x^{3} - x^{2} + 17 x - 22$	$3$	[1,1]	$-\,107\cdot 241$	$2$	$29.5438398257$	$160.58331171077523$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$23.6074314529$
3.1.26215.1	$x^{3} - 35 x - 175$	$3$	[1,1]	$-\,5\cdot 7^{2}\cdot 107$	$3$	$29.7063951735$	$84.63998629183843$				$S_3$ (as 3T2)	$[6]$	$2$	$1$	$4.0079996821$
3.1.26536.1	$x^{3} - x^{2} + 9 x + 59$	$3$	[1,1]	$-\,2^{3}\cdot 31\cdot 107$	$3$	$29.8271542051$	$162.8987415543779$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$53.0906307666$
3.1.26643.1	$x^{3} - x^{2} + 11 x - 32$	$3$	[1,1]	$-\,3\cdot 83\cdot 107$	$3$	$29.8671907017$	$163.22683602888344$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$50.2920735393$

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