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 )

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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	Narrow class group	Unit group torsion	Unit group rank	Regulator
3.1.519.1	$x^{3} - x^{2} - 4 x + 7$	$3$	[1,1]	$-\,3\cdot 173$	$2$	$8.03629343269$	$22.781571499789035$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$2.68057999706$
3.3.1384.1	$x^{3} - x^{2} - 10 x + 14$	$3$	[3,0]	$2^{3}\cdot 173$	$2$	$11.1441093111$	$37.20215047547655$			✓	$S_3$ (as 3T2)	trivial	$[2]$	$2$	$2$	$10.3825345235$
3.1.2595.1	$x^{3} - x^{2} - 10 x - 20$	$3$	[1,1]	$-\,3\cdot 5\cdot 173$	$3$	$13.7418684703$	$50.941142507800116$				$S_3$ (as 3T2)	$[5]$	$[5]$	$2$	$1$	$2.8905431522$
3.3.2941.1	$x^{3} - x^{2} - 14 x + 4$	$3$	[3,0]	$17\cdot 173$	$2$	$14.3273215579$	$54.230987451824994$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$2$	$13.7176469282$
3.1.4152.1	$x^{3} - x^{2} + 16 x - 12$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 173$	$3$	$16.0725868654$	$64.43601477434805$				$S_3$ (as 3T2)	$[4]$	$[4]$	$2$	$1$	$6.55830040041$
3.1.4844.1	$x^{3} - x^{2} - x - 13$	$3$	[1,1]	$-\,2^{2}\cdot 7\cdot 173$	$3$	$16.9200397177$	$55.24064430150487$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$7.4747660696$
3.3.4844.1	$x^{3} - x^{2} - 12 x + 14$	$3$	[3,0]	$2^{2}\cdot 7\cdot 173$	$3$	$16.9200397177$	$69.59885056522126$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$2$	$28.5205410014$
3.1.6055.1	$x^{3} - x^{2} + 45$	$3$	[1,1]	$-\,5\cdot 7\cdot 173$	$3$	$18.2265602623$	$77.8138805098422$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$10.5987576975$
3.3.6401.1	$x^{3} - x^{2} - 22 x + 45$	$3$	[3,0]	$37\cdot 173$	$2$	$18.5673222818$	$80.00624975587844$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$2$	$16.5600241192$
3.1.6920.1	$x^{3} + 2 x - 32$	$3$	[1,1]	$-\,2^{3}\cdot 5\cdot 173$	$3$	$19.0561588691$	$83.18653737234169$				$S_3$ (as 3T2)	$[7]$	$[7]$	$2$	$1$	$3.35646112192$
3.1.8131.1	$x^{3} - x^{2} + 13 x - 4$	$3$	[1,1]	$-\,47\cdot 173$	$2$	$20.1085761609$	$90.17205775626948$			✓	$S_3$ (as 3T2)	$[2]$	$[2]$	$2$	$1$	$8.79482373426$
3.1.8823.1	$x^{3} - x^{2} - 4 x - 17$	$3$	[1,1]	$-\,3\cdot 17\cdot 173$	$3$	$20.6635733606$	$93.93082561119114$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$16.1826516407$
3.1.11591.1	$x^{3} - x^{2} + 14 x + 32$	$3$	[1,1]	$-\,67\cdot 173$	$2$	$22.6311680018$	$107.66150658429409$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$34.6671971543$
3.1.12283.1	$x^{3} - x^{2} + 12 x + 80$	$3$	[1,1]	$-\,71\cdot 173$	$2$	$23.0728628184$	$110.82869664486721$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$25.8418974799$
3.3.13148.1	$x^{3} - x^{2} - 16 x + 18$	$3$	[3,0]	$2^{2}\cdot 19\cdot 173$	$3$	$23.6022405227$	$114.6647286657933$			✓	$S_3$ (as 3T2)	trivial	$[2]$	$2$	$2$	$50.6449277141$
3.3.14013.1	$x^{3} - 30 x - 59$	$3$	[3,0]	$3^{4}\cdot 173$	$2$	$24.1088802981$	$56.909494045298054$			✓	$S_3$ (as 3T2)	$[2]$	$[2, 2]$	$2$	$2$	$18.6925849015$
3.1.14359.1	$x^{3} - 11 x - 27$	$3$	[1,1]	$-\,83\cdot 173$	$2$	$24.3056961927$	$119.82904489313098$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$9.64982074067$
3.1.14532.1	$x^{3} - x^{2} - 8 x + 96$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 7\cdot 173$	$4$	$24.4029200125$	$120.5487453273571$				$S_3$ (as 3T2)	$[13]$	$[13]$	$2$	$1$	$4.48648466448$
3.1.15916.1	$x^{3} - x^{2} + 13 x - 75$	$3$	[1,1]	$-\,2^{2}\cdot 23\cdot 173$	$3$	$25.1542463651$	$100.13217122914793$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$27.1587815492$
3.1.17300.1	$x^{3} - x^{2} + 32 x + 22$	$3$	[1,1]	$-\,2^{2}\cdot 5^{2}\cdot 173$	$3$	$25.8631866694$	$76.91889738875209$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$76.2714302017$
3.3.17300.1	$x^{3} - x^{2} - 33 x - 43$	$3$	[3,0]	$2^{2}\cdot 5^{2}\cdot 173$	$3$	$25.8631866694$	$61.05056931556952$			✓	$S_3$ (as 3T2)	trivial	$[2]$	$2$	$2$	$35.1098912264$
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	trivial	$2$	$1$	$71.9532396864$
3.1.19203.1	$x^{3} + 30 x - 49$	$3$	[1,1]	$-\,3\cdot 37\cdot 173$	$3$	$26.7787125826$	$138.57488950022656$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$42.4002962838$
3.1.19895.1	$x^{3} + 17 x - 3$	$3$	[1,1]	$-\,5\cdot 23\cdot 173$	$3$	$27.0965904853$	$141.0496366532009$			✓	$S_3$ (as 3T2)	$[4]$	$[4]$	$2$	$1$	$8.10136787184$
3.1.21452.1	$x^{3} - x^{2} - 13 x - 55$	$3$	[1,1]	$-\,2^{2}\cdot 31\cdot 173$	$3$	$27.7857802129$	$116.24935776670945$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$23.3419486255$
3.1.22836.1	$x^{3} + 18 x - 172$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 11\cdot 173$	$4$	$28.3709151423$	$151.1158495989087$			✓	$S_3$ (as 3T2)	$[11]$	$[11]$	$2$	$1$	$5.75230045088$
3.3.22836.1	$x^{3} - 42 x - 58$	$3$	[3,0]	$2^{2}\cdot 3\cdot 11\cdot 173$	$4$	$28.3709151423$	$119.94072931118795$			✓	$S_3$ (as 3T2)	trivial	$[2]$	$2$	$2$	$44.2300074263$
3.1.23528.1	$x^{3} + 5 x - 118$	$3$	[1,1]	$-\,2^{3}\cdot 17\cdot 173$	$3$	$28.6546431159$	$153.3883959105121$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$34.1312811676$
3.1.24047.1	$x^{3} - x^{2} - 22 x - 43$	$3$	[1,1]	$-\,139\cdot 173$	$2$	$28.8638084975$	$155.0709515028524$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$10.7352440192$
3.3.24393.1	$x^{3} - x^{2} - 18 x + 3$	$3$	[3,0]	$3\cdot 47\cdot 173$	$3$	$29.0015853275$	$156.182585456894$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$2$	$34.5480618231$
3.1.25604.1	$x^{3} - 7 x - 62$	$3$	[1,1]	$-\,2^{2}\cdot 37\cdot 173$	$3$	$29.4737869223$	$160.0124995117569$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$39.2952965406$
3.1.26988.1	$x^{3} - x^{2} - 39 x - 87$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 13\cdot 173$	$4$	$29.995554897$	$130.38931952917545$			✓	$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$50.8152399354$
3.1.27507.1	$x^{3} - x^{2} - x + 160$	$3$	[1,1]	$-\,3\cdot 53\cdot 173$	$3$	$30.1866145379$	$165.85234396896536$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$48.952377596$
3.1.28199.1	$x^{3} - x^{2} + 10 x + 93$	$3$	[1,1]	$-\,163\cdot 173$	$2$	$30.4376582021$	$167.92557875439942$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$21.4601819918$
3.1.28372.1	$x^{3} - x^{2} + 8 x - 132$	$3$	[1,1]	$-\,2^{2}\cdot 41\cdot 173$	$3$	$30.4997760442$	$168.43990026119107$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$59.3737036583$
3.1.28891.1	$x^{3} - x^{2} - 7 x + 36$	$3$	[1,1]	$-\,167\cdot 173$	$2$	$30.6846276847$	$169.9735273505848$			✓	$S_3$ (as 3T2)	$[4]$	$[4]$	$2$	$1$	$8.29479318072$
3.3.29237.1	$x^{3} - 26 x - 39$	$3$	[3,0]	$13^{2}\cdot 173$	$2$	$30.80663544$	$72.71967899189313$			✓	$S_3$ (as 3T2)	$[3]$	$[3]$	$2$	$2$	$19.728155628$
3.1.32351.1	$x^{3} - x^{2} - 173$	$3$	[1,1]	$-\,11\cdot 17\cdot 173$	$3$	$31.863677896$	$179.8638373881754$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$21.6426784985$
3.1.33043.1	$x^{3} - 2 x - 35$	$3$	[1,1]	$-\,173\cdot 191$	$2$	$32.089268968$	$181.77733632111568$			✓	$S_3$ (as 3T2)	$[4]$	$[4]$	$2$	$1$	$13.5374275982$
3.1.33908.1	$x^{3} - x^{2} + 5 x + 211$	$3$	[1,1]	$-\,2^{2}\cdot 7^{2}\cdot 173$	$3$	$32.3668715898$	$96.26130400814988$			✓	$S_3$ (as 3T2)	$[6]$	$[6]$	$2$	$1$	$18.1789993869$
3.3.36157.1	$x^{3} - x^{2} - 43 x + 16$	$3$	[3,0]	$11\cdot 19\cdot 173$	$3$	$33.0672031181$	$190.14994083617276$			✓	$S_3$ (as 3T2)	trivial	$[2]$	$2$	$2$	$107.04582958$
3.1.36503.1	$x^{3} - x^{2} - 16 x + 191$	$3$	[1,1]	$-\,173\cdot 211$	$2$	$33.1723459659$	$191.05758294294418$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$14.4871965869$
3.1.37368.1	$x^{3} + 27 x - 178$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 173$	$3$	$33.4323279333$	$134.03231195405488$				$S_3$ (as 3T2)	$[3]$	$[3]$	$2$	$1$	$20.814070114$
3.1.37368.2	$x^{3} + 3 x - 186$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 173$	$3$	$33.4323279333$	$134.03231195405488$			✓	$S_3$ (as 3T2)	$[3]$	$[3]$	$2$	$1$	$22.3165451957$
3.1.37368.3	$x^{3} - 45 x - 122$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 173$	$3$	$33.4323279333$	$134.03231195405488$			✓	$S_3$ (as 3T2)	$[3]$	$[3]$	$2$	$1$	$22.149436165$
3.3.37541.1	$x^{3} - x^{2} - 21 x + 14$	$3$	[3,0]	$7\cdot 31\cdot 173$	$3$	$33.4838416171$	$193.75499993548553$			✓	$S_3$ (as 3T2)	trivial	$[2]$	$2$	$2$	$67.8705575503$
3.1.38060.1	$x^{3} + 32 x - 28$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 11\cdot 173$	$4$	$33.6374393706$	$154.84281571806758$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$31.1037994384$
3.1.39444.1	$x^{3} - x^{2} - 35 x + 123$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 19\cdot 173$	$4$	$34.0403212522$	$198.60513588525347$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$69.4768938252$
3.1.40136.1	$x^{3} - x^{2} - 22 x + 130$	$3$	[1,1]	$-\,2^{3}\cdot 29\cdot 173$	$3$	$34.2382345437$	$200.33971149025845$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$145.43641298$
3.1.40655.1	$x^{3} - x^{2} + 10 x - 80$	$3$	[1,1]	$-\,5\cdot 47\cdot 173$	$3$	$34.385181557$	$201.63085081405575$				$S_3$ (as 3T2)	trivial	trivial	$2$	$1$	$116.483276361$

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