LMFDB - 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.

Refine search

Degree	Signature	Class number	Class group structure	CM field

Ramified prime count	Ramified	Unramified primes	Galois group	Galois

Discriminant	Root discriminant	Galois root discriminant	Regulator	Intermediate field

$p$-adic completions	Minimal sibling	Monogenic	Index	Ines. $p$

		Sort order	Select

Results (1-50 of 793354 matches)

Next Download displayed columns for results to

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
3.1.44.1	$x^{3} - x^{2} + x + 1$	$3$	[1,1]	$-\,2^{2}\cdot 11$	$2$	$3.53034833533$	$5.264813681193971$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$0.609377863436$
3.1.231.1	$x^{3} - x^{2} + 3$	$3$	[1,1]	$-\,3\cdot 7\cdot 11$	$3$	$6.13579243966$	$15.198684153570664$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$1.74549013515$
3.1.440.1	$x^{3} + 2 x - 8$	$3$	[1,1]	$-\,2^{3}\cdot 5\cdot 11$	$3$	$7.60590492152$	$20.97617696340303$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$4.53433053794$
3.1.451.1	$x^{3} - x^{2} - 5 x + 8$	$3$	[1,1]	$-\,11\cdot 41$	$2$	$7.66876649057$	$21.236760581595302$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$3.57573413339$
3.3.473.1	$x^{3} - 5 x - 1$	$3$	[3,0]	$11\cdot 43$	$2$	$7.79148753564$	$21.748563170931547$	✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$2.84322939957$
3.1.671.1	$x^{3} - x - 5$	$3$	[1,1]	$-\,11\cdot 61$	$2$	$8.7546913618$	$25.903667693977237$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$2.34508410892$
3.1.748.1	$x^{3} - x^{2} + x + 5$	$3$	[1,1]	$-\,2^{2}\cdot 11\cdot 17$	$3$	$9.07751968323$	$21.707382906759687$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$4.53179041397$
3.1.759.1	$x^{3} - x^{2} + 6 x - 3$	$3$	[1,1]	$-\,3\cdot 11\cdot 23$	$3$	$9.12180096782$	$27.54995462791182$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$3.13746079313$
3.1.891.1	$x^{3} + 6 x - 1$	$3$	[1,1]	$-\,3^{4}\cdot 11$	$2$	$9.62260298999$	$14.350202036282921$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$1.79633642278$
3.1.1067.1	$x^{3} - 4 x - 7$	$3$	[1,1]	$-\,11\cdot 97$	$2$	$10.2185233064$	$32.66496594212215$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$5.61270164756$
3.1.1144.1	$x^{3} - x^{2} + 6 x + 2$	$3$	[1,1]	$-\,2^{3}\cdot 11\cdot 13$	$3$	$10.4586430635$	$33.823069050575526$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$8.79557852648$
3.1.1188.1	$x^{3} + 6 x - 12$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 11$	$3$	$10.591045006$	$23.898343663143972$		$S_3$ (as 3T2)	trivial	$2$	$1$	$9.56682634196$
3.1.1419.1	$x^{3} - x^{2} + 10 x - 12$	$3$	[1,1]	$-\,3\cdot 11\cdot 43$	$3$	$11.2372695503$	$37.66961640367472$		$S_3$ (as 3T2)	trivial	$2$	$1$	$8.61938596484$
3.1.1727.1	$x^{3} - x - 16$	$3$	[1,1]	$-\,11\cdot 157$	$2$	$11.9976847385$	$41.557189510360296$		$S_3$ (as 3T2)	trivial	$2$	$1$	$15.4230424552$
3.1.1892.1	$x^{3} - x^{2} + x - 17$	$3$	[1,1]	$-\,2^{2}\cdot 11\cdot 43$	$3$	$12.3682155105$	$43.497126341863094$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$10.1412831342$
3.3.2024.1	$x^{3} - x^{2} - 10 x - 6$	$3$	[3,0]	$2^{3}\cdot 11\cdot 23$	$3$	$12.6494070868$	$44.98888751680797$	✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$15.7709818173$
3.1.2068.1	$x^{3} - x^{2} - 8 x - 10$	$3$	[1,1]	$-\,2^{2}\cdot 11\cdot 47$	$3$	$12.7404131445$	$45.47526800360829$	✓	$S_3$ (as 3T2)	$[4]$	$2$	$1$	$3.3613387902$
3.3.2101.1	$x^{3} - x^{2} - 11 x - 8$	$3$	[3,0]	$11\cdot 191$	$2$	$12.8078239927$	$45.83666654546336$	✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$8.54265444809$
3.1.2167.1	$x^{3} - x^{2} - 12 x + 23$	$3$	[1,1]	$-\,11\cdot 197$	$2$	$12.9405570113$	$46.551047249229526$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$5.03077977406$
3.1.2200.1	$x^{3} - 5 x - 10$	$3$	[1,1]	$-\,2^{3}\cdot 5^{2}\cdot 11$	$3$	$13.0059144685$	$27.42971776263377$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$14.6423723013$
3.3.2233.1	$x^{3} - x^{2} - 8 x + 1$	$3$	[3,0]	$7\cdot 11\cdot 29$	$3$	$13.0706215758$	$47.25462940284264$	✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$5.52254734341$
3.1.2376.1	$x^{3} - 9 x - 14$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 11$	$3$	$13.3438805434$	$33.79736172667132$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$14.9005947529$
3.1.2387.1	$x^{3} - x^{2} + 6 x - 20$	$3$	[1,1]	$-\,7\cdot 11\cdot 31$	$3$	$13.3644412547$	$48.85693400122443$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$8.45829604356$
3.1.2508.1	$x^{3} - x^{2} - 5 x - 9$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 11\cdot 19$	$4$	$13.5865495623$	$39.7484716255628$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$11.7995094656$
3.1.2563.1	$x^{3} - x^{2} + x - 10$	$3$	[1,1]	$-\,11\cdot 233$	$2$	$13.6851491622$	$50.62608023538856$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$5.65949439833$
3.3.2673.1	$x^{3} - 9 x - 3$	$3$	[3,0]	$3^{5}\cdot 11$	$2$	$13.8781950275$	$24.85527902572038$	✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$7.76010270745$
3.1.2695.1	$x^{3} + 7 x - 7$	$3$	[1,1]	$-\,5\cdot 7^{2}\cdot 11$	$3$	$13.9161656546$	$27.138137470492882$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.27226928459$
3.1.2728.1	$x^{3} + 10 x - 16$	$3$	[1,1]	$-\,2^{3}\cdot 11\cdot 31$	$3$	$13.9727360556$	$52.230259428802384$		$S_3$ (as 3T2)	trivial	$2$	$1$	$15.8633410692$
3.1.2860.1	$x^{3} - x^{2} - x + 21$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 11\cdot 13$	$4$	$14.1945624886$	$42.4462848945543$		$S_3$ (as 3T2)	trivial	$2$	$1$	$11.5965585919$
3.1.2915.1	$x^{3} - x^{2} - x - 10$	$3$	[1,1]	$-\,5\cdot 11\cdot 53$	$3$	$14.2849761523$	$53.99073994677235$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$9.12847812049$
3.3.2981.1	$x^{3} - x^{2} - 11 x + 14$	$3$	[3,0]	$11\cdot 271$	$2$	$14.391983707$	$54.59853477887479$	✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$14.6286222016$
3.3.3124.1	$x^{3} - 16 x - 12$	$3$	[3,0]	$2^{2}\cdot 11\cdot 71$	$3$	$14.6185290486$	$44.36210860560837$		$S_3$ (as 3T2)	trivial	$2$	$2$	$19.5609726932$
3.1.3179.1	$x^{3} - x^{2} - 11 x + 22$	$3$	[1,1]	$-\,11\cdot 17^{2}$	$2$	$14.7038199461$	$21.92782837978011$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$7.65493163366$
3.1.3212.1	$x^{3} + 8 x - 20$	$3$	[1,1]	$-\,2^{2}\cdot 11\cdot 73$	$3$	$14.7545231747$	$44.982587810520265$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$6.02364102111$
3.1.3223.1	$x^{3} - x^{2} + 11$	$3$	[1,1]	$-\,11\cdot 293$	$2$	$14.7713470469$	$56.77147170894903$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.7443236948$
3.1.3256.1	$x^{3} - x^{2} + 14 x + 22$	$3$	[1,1]	$-\,2^{3}\cdot 11\cdot 37$	$3$	$14.8215901108$	$57.06137047074842$		$S_3$ (as 3T2)	trivial	$2$	$1$	$16.5966582352$
3.1.3300.1	$x^{3} - x^{2} + 12 x + 12$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 11$	$4$	$14.8880555295$	$33.59440615350449$		$S_3$ (as 3T2)	trivial	$2$	$1$	$22.1211584656$
3.1.3311.1	$x^{3} - x^{2} - 11$	$3$	[1,1]	$-\,7\cdot 11\cdot 43$	$3$	$14.9045794671$	$57.54128952326321$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$4.33090870198$
3.1.3564.1	$x^{3} - 12 x - 28$	$3$	[1,1]	$-\,2^{2}\cdot 3^{4}\cdot 11$	$3$	$15.274930109$	$22.779525808351707$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$3.03776019659$
3.1.3564.2	$x^{3} + 6 x - 10$	$3$	[1,1]	$-\,2^{2}\cdot 3^{4}\cdot 11$	$3$	$15.274930109$	$22.779525808351707$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$4.70782215633$
3.1.3575.1	$x^{3} - x^{2} - 8 x - 33$	$3$	[1,1]	$-\,5^{2}\cdot 11\cdot 13$	$3$	$15.2906289177$	$34.966166531003054$		$S_3$ (as 3T2)	trivial	$2$	$1$	$11.1512809626$
3.1.3619.1	$x^{3} - x^{2} - x + 12$	$3$	[1,1]	$-\,7\cdot 11\cdot 47$	$3$	$15.3531040913$	$60.15812497078013$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$13.0658946129$
3.1.3652.1	$x^{3} - x^{2} + x + 23$	$3$	[1,1]	$-\,2^{2}\cdot 11\cdot 83$	$3$	$15.3996289335$	$60.43177971895251$		$S_3$ (as 3T2)	trivial	$2$	$1$	$18.5600434501$
3.1.3916.1	$x^{3} - x^{2} + 3 x + 11$	$3$	[1,1]	$-\,2^{2}\cdot 11\cdot 89$	$3$	$15.7621054159$	$49.66815293217739$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$12.2557528981$
3.1.4103.1	$x^{3} - x^{2} + 10 x + 1$	$3$	[1,1]	$-\,11\cdot 373$	$2$	$16.009109396$	$64.05466415492317$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.31339749352$
3.1.4147.1	$x^{3} - x^{2} - x - 12$	$3$	[1,1]	$-\,11\cdot 13\cdot 29$	$3$	$16.0661325289$	$64.39720490828775$	✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$14.0836917164$
3.1.4191.1	$x^{3} - x^{2} - 12 x + 45$	$3$	[1,1]	$-\,3\cdot 11\cdot 127$	$3$	$16.1227537283$	$64.73793323855806$		$S_3$ (as 3T2)	trivial	$2$	$1$	$11.9972695015$
3.3.4312.1	$x^{3} - x^{2} - 16 x + 8$	$3$	[3,0]	$2^{3}\cdot 7^{2}\cdot 11$	$3$	$16.2764460888$	$34.32733034460722$		$S_3$ (as 3T2)	$[3]$	$2$	$2$	$7.2288617767$
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	$2$	$2$	$9.1586897766$
3.1.4411.1	$x^{3} - x^{2} + 14 x + 12$	$3$	[1,1]	$-\,11\cdot 401$	$2$	$16.4000694028$	$66.41535966928132$		$S_3$ (as 3T2)	trivial	$2$	$1$	$13.9934441671$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 793354 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.