LMFDB - Number field search results

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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

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Results (1-50 of 389451 matches)

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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
3.1.283.1	$x^{3} + 4 x - 1$	$3$	[1,1]	$-\,283$	$1$	$6.56541442735$	$16.822603841260722$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$1.40134232731$
3.1.331.1	$x^{3} - x^{2} + 3 x - 4$	$3$	[1,1]	$-\,331$	$1$	$6.91739641661$	$18.193405398660254$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$1.50285283332$
3.1.491.1	$x^{3} - x^{2} + x + 4$	$3$	[1,1]	$-\,491$	$1$	$7.88909460402$	$22.15851980616034$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$1.89106446106$
3.1.563.1	$x^{3} - x^{2} + 5 x - 4$	$3$	[1,1]	$-\,563$	$1$	$8.25726326993$	$23.727621035409346$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$1.73674399826$
3.1.588.1	$x^{3} - x^{2} + 5 x + 1$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 7^{2}$	$3$	$8.37771872824$	$10.061112020813587$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$1.65400419943$
3.1.643.1	$x^{3} - 2 x - 5$	$3$	[1,1]	$-\,643$	$1$	$8.63118299216$	$25.357444666211933$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.35861081459$
3.1.648.1	$x^{3} - 3 x - 10$	$3$	[1,1]	$-\,2^{3}\cdot 3^{4}$	$2$	$8.65349742184$	$12.237893415933033$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.23354828774$
3.1.676.1	$x^{3} - x^{2} - 4 x + 12$	$3$	[1,1]	$-\,2^{2}\cdot 13^{2}$	$2$	$8.77638295533$	$11.057549627357744$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.18608135926$
3.1.731.1	$x^{3} - x^{2} + 3 x + 4$	$3$	[1,1]	$-\,17\cdot 43$	$2$	$9.00822293742$	$27.03701166919155$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.01267869245$
3.1.751.1	$x^{3} - x^{2} + 6 x - 1$	$3$	[1,1]	$-\,751$	$1$	$9.08963921656$	$27.40437921208944$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$1.76788379238$
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)	$[3]$	$2$	$1$	$1.79633642278$
3.1.931.1	$x^{3} - x^{2} + 5 x - 6$	$3$	[1,1]	$-\,7^{2}\cdot 19$	$2$	$9.7644973898$	$15.950543793511486$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$1.84692884153$
3.1.980.1	$x^{3} - x^{2} + 5 x - 13$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 7^{2}$	$3$	$9.93288388379$	$16.364912636128995$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.534472002$
3.1.1083.1	$x^{3} - x^{2} - 6 x - 12$	$3$	[1,1]	$-\,3\cdot 19^{2}$	$2$	$10.2693467638$	$12.332838034173273$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.62907295987$
3.1.1099.1	$x^{3} - x^{2} - x - 6$	$3$	[1,1]	$-\,7\cdot 157$	$2$	$10.3196720846$	$33.15116890850155$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$3.18157943984$
3.1.1107.1	$x^{3} + 6 x - 3$	$3$	[1,1]	$-\,3^{3}\cdot 41$	$2$	$10.3446517211$	$23.06924557594881$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$3.29174765018$
3.1.1176.1	$x^{3} - x^{2} - 2 x - 6$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 7^{2}$	$3$	$10.5552641758$	$17.926863604818365$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$3.71059897095$
3.1.1192.1	$x^{3} - x^{2} + 2 x + 6$	$3$	[1,1]	$-\,2^{3}\cdot 149$	$2$	$10.6029183848$	$34.52535300326414$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$4.9895524775$
3.1.1228.1	$x^{3} - x^{2} + x - 7$	$3$	[1,1]	$-\,2^{2}\cdot 307$	$2$	$10.7086022767$	$27.813513345772268$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.25500722783$
3.1.1228.2	$x^{3} - x^{2} + 7 x - 1$	$3$	[1,1]	$-\,2^{2}\cdot 307$	$2$	$10.7086022767$	$27.813513345772268$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$1.92799537312$
3.1.1228.3	$x^{3} + 4 x - 6$	$3$	[1,1]	$-\,2^{2}\cdot 307$	$2$	$10.7086022767$	$27.813513345772268$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.00449398282$
3.1.1255.1	$x^{3} - x^{2} + 4 x + 5$	$3$	[1,1]	$-\,5\cdot 251$	$2$	$10.78651724$	$35.4259791678367$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.14541855085$
3.1.1323.1	$x^{3} - 7$	$3$	[1,1]	$-\,3^{3}\cdot 7^{2}$	$2$	$10.9779171301$	$13.183786372359444$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.44105647039$
3.1.1356.1	$x^{3} - x^{2} + x + 21$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 113$	$3$	$11.068443772$	$29.22715298876584$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.72140555263$
3.1.1356.2	$x^{3} - x^{2} + 11 x + 1$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 113$	$3$	$11.068443772$	$29.22715298876584$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.40678503563$
3.1.1356.3	$x^{3} - x^{2} + 3 x - 15$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 113$	$3$	$11.068443772$	$29.22715298876584$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$3.12599092174$
3.1.1371.1	$x^{3} - x^{2} + 3 x + 6$	$3$	[1,1]	$-\,3\cdot 457$	$2$	$11.109107046$	$37.027017163147235$	✓	$S_3$ (as 3T2)	$[4]$	$2$	$1$	$2.13833439909$
3.1.1399.1	$x^{3} + 7 x - 1$	$3$	[1,1]	$-\,1399$	$1$	$11.1842252413$	$37.403208418530085$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$1.94880457965$
3.1.1423.1	$x^{3} - x^{2} + 6 x - 7$	$3$	[1,1]	$-\,1423$	$1$	$11.2478185071$	$37.72267222772003$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$1.98691983026$
3.1.1563.1	$x^{3} - x^{2} + 7 x - 6$	$3$	[1,1]	$-\,3\cdot 521$	$2$	$11.6052097091$	$39.534794801541594$	✓	$S_3$ (as 3T2)	$[5]$	$2$	$1$	$2.04883295994$
3.1.1572.1	$x^{3} - x^{2} + x + 15$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 131$	$3$	$11.6274419659$	$39.64845520319802$		$S_3$ (as 3T2)	$[5]$	$2$	$1$	$2.85678470938$
3.1.1588.1	$x^{3} - 11 x - 16$	$3$	[1,1]	$-\,2^{2}\cdot 397$	$2$	$11.6667573689$	$39.84971769034255$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$5.73370767443$
3.1.1620.1	$x^{3} - 3 x - 8$	$3$	[1,1]	$-\,2^{2}\cdot 3^{4}\cdot 5$	$3$	$11.7446029235$	$19.349808478363364$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$4.13933789115$
3.1.1732.1	$x^{3} + x - 8$	$3$	[1,1]	$-\,2^{2}\cdot 433$	$2$	$12.0092521239$	$41.617304093369626$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$5.98916865333$
3.1.1823.1	$x^{3} + 5 x - 7$	$3$	[1,1]	$-\,1823$	$1$	$12.2159962168$	$42.69660408041839$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.1249618304$
3.1.1836.1	$x^{3} - 6 x - 10$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 17$	$3$	$12.2449653058$	$23.58047712423637$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$3.0644325275$
3.1.1836.2	$x^{3} + 6 x - 6$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 17$	$3$	$12.2449653058$	$23.58047712423637$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.1595433212$
3.1.1879.1	$x^{3} - x^{2} - 2 x - 16$	$3$	[1,1]	$-\,1879$	$1$	$12.3398228975$	$43.347433603386484$		$S_3$ (as 3T2)	$[4]$	$2$	$1$	$4.71090783975$
3.1.1927.1	$x^{3} - x^{2} + 2 x - 9$	$3$	[1,1]	$-\,41\cdot 47$	$2$	$12.4440163071$	$43.89760813529594$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.35003381942$
3.1.1931.1	$x^{3} - 4 x - 9$	$3$	[1,1]	$-\,1931$	$1$	$12.4526206426$	$43.94314508543966$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$6.41519605924$
3.3.1957.1	$x^{3} - x^{2} - 9 x + 10$	$3$	[3,0]	$19\cdot 103$	$2$	$12.5082612057$	$44.23799272118933$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$2$	$4.5514507373$
3.1.1960.1	$x^{3} - x^{2} + 5 x + 15$	$3$	[1,1]	$-\,2^{3}\cdot 5\cdot 7^{2}$	$3$	$12.5146494914$	$23.143481397064466$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$4.86047323248$
3.1.1963.1	$x^{3} - x^{2} + 5 x + 6$	$3$	[1,1]	$-\,13\cdot 151$	$2$	$12.5210312617$	$44.30575583375144$	✓	$S_3$ (as 3T2)	$[4]$	$2$	$1$	$2.26113105698$
3.1.1972.1	$x^{3} + 10 x - 12$	$3$	[1,1]	$-\,2^{2}\cdot 17\cdot 29$	$3$	$12.5401376463$	$44.40720662234904$		$S_3$ (as 3T2)	$[5]$	$2$	$1$	$2.58267040025$
3.1.1999.1	$x^{3} - x^{2} + 10 x - 16$	$3$	[1,1]	$-\,1999$	$1$	$12.5971102805$	$44.710177812216315$		$S_3$ (as 3T2)	$[5]$	$2$	$1$	$4.0050171284$
3.1.2028.1	$x^{3} - 26$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 13^{2}$	$3$	$12.6577345462$	$15.201141185311545$		$S_3$ (as 3T2)	$[3]$	$2$	$1$	$3.28330950903$
3.1.2051.1	$x^{3} - x^{2} - 7 x + 14$	$3$	[1,1]	$-\,7\cdot 293$	$2$	$12.7054061758$	$45.28796749689701$	✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$3.24302461654$
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)	$[4]$	$2$	$1$	$3.3613387902$
3.1.2075.1	$x^{3} - 10 x - 15$	$3$	[1,1]	$-\,5^{2}\cdot 83$	$2$	$12.7547720187$	$26.63906938822806$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$4.85337081513$
3.1.2075.2	$x^{3} - x^{2} + 7 x - 8$	$3$	[1,1]	$-\,5^{2}\cdot 83$	$2$	$12.7547720187$	$26.63906938822806$	✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.11104798206$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.