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

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Results (1-50 of 21954 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
3.1.507403575.6	$x^{3} - 2415 x - 69230$	$3$	[1,1]	$-\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 23^{2}\cdot 29$	$5$	$797.5988288276302$	$1678.9498204335441$		$S_3$ (as 3T2)	$[3, 6, 60]$	$2$	$1$	$19.409295348564182$
3.1.833945112.2	$x^{3} + 714 x - 8344$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 7^{2}\cdot 11\cdot 13\cdot 19\cdot 29$	$7$	$941.2662548580935$	$10467.162555598208$		$S_3$ (as 3T2)	$[3, 372]$	$2$	$1$	$10.152415570328245$
3.1.1080202440.2	$x^{3} - x^{2} + 114 x - 94914$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 5\cdot 17\cdot 19\cdot 29\cdot 31^{2}$	$7$	$1026.0496690993214$	$10462.416678948257$		$S_3$ (as 3T2)	$[3, 624]$	$2$	$1$	$14.325611318785532$
3.1.1120832559.1	$x^{3} + 1023 x - 321904$	$3$	[1,1]	$-\,3^{4}\cdot 7\cdot 11^{2}\cdot 17\cdot 31^{2}$	$5$	$1038.7560814981045$	$2303.7644537380297$		$S_3$ (as 3T2)	$[3, 345]$	$2$	$1$	$41.22245512364951$
3.1.1281416620.3	$x^{3} + 682 x - 682$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 11^{2}\cdot 19\cdot 29\cdot 31^{2}$	$6$	$1086.1674508651495$	$4066.777243422689$	✓	$S_3$ (as 3T2)	$[3, 528]$	$2$	$1$	$6.529412447790959$
3.1.1317249675.4	$x^{3} + 690 x - 345$	$3$	[1,1]	$-\,3^{3}\cdot 5^{2}\cdot 7\cdot 17\cdot 23^{2}\cdot 31$	$6$	$1096.1989120189182$	$5174.809320390104$	✓	$S_3$ (as 3T2)	$[3, 456]$	$2$	$1$	$7.924071932000514$
3.1.1545172200.6	$x^{3} - 75 x - 75650$	$3$	[1,1]	$-\,2^{3}\cdot 3^{4}\cdot 5^{2}\cdot 11\cdot 13\cdot 23\cdot 29$	$7$	$1156.0917321234485$	$11051.40780621202$		$S_3$ (as 3T2)	$[3, 450]$	$2$	$1$	$12.406369196624114$
3.1.1628681175.7	$x^{3} + 8415 x - 134640$	$3$	[1,1]	$-\,3^{4}\cdot 5^{2}\cdot 11^{2}\cdot 17^{2}\cdot 23$	$5$	$1176.55443583$	$1984.1141980999416$		$S_3$ (as 3T2)	$[3, 6, 60]$	$2$	$1$	$22.2693690864$
3.1.1727568027.1	$x^{3} - 7999$	$3$	[1,1]	$-\,3^{3}\cdot 19^{2}\cdot 421^{2}$	$3$	$1199.89999792$	$1441.0042500135946$	✓	$S_3$ (as 3T2)	$[3, 390]$	$2$	$1$	$7.090035167083817$
3.1.1829530395.1	$x^{3} + 7497 x - 644742$	$3$	[1,1]	$-\,3^{4}\cdot 5\cdot 7^{2}\cdot 11\cdot 17^{2}\cdot 29$	$6$	$1223.0565646719483$	$4180.613233098299$		$S_3$ (as 3T2)	$[3, 3, 114]$	$2$	$1$	$10.156500148590517$
3.1.1834982380.3	$x^{3} + 8092 x - 8092$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 7^{2}\cdot 11\cdot 17^{2}\cdot 19\cdot 31$	$7$	$1224.2702592523947$	$6912.316736333661$		$S_3$ (as 3T2)	$[3, 432]$	$2$	$1$	$8.999001820332378$
3.1.2103730083.1	$x^{3} - 8827$	$3$	[1,1]	$-\,3^{3}\cdot 7^{2}\cdot 13^{2}\cdot 97^{2}$	$4$	$1281.33691756$	$1538.8048563293723$	✓	$S_3$ (as 3T2)	$[3, 3, 6, 24]$	$2$	$1$	$9.352882457388707$
3.1.2150268120.4	$x^{3} - 4563 x - 260598$	$3$	[1,1]	$-\,2^{3}\cdot 3^{5}\cdot 5\cdot 7\cdot 11\cdot 13^{2}\cdot 17$	$7$	$1290.71653$	$9480.931761947584$		$S_3$ (as 3T2)	$[3, 396]$	$2$	$1$	$17.3039026415$
3.1.2187162003.1	$x^{3} - 27001$	$3$	[1,1]	$-\,3\cdot 13^{2}\cdot 31^{2}\cdot 67^{2}$	$4$	$1298.0566630692826$	$1558.8842165923468$		$S_3$ (as 3T2)	$[3, 3, 171]$	$2$	$1$	$7.901019397493618$
3.1.2235182040.11	$x^{3} - 1197 x - 209874$	$3$	[1,1]	$-\,2^{3}\cdot 3^{5}\cdot 5\cdot 7^{2}\cdot 13\cdot 19^{2}$	$6$	$1307.4877634$	$4452.716717338956$		$S_3$ (as 3T2)	$[3, 3, 183]$	$2$	$1$	$12.1418700576$
3.1.2336904300.1	$x^{3} - 27910$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 2791^{2}$	$4$	$1327.02868064$	$1593.677783162018$		$S_3$ (as 3T2)	$[3, 648]$	$2$	$1$	$10.120330859363257$
3.1.2372430060.4	$x^{3} + 2772 x - 2772$	$3$	[1,1]	$-\,2^{2}\cdot 3^{4}\cdot 5\cdot 7^{2}\cdot 11^{2}\cdot 13\cdot 19$	$7$	$1333.71941333$	$4368.600176501131$		$S_3$ (as 3T2)	$[3, 3, 138]$	$2$	$1$	$7.92840563665$
3.1.2619661176.1	$x^{3} - 2523 x - 52606$	$3$	[1,1]	$-\,2^{3}\cdot 3^{4}\cdot 11\cdot 19\cdot 23\cdot 29^{2}$	$6$	$1378.5262527842774$	$8008.9526510254955$		$S_3$ (as 3T2)	$[3, 393]$	$2$	$1$	$10.340935340662822$
3.1.2634579675.6	$x^{3} + 870 x - 145$	$3$	[1,1]	$-\,3^{4}\cdot 5^{2}\cdot 7\cdot 13\cdot 17\cdot 29^{2}$	$6$	$1381.1381206515953$	$4696.981301737708$	✓	$S_3$ (as 3T2)	$[3, 501]$	$2$	$1$	$10.352107927900555$
3.1.2888768883.3	$x^{3} - x^{2} + 10344 x + 81600$	$3$	[1,1]	$-\,3\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 31^{2}$	$5$	$1424.1998393620083$	$1710.3742186455625$		$S_3$ (as 3T2)	$[3, 3, 3, 51]$	$2$	$1$	$11.254594962704639$
3.1.2970138675.2	$x^{3} - x^{2} - 10488 x - 418368$	$3$	[1,1]	$-\,3\cdot 5^{2}\cdot 7^{2}\cdot 29^{2}\cdot 31^{2}$	$5$	$1437.4483288295241$	$1726.2848192473623$		$S_3$ (as 3T2)	$[3, 3, 225]$	$2$	$1$	$10.22911567249631$
3.1.3061832427.1	$x^{3} - 10649$	$3$	[1,1]	$-\,3^{3}\cdot 23^{2}\cdot 463^{2}$	$3$	$1452.09090767$	$1743.8696332935947$	✓	$S_3$ (as 3T2)	$[3, 438]$	$2$	$1$	$7.280728499024852$
3.1.3063871980.3	$x^{3} + 1482 x - 329498$	$3$	[1,1]	$-\,2^{2}\cdot 3^{4}\cdot 5\cdot 13^{2}\cdot 19^{2}\cdot 31$	$6$	$1452.4132591881107$	$3366.2431912610177$		$S_3$ (as 3T2)	$[3, 3, 3, 42]$	$2$	$1$	$13.784524405461564$
3.1.3066512904.3	$x^{3} - 7203 x - 278614$	$3$	[1,1]	$-\,2^{3}\cdot 3^{4}\cdot 7^{2}\cdot 13\cdot 17\cdot 19\cdot 23$	$7$	$1452.83044497$	$13916.890659029155$		$S_3$ (as 3T2)	$[3, 360]$	$2$	$1$	$17.8629300082$
3.1.3221422083.1	$x^{3} - 32769$	$3$	[1,1]	$-\,3^{5}\cdot 11^{2}\cdot 331^{2}$	$3$	$1476.89360671$	$1773.6561111588226$		$S_3$ (as 3T2)	$[3, 390]$	$2$	$1$	$8.03009426667288$
3.1.3445795080.2	$x^{3} + 3042 x - 20592$	$3$	[1,1]	$-\,2^{3}\cdot 3^{4}\cdot 5\cdot 7\cdot 13^{2}\cdot 29\cdot 31$	$7$	$1510.4156684989573$	$12001.884306912323$		$S_3$ (as 3T2)	$[3, 846]$	$2$	$1$	$15.379999847929923$
3.1.3762649800.3	$x^{3} + 15990 x - 36920$	$3$	[1,1]	$-\,2^{3}\cdot 3^{3}\cdot 5^{2}\cdot 7\cdot 13^{2}\cdot 19\cdot 31$	$7$	$1555.36121990254$	$10577.962648555529$		$S_3$ (as 3T2)	$[3, 9, 54]$	$2$	$1$	$21.56220447749029$
3.1.3874619532.1	$x^{3} - 35938$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 7^{2}\cdot 17^{2}\cdot 151^{2}$	$5$	$1570.638918284598$	$1886.2383202056358$		$S_3$ (as 3T2)	$[3, 3, 195]$	$2$	$1$	$8.091636686992066$
3.1.3942158220.8	$x^{3} - 8580 x - 521950$	$3$	[1,1]	$-\,2^{2}\cdot 3^{4}\cdot 5\cdot 7\cdot 11^{2}\cdot 13^{2}\cdot 17$	$7$	$1579.71236285$	$4581.392613059167$		$S_3$ (as 3T2)	$[3, 3, 150]$	$2$	$1$	$10.4182553929$
3.1.3996312012.1	$x^{3} - 12166$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 79^{2}$	$5$	$1586.91304229$	$1905.7825171333147$	✓	$S_3$ (as 3T2)	$[3, 3, 3, 42]$	$2$	$1$	$7.36957332314102$
3.1.4014728172.1	$x^{3} - 24388$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 13^{2}\cdot 67^{2}$	$5$	$1589.34695859$	$1908.7054971697642$		$S_3$ (as 3T2)	$[3, 3, 3, 48]$	$2$	$1$	$7.833190281059421$
3.1.4028568075.1	$x^{3} - 427525$	$3$	[1,1]	$-\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 349^{2}$	$4$	$1591.17117343$	$1910.896264181469$		$S_3$ (as 3T2)	$[3, 3, 126]$	$2$	$1$	$11.93968225833559$
3.1.4285536255.3	$x^{3} + 1023 x - 21824$	$3$	[1,1]	$-\,3^{4}\cdot 5\cdot 7\cdot 11^{2}\cdot 13\cdot 31^{2}$	$6$	$1624.3080294839613$	$4504.745816358221$		$S_3$ (as 3T2)	$[3, 450]$	$2$	$1$	$50.903064180571285$
3.1.4285536255.4	$x^{3} + 1023 x - 341$	$3$	[1,1]	$-\,3^{4}\cdot 5\cdot 7\cdot 11^{2}\cdot 13\cdot 31^{2}$	$6$	$1624.3080294839613$	$4504.745816358221$	✓	$S_3$ (as 3T2)	$[3, 348]$	$2$	$1$	$9.128045093883323$
3.1.4595066476.1	$x^{3} + 14212 x - 14212$	$3$	[1,1]	$-\,2^{2}\cdot 7\cdot 11^{2}\cdot 13\cdot 17^{2}\cdot 19^{2}$	$6$	$1662.50872376$	$3525.9068255807083$		$S_3$ (as 3T2)	$[3, 3, 246]$	$2$	$1$	$9.56205300924$
3.1.4634177427.1	$x^{3} - 39303$	$3$	[1,1]	$-\,3^{5}\cdot 11^{2}\cdot 397^{2}$	$3$	$1667.21222375$	$2002.2167716250667$		$S_3$ (as 3T2)	$[3, 522]$	$2$	$1$	$8.151324856915506$
3.1.4640546700.4	$x^{3} - 1494540$	$3$	[1,1]	$-\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 19^{2}\cdot 23^{2}$	$5$	$1667.97568672$	$2003.1336425193315$	✓	$S_3$ (as 3T2)	$[3, 3, 114]$	$2$	$1$	$12.776975918$
3.1.4700916675.2	$x^{3} - 382655$	$3$	[1,1]	$-\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 29^{2}$	$5$	$1675.1775767774266$	$2011.7826584341974$		$S_3$ (as 3T2)	$[3, 3, 120]$	$2$	$1$	$14.275086886373547$
3.1.4737968235.2	$x^{3} + 12168 x - 1521$	$3$	[1,1]	$-\,3^{4}\cdot 5\cdot 7\cdot 11\cdot 13^{2}\cdot 29\cdot 31$	$7$	$1679.567187612812$	$14073.456825179766$	✓	$S_3$ (as 3T2)	$[3, 594]$	$2$	$1$	$13.565451769603987$
3.1.4768158395.4	$x^{3} - x^{2} - 5763 x + 262872$	$3$	[1,1]	$-\,5\cdot 7^{2}\cdot 11\cdot 13^{2}\cdot 19^{2}\cdot 29$	$6$	$1683.1270174441697$	$5753.211491080724$		$S_3$ (as 3T2)	$[3, 3, 114]$	$2$	$1$	$45.29598187934095$
3.1.4948490988.1	$x^{3} - 13538$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 967^{2}$	$4$	$1704.08372183$	$2046.4971162639538$	✓	$S_3$ (as 3T2)	$[3, 3, 114]$	$2$	$1$	$11.024301663178928$
3.1.5260778523.3	$x^{3} - 11466 x - 556101$	$3$	[1,1]	$-\,3^{4}\cdot 7^{2}\cdot 11\cdot 13^{2}\cdot 23\cdot 31$	$6$	$1739.201919972331$	$7752.296511436238$	✓	$S_3$ (as 3T2)	$[3, 366]$	$2$	$1$	$19.30958498189436$
3.1.5262499935.4	$x^{3} + 2277 x - 2277$	$3$	[1,1]	$-\,3^{4}\cdot 5\cdot 7\cdot 11^{2}\cdot 23^{2}\cdot 29$	$6$	$1739.3915976377632$	$5514.105124658666$		$S_3$ (as 3T2)	$[6, 168]$	$2$	$1$	$7.731930144931712$
3.1.5538231468.1	$x^{3} - 300762$	$3$	[1,1]	$-\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 31^{2}$	$5$	$1769.2547394$	$2124.7633996619365$		$S_3$ (as 3T2)	$[3, 3, 3, 48]$	$2$	$1$	$9.507996419156255$
3.1.5707328067.1	$x^{3} - 974113$	$3$	[1,1]	$-\,3^{3}\cdot 7^{2}\cdot 31^{2}\cdot 67^{2}$	$4$	$1787.08117119$	$2146.1718203802297$		$S_3$ (as 3T2)	$[3, 3, 138]$	$2$	$1$	$13.272161746405821$
3.1.5805096363.1	$x^{3} - 630509$	$3$	[1,1]	$-\,3^{3}\cdot 11^{2}\cdot 31^{2}\cdot 43^{2}$	$4$	$1797.22786902$	$2158.3573647775543$		$S_3$ (as 3T2)	$[6, 168]$	$2$	$1$	$12.771144948122952$
3.1.5812895340.2	$x^{3} + 3312 x - 138$	$3$	[1,1]	$-\,2^{2}\cdot 3^{5}\cdot 5\cdot 7\cdot 17\cdot 19\cdot 23^{2}$	$7$	$1798.03234987$	$10229.697813277313$		$S_3$ (as 3T2)	$[3, 426]$	$2$	$1$	$14.4614167488$
3.1.5953164360.3	$x^{3} - x^{2} - 11976 x + 529860$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 5\cdot 11\cdot 13\cdot 19^{2}\cdot 31^{2}$	$7$	$1812.3801253101399$	$9204.541743134972$		$S_3$ (as 3T2)	$[3, 570]$	$2$	$1$	$27.306901877370287$
3.1.5961205635.2	$x^{3} - x^{2} - 918 x - 148668$	$3$	[1,1]	$-\,3\cdot 5\cdot 7\cdot 11\cdot 17\cdot 19^{2}\cdot 29^{2}$	$7$	$1813.1957861993287$	$9417.808428569166$		$S_3$ (as 3T2)	$[3, 966]$	$2$	$1$	$17.133750697152927$
3.1.6003123867.1	$x^{3} - 14911$	$3$	[1,1]	$-\,3^{3}\cdot 13^{2}\cdot 31^{2}\cdot 37^{2}$	$4$	$1817.43589607$	$2182.625931248675$	✓	$S_3$ (as 3T2)	$[3, 3, 3, 60]$	$2$	$1$	$13.653650235946081$

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Hilbert	Bianchi

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

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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.