curve #1985

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y² = x³ − 85420539449122467123280545046637233572x + 303555347574175519296580563016516197355260069425564120964

a-invariants

[0, 0, 0, -85420539449122467123280545046637233572, 303555347574175519296580563016516197355260069425564120964]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

794305558323771776614171362957416888386693077169888640749181303198159255783739149335814003315880

discriminant (Δ)

83256546038479868484648702620309036155636231197482280675860898075881991154252244785163262796444206922865460000000

Faltings height

20.5780

naive height

273.6356

primes of bad reduction

2, 3, 5, 19, 29, 37, 47, 73, 165196926068094628032447667782767069637697, 190945354997611345345274741477472942224622437

regulator

337223627425393304083095043.9572573101146162230413687040182539343280531842610416538180817

submitted by

Ritik Jain

submitted at

2026-09-25 23:06:06 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:16:59 UTC

Witness: 25 independent points log in to add more points →

(82741781441874762255238952896934628662946768456120/13970760115417788455578103555401, 121231587183751680901114813689587908553854281515948533685743907055508354818/52219180687196985451927013136122437486326638149)
(50980873883922391441900751264082/691879594849, 361272355420568905327495966760377282791418944750/575500603838234257)
(6980481393225227420808/1681, -311646372939110718110808440091450/68921)
(14726245154604670376878992/34969, 56498160085975355251401668204109650250/6539203)
(973178485078764852642/169, -3552230405845477270545408310950/2197)
(59463660280285683423177/289, -14485932645812533356662494068668325/4913)
(8287648040451164158, -12839704001471129119413443470)
(3400305373832753118, -7239752728191929187159174450)
(4446322473102325168, 3413343840903498892187969650)
(-29306773487117121677142/3481, 4238811978378860779981239190587750/205379)
(-183595884757186244245983/44944, -230322793412348583656380431076098225/9528128)
(11433868933356340497/4, 72769047663608690213627681625/8)
(-997159608344779567272/121, 28166533584198605856707569865550/1331)
(3298442871520895111182/729, -61267261970067183484212374460010/19683)
(7721658399838671547290, 678524551027774304433812230123422)
(9836066083732474372895097/1261129, -14972772009522970582700260637995618275/1416247867)
(1823215367263225481604501579178377/3624252749922289, 3522957607022971490046725961212933633894934007198875/218186419599930910484663)
(-384743796218660847813395546266840292856/38969223811943568025, 3304552579966789765853187407780863957966149089594148416478/243266682971748113848695096125)
(-1439946614152303057317927322263014162127/687805812371109604561, 392397293166715577578130441097447398354875025322193815927975/18038431117386146077633746342809)
(22670566933488459712860235906489427769802/26773771207719705171409, 66704010774174886892497711941822972322900226127401549612093390/4380909904323198227394851528516327)
(36524604882245700542989800166854535097501768921266899328585/83052267256268056615342590502294623998761, 390416972480800943048236020382901134362259589456801632692192673015615922859040005347137867/23934658714147825515728044681820491839986728772810405475207509)
(-438742747280343441554401738214953472429152974797280/41136801809308253778549446907289, 310834957474078610563481191638295730562622114509077114824628890364739757626/263843127628823844054674926635543158943192491587)
(3591796027470175698761823205746656790624962828033728589955341166168/585720301614756490721257323693078261642597098401, 1441156351881515108840384350158714933348421160963684443541751571266209392338654317601315713410971750/448265603842685944067636333567780509392044082956758557987621198369326351)
(920573518374780234575191108059383242356653379897794233934242/168052945766960914384130260312787780239369, 5984428379185149701824354529824606773419687235861470627376925663359908146892003072354950/68892063671867686942730887153756598166022832686837908717240347)
(21965279827315215395032309623723008745369413673/4278362493578642016594067921, 160220724897250078444885516420585953824606815878604481168166070664085/279844236910908008813148747679922542285031)

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