curve #1982

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y² = x³ + x² − 24353857452251016019175627840020300x + 1459867823714017402564941512177097120516060510070448

a-invariants

[0, 1, 0, -24353857452251016019175627840020300, 1459867823714017402564941512177097120516060510070448]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

96597465777725248099904851981621215689758735939439437245254927794044597902858520

discriminant (Δ)

3765155161864611454935298710599200385232177646309565449865794185363249081587308223201185140010548000000

Faltings height

18.5624

naive height

249.1476

primes of bad reduction

2, 3, 5, 7, 11, 13, 17, 29, 332403443, 701035379982814964383794023416057287378479137594319509022967397

regulator

33142152184103033812765.4558117771773556208713373147856141649579475352414281975629958

submitted by

Ritik Jain

submitted at

2026-09-25 23:05:58 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:17:29 UTC

Witness: 23 independent points log in to add more points →

(-5305517970408871269909439/105349696, -54695715108998553421719140324554212225/1081309279744)
(1196324517159773380802/529, -41282361973690818758545302306486/12167)
(357177325774219077998415084853591726268969/3507517009887624605077504, 39325555558005724078762418140011669795006292256403930149221845/6569006305767826673541942936533204992)
(-5408409684530364559351/61504, -824432653363838125107237720218235/15252992)
(1707502753054994818343/25921, -49632561564336639543885083481342/4173281)
(8745338029470812846900884/78588225, -7875430422800629704514350253338884948/696684614625)
(14717497892834771, 33235942259018818323023760)
(-105240570444448834, 53453545839214907776180050)
(82683211049021045786/3721, 6920798569430600030235226917750/226981)
(13719649859518033754/289, -99566674382281240523485080270/4913)
(57269994673906646, 15904705602780477575582490)
(-525389235850232, -38375290660080321657888948)
(373730515042107749/4, -1920344758242327508426335/8)
(96240117197199266, 2727839332368813771380250)
(118006377907345701629/484, -1065639397992987576614693020365/10648)
(97196465491064967809/1024, -60476982170858679735149925825/32768)
(575983045239699667070627531/6139506025, -430843122900495670276041806520034888104/481060994588875)
(779911057549349103235853999863366676/14587280648235557161, 981914875863950822274717542156434497268698925468137300/55713636687291745612864141909)
(-10110096989186325509629951380370544042674/57142879978477121876161, 207328915433095001084437959485609170000764150777076057722750/13659763723386924314212692916666591)
(638055891300649085882915390723538925351728985575097/6410511992635796437850294739344016, 2402445188245452134586122425457423585251136186121301437066583743458099291125/513261956952660698043563093442955602851527219935936)
(-7042078255451586913225970022851/57429751810564, 22202228096239645110163538294440634676078943875/435216557220392148488)
(468645516858480640818512588056783005062303771/4520130609652746286222977241, 2135287148916303805632004831312623152472447729945132589391740082280/303897044167377618289639128684110227181539)
(3983211491281012111210439745714304134626/41753204706866486955625, 18608776482086251219190145795826419793558467917806968414126/8531683226330904370094580861203125)

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