curve #417

y² + xy + y = x³ − x² − 90727410878564661344565489473501960846232523437x + 12098701628080370470556151946562046635806600287349459526333680614637461

a-invariants: [1, -1, 1, -90727410878564661344565489473501960846232523437, 12098701628080370470556151946562046635806600287349459526333680614637461]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 1825384943605980666531033921907301558461995917638269840265421504917327139602394864697536542259505982063511704804368839990
discriminant (Δ): -15439109689985837477065269882391384566307066564733753168278692405867817968998372518404179248111503571943794320665209194237939134339960000000000
Faltings height: 26.0078
naive height: 336.2661
primes of bad reduction: 2, 5, 7, 13, 17, 31, 47, 61, 12220627, 2169117173694741865264847227374427420300469409145639, 50083914098538554646447436705719017702826310244279357
regulator: 3657660886688542337616779144917.58770810646678070221291184987357620287636293285214400676122
submitted by: 7fff-zip
submitted at: 2026-08-29 12:34:09 UTC
last updated: 2026-08-29 12:34:09 UTC

Witness: 26 independent points log in to add more points →

(148204172276492112649631, 43677773316601940306465995338838984)
(-47550847796236043629279, -127692405859243399280086611697376846)
(13884564269004469817536431, -51724600599879534957250482518512107816)
(31722666668217119152181, -96189966262125970878432112689532066)
(446375619051801208214831, 246050954440306102353955063284602584)
(98025936100458621414831, 64397218227528965017072362183802584)
(79091984244907590700831, 73604713866453952650171464902418584)
(-2098021814627376052833131/16, -9436659310407960680811692352210483209/64)
(1507109407391220864328681, -1816199017989035037451485279450149366)
(60121900494621790696700661/16, 464728258090821225256596466911786428231/64)
(-340022507831887124881889, -60301386146912549398498186273123176)
(266366586031002689170701, -82649674562720369212373462715237556)
(9565426426328642571392341/16, 26506585838416324643955185622117933781/64)
(216856792190935176333595, 51204903590114251881163328192483692)
(315840364634345469932671, -122270280939102929072834582143307496)
(220965971858277266111721, -53290777545210324596506184303492596)
(216133690502877034587631, 50851464694854681109677495586972984)
(269178025704715644025254151/841, -3070387234812784989211813055235898041864/24389)
(5810694423272101598107779680789/4464769, -13666052757490330737096419075833185462090790402/9434056897)
(732407460961843634273239561/961, 18499965148403471773572221971496215964404/29791)
(333269877079779514677549142858192689/1034061204544, 134394482213104051057871971658791503501046012128983923/1051524430166339072)
(8008358677949895587703780674710861/2985638881, 712356510312739867779566065726266834221496773099814/163138294096721)
(42742303257090555749325998359/466489, -21503293740071898247886781475851507771825592/318611987)
(10216100392602569898121986482674830311/46339796187556, 16727511150210472167635839231961839563272322453395232061/315450470140620335704)
(16385670508605045728947858071/5041, 2088818808077646671069993090526591856257024/357911)
(109001193878411861252418997636699/558046129, -563847261396238139771324360444392818070639694172/13182723705367)

Commentary

Found in this search by specializing Noam D. Elkies's rank-17 elliptic K3 family (arXiv:2608.25406) at t=-3589/248.

last edited by 7fff-zip at 2026-08-29 12:34:09 UTC · history