curve #1991

y² = x³ + x² − 356711569842273015674406518765442495844380x + 83494519247819207086849399458760421415879350908589784926938128

a-invariants

[0, 1, 0, -356711569842273015674406518765442495844380, 83494519247819207086849399458760421415879350908589784926938128]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

323881193400294594843112918466622265918992630142824110146026356983161552164527278414700915016652688428840

discriminant (Δ)

-106714102770675534612586055746655662140695107435937939039776490578395674726272123697357617212276708474254804778648627660000000

Faltings height

22.7810

naive height

298.6829

primes of bad reduction

2, 3, 5, 7, 13, 17, 29, 61, 107, 49207057, 1554826159, 11254627411, 484890942493756791991, 22075885687502814058359710433004089511204420289

regulator

23723466719838512756199941043.0119144084515035933804033290885072012011055039977154161258550

submitted by

Ritik Jain

submitted at

2026-09-25 23:06:24 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:14:27 UTC

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

(2154216810894413077657247828905252674/5520948737729569, -790671315619500654828722565893520328229958222604934070/410223534382060347879503)
(52692352625950647895095909/31684, -360674849010610081431372064823634510975/5639752)
(5350047745047009876169044066/6145441, 316920261449606014084974903210646094217750/15234548239)
(4947310646363734102326, 345555388171951952188240968162150)
(3122449929221825270393326356497847197937235574258094/8758090022716108603654860488329, 33149340676544540160419256582580765045095534513147635571885630990554732913510/25918753261767026915670283269640120132304347483)
(2848865434904690394784/9, -40925662306561525558977633824900/27)
(-212481542952738090514, 12235029260608816384064096420130)
(3074503373721748263109314/289, -5382599592772231996630997963970280650/4913)
(-535221023726829637374, 11004263258752688055751382169750)
(363289232249260211718, -1360742651260985215998436411638)
(43667569694398457523996594/97969, -110785185920342493011347334364040274250/30664297)
(288472167163142271276734262/97969, 4805874043382441288128933808810426431434/30664297)
(1636222355249855525277/4, 19637495005915420072072918152141/8)
(1420383931874421073696150614/4765489, 19883145713982400225536364166032109198250/10403062487)
(348481380414510002132461494/97969, -6419092039687846763572338685017523783350/30664297)
(47830980447679336948026, 10459964980437427079154469493653950)
(913943545254060269106, -22823031109061019578284239009690)
(-898735333258006669856430592642324364780943837801213991825177023199522565939002239201/4735216994487144152358193852424848244046867452322122358959628409, 3915020935883517857852335016169162869390874980480757500072009440263972265823433545781947892694811366027640072311709008822955390/325844075041348681701881147304018348435575157902421864305304448308515644973334803089320892304077)
(292623290116549278207455935861048388038263719172742287939439273374869633183337296424354/44642585251819760445221829622019136631685825505324065200790483402929, 2687113434006716829179823679625888113527870413702412650544935948887539252067667361931831675918010683107150672862193157436842385940550/298279911094510825331653831421732585652923421044536729392634824434285455001991694516367792134073314967)
(-52098667521019275047450861576953734017358222/86068934891185941646249, 222473034057063455747647464113043001144761868557039061620923045970/25250480267000330626209295992963307)
(-10139043872071425901276590999199987692965534/22262191555149106659081, 40882550823323405988220701888939764378005631685671540947886082530/3321634732092877987318617131727771)
(5197726653831679177131387833459208211884939197886/131231441892091753201236530761, 396118380384477735896057342647318218892951142752571636592777010507352018250/47539745334931545554821077143353525332269509)
(297288417631377929990115557646919819172657959129768450476392455020018560936226/835689860241134762724072048210842173112439650147411464801, 30721838735241085215357119937764096715131710112552595068921980593169356898253319620822006834520038377746025026527850/24158373929045834798397114456835738449601243003480759817916739962738324499579219837201)
(1220895509630766512905119718156742009830771025542147938059874/3598010544251957011013162508620464689169, 266408977780777109512886402663611419577869575818761637718454083895383834408886932588805030/215820973722043582680622853866804685111954358490630360781447)
(-102684780967310972711366896105871315412449890993101790167713777691/3874307584543518932925933221842243266176864164, 2324714227489131179684205295462072866483726235232401672615205751766899714411524982592483348602123855/241152153827479103007383469562226957803232515547238620869069945114712)
(-139405356415636691009278370710975842180906666225144745984575605444529196134/243428454348765722191752510872778606287908247553645241, 1200809468798971739580048534151174686879160632362613291842560012513800003357908160780110963328361281364707002250/120103872984948035390064439887932590802065246904721147955765525964245010883504211)

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