curve #1981

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y² + xy = x³ − 2009475594014508266593334968490730x + 34468074562278990074407873674671816552432510686116

a-invariants

[1, 0, 0, -2009475594014508266593334968490730, 34468074562278990074407873674671816552432510686116]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

13880002603212809789830792008461273852440245181989904231017295286668314077997927726

discriminant (Δ)

6074981954665270565604933820282020958543295518854352722689917734845059526776892906286655175072120832

Faltings height

17.9811

naive height

241.6631

primes of bad reduction

2, 3, 11, 13, 29, 43, 59, 19249, 24402646951486906927262679865889, 468100047658450513124402545107490495399

regulator

154144961899728329118250.463779049285848451237686277310710849581266675601047732159889

submitted by

Ritik Jain

submitted at

2026-09-25 23:05:55 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:17:28 UTC

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

(-36926208811919382, 7636743195373482208130874)
(8927235902721389486820753326016805526831804946/368207939639114471584914186601, 783718225310955976389171759437920571728280957429191029889943470878/223429093445307241025352062167176651831208651)
(1201764747784298145/64, 937941421181178969622352547/512)
(445140967613480272308/5041, -8359995268725844115548190921142/357911)
(2302762245965074314/49, 2270632017214932092322262404/343)
(9889902120562430, -3944856221807702392289944)
(33130975636492194, -2063682543805000328603580)
(24014649412036596, -246073799110555262585274)
(828879907257002379960/4489, -23217001665200940578539238786058/300763)
(205875222230931918, 91360315416742509454814808)
(784650548676875226/121, -6201644454703954708525498482/1331)
(41002921985076534, 4583605565816617444587066)
(31952458706786034654/289, -167605058092649469288704894136/4913)
(27568667818052364, -150212756636215128585690)
(-18440831644318597704/361, 13406722427721931247231500674/6859)
(2473407136640034849/64, 1951696322529745498230426261/512)
(-10226328894255495274367370/332296441, -49642455269867657972574176255825388366/6057431822989)
(35688548185415439360600119020192105195708704/1474702016203057685294294521, 5972694884345884142711241522493817503427493522366240387153481074/56631284330251964468924384247159047981069)
(92071290323199717697181142067079036466670627137198/3885406272015607506555327040985521, 95849594394736608288276894855493060321871650347606388589308707284229196182/242189134590373646791308908453914565715591361623319)
(3248386531848666686340427891151119683830967434870854984914501793612711068/117695596648770378948025123335055169085407914472639155801, 225161399511511349725232545432106600694565195876177453506982771560957792054411384551098906244032885238537574/1276851297975484851053324044700923874590302118985312519675491540543244711517429348701)
(9982530061596414344335260004683667020717792457377329462296012570787216873007559227/703258538287146984963560681105426593942446672300931969267468288804, 1749925251803937411060746819635143098114303951516953649563557750543351838529332476716161694338082126544087886633205708163699/589756207116308313051199269442435348754899421255875896547209625520388206121196905912830381219386408)
(68493922791578649807808558121852371304465574515713335942799296/187829044309705362248705162887070923306372441, 562766554910786154368553254157171924508146674724678359864644252914210399779234297030492147442/2574210889695840523096121945974532449630520797303190203985332928989)
(71377479006000647106023672102802189967528136746958560606298593986989240584660/1036692111664662529681579060267600319534453288007945306724209, 15744939792048122714093892155078488424369997384442344464035579776345831506884456038777229363478104010581001962305398/1055539988425315133840992233296289258212248091110852517393149953355588591374923261370536073)

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