curve #1859

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y² + xy = x³ − 255752758889465728975690520512499105x + 50372551092376978482499909042734796870747447770545481

a-invariants: [1, 0, 0, -255752758889465728975690520512499105, 50372551092376978482499909042734796870747447770545481]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 27587219483826099530904184990267107746801232595403861884360490218959899240737752834
discriminant (Δ): -25520351867624605698197481566747453104374113332408068404626234395351616214367190499130992991648845049888768
Faltings height: 19.2240
naive height: 256.2257
primes of bad reduction: 2, 3, 11, 13, 17, 19, 23, 43, 53, 11971, 158641032568722375282207670651393753787341193509118074577166831133693
regulator: 77072401195367600000532.1090554561754350733059043434978890942707034662010219168084835
submitted by: Ritik Jain
submitted at: 2026-09-25 17:14:28 UTC
last updated: 2026-09-25 17:14:28 UTC

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

(-407859420683396864499446/148084561, -407264990635104197981151917628805319981/1802041022809)
(-6296478552664178446310/19321, -845475507205249407686359581450959/2685619)
(171461256422568024897898/170569, -63363594754600560346629454825692457/70444997)
(1182696564575704270810/3481, -10669063457290865784517208099359/205379)
(118052487661602072025549/446224, -10444368840623473379359418931026593/298077632)
(4941492965587878196459642/1369, 10984676411753214307043293638987531679/50653)
(30413021272880446234/121, -59057557516505345027965317199/1331)
(441620233793016810, -153477878648658205065804789)
(6581812883111698375642/17689, -192929742643259757662305894091297/2352637)
(560753851956688438, 288590341688438715078166099)
(8069947024091320042, 22880866549731462558955582219)
(50528568578188772842, -359156577681059588776887634421)
(-1287849602325649395770726/4765489, -3285652528218534043406278494532265299/10403062487)
(109472222314965592636/441, -432605092495047074877988735547/9261)
(-13547550828290587646/25, -21589828635538369180085288977/125)
(8275995116020548634/9, 20787412994453326757058601321/27)
(3244704853183946861516567461248935346482122/155262314016542131488049, 5843012261974228193351119415858649386463614168880727519271072317/61178536242794076379261749852624343)
(44505255649980429588826/177241, 3324649724235826504681267976241151/74618461)
(16444046601327279508508218/73496329, 41560681662179413554920900560392336983/630084028517)
(1975635707154565321486/9409, 70274687096673824176681486509583/912673)
(-14311242431669057/4, 1811740206159600158749687397/8)
(135516020506576198, 134917201856056478241393523)
(1458524466280617025130674/5148361, 299003226974364047915127688836331879/11681631109)

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