curve #3572

y² + xy = x³ − x² − 24794329285306923311812418389456329607688372899x + 1500482193716351117618793789422970798539893615408195106365828799791393

a-invariants: [1, -1, 0, -24794329285306923311812418389456329607688372899, 1500482193716351117618793789422970798539893615408195106365828799791393]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 48870518486191483035882278115591920792856727239322199690390853187559029695258153620208499133858228823266533413910539345170
discriminant (Δ): 2896976064029638589863594830450956003042964961982769618885733767896668380360994711391063597998656190315191882813947185657382703099264062500
Faltings height: 25.4626
naive height: 332.0944
primes of bad reduction: 2, 5, 7, 13, 23, 53, 59, 18367, 40654779608484678938197323695433999938708305972688056492264392000687382635425109705015350126080846450432014241
regulator: 288028798150625017872071185409507.2369990461058676370263178453980403409185510111869036851639007
submitted by: Ritik Jain
submitted at: 2026-09-28 19:32:09 UTC
last updated: 2026-09-28 19:32:09 UTC

Witness: 28 independent points log in to add more points →

(-16407843865143959755525943/576, 645989892436298713126814298496569425191/13824)
(463855769378190861617987376110277756712/4112710897637241, -3106681981081036463960948190142252039725385987006673720501/263749881316764170608461)
(5744788041964251743581132, -13764154339238326601736571523959855741)
(-5402694295508491705546508/81, -38969275705651411706249530584010561639/729)
(-71589464929551961539076398/961, -1613705469345740868538722012415144854631/29791)
(86146939468219102753112, 1961753359800628573425830348050279)
(962289129664364519548532, 932052175506121018062150366191478859)
(3250921335891477356827443/49, -4166096434822176874928574190349150738/343)
(8416608603426485700196574723/47089, -538671577178101478049679404739748474019758/10218313)
(641255649952769874902257, -499290446810070832315071634894052491)
(1016243682147885184349473537/576, 32271564327142874659048736673219595096171/13824)
(103590894007698330228607, 6607339536194881905729469149284159)
(470754920114113251321161653/729, 9934908144840563029645044662332091157547/19683)
(7032600372046474521598283233/12769, -567898052245299198000219399019386910929227/1442897)
(13782862181797235419024503/4, -51116741071170801998612707377303084253/8)
(197802726414547381989711619/900, -2204656953386747319577760340426254773513/27000)
(18883310213494419251253933946046601493134541423764115552094008/241311045686763589683897183214234320729, 23540424981039262873181957491653307546694243207279078296485014329915877279351945952788942347/3748571529732673851857802907475814562621486643385787635933)
(189074066147011740499520573627/466489, 76755268898995643266783136399849629874351462/318611987)
(-502237099099554454739983923304265612049848/4191996757960630161, 450195692233071437548814420574358090361397691417287277064187169/8582847719281835047474827591)
(-22808937421743115092817203990253951228/130315489567561, 32530972029997353509230887114002021002503505369125514599/1487627026713147567941)
(10050670880478541923822203641191553054915012889077469654143856032497336688/191938284475143878992499422563607728567285364631209, 49443852907067584086302828860338736637855433295431475723816143343847575202446235541024666649670626813155794043/2659147410414155690787717943510509007142898174699029157043045272622038520427)
(12443775659486764430343003713775492919239636768/340396963006642030686649, 5035738370149100459769586338911439021718477981403228160386581365063587/198599666576955648573808679784270893)
(-14413539299026867516447875465706191262002062889792763768/96833795615986058122553039608561, 41461149512592484841681425792704829256758970881106687804543150521437849846690831319/952884873851678831774015818710496693201111643191)
(201428199233741632800823979133312535225729/2315381764812276736, 4840457931956638574946612713202620317762424084412198181243345/3523172544430449015045718016)
(18439334551429518380195360843281457479476254144579103948196/236648513945309316225241022144694225, 742601302148489566155190401286293596752967134687205169130437123166129969093611672872839/115121296616387848387676546749355433166445734414950375)
(2861792734784787876458173646194003054507145676/33647553673105353115369, 16245068722237117587671576496903457359865699623023515781666314661285/6172061457581792873250221803028597)
(8935641584507238525433050205724705447424350232800867088046012793244558253662902805072/85160820834509014141655139351805560256341669508128858507747721, 5780252442000746703820655314242219004839523232537066901297842002273007783269808306634991425631768814636700961144750775930241179/785886372765970563455596707840432665370464090310585583920946483404925007689361570041074802981)
(12617986984190617973462420919347893447388925226547/121439239826295486014251396, 9076661187325077458326334679217811720823655881457931127485152507771931771/1338254030374467644970752924936414637944)

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