curve #3522

y² = x³ + x² − 588916463208316968687879169038269890748060x + 187009572281432448919818622917609056515595834833701046269344304

a-invariants

[0, 1, 0, -588916463208316968687879169038269890748060, 187009572281432448919818622917609056515595834833701046269344304]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

66688192800226442678265158959695909411320790422634242165572316538405201647563920749005396866235704830098668696

discriminant (Δ)

-2036184096937566321701738499124806839179116158993658335480089905349732283727749335974169616675339616048009485531067916730450688

Faltings height

22.9796

naive height

300.2957

primes of bad reduction

2, 3, 7, 29, 47, 53, 211, 165719, 8433241879, 642570269091963243860833283258351142235846847862092229514777063743981511379803775167

regulator

381305818735144196131625555253.570242692428083287033097703995120266996266943184651215471428

submitted by

Ritik Jain

submitted at

2026-09-27 16:25:43 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-27 16:31:43 UTC

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

(-886662186331439584028, -3480297178869982887720912864396)
(669636763477369922890303/1369, -202472582186295212240468617001452998/50653)
(73794070069776411763729/16, -19786131330337512220815135816067233/64)
(14651988272175468958, -13356044349626715721250188171050)
(1537300875556510355095, -53988532907159121192525727667502)
(2684707478015046742693/4, -77601294748220851716189640107777/8)
(-163643240273755578507453475524336351392939072343753047750/230243785463085321230729592404821969, 1734724842797381117004210349746535065807860103349606715909978180939550336138021970506/110479544600405681800759132426700366701357695430582297)
(188105377689612126625/16, -858858897234652996672835885156697/64)
(16473438108550858905251482/52441, 68996879264102007972655181298685390146/12008989)
(1178132654247837278628904/1369, -902621658344106632065284173434785108/50653)
(-784453201112942066492, -12894204182894679778395471711780)
(-158607085398114975320, -16626062170475624389477709433852)
(-9964027845042006475535/16, 1130905376634887839243788188304753/64)
(-634903362017327091548, -17463780303294439691744688214164)
(88641594394631492554, 11640599833184413632069245649462)
(-473201755461692344553, 18966459503023933390740818146446)
(3122346153293831878939717481650/3091693609, -4288370967464117187339482002664417795578972854/171907439741227)
(-427585558769692620659760847613400418265715979385417490653/1194350672899823031970983425568929761, 24487510980716424150512886589556834793700509148955168804383114261486628580122445981024/1305262280255432040590769728272591495354638753942659759)
(2159180046889534051877009823895683463124404695537513489118772479/12884092312408668546497086049348732981244025, 446041224112630080581956610431339116527635625432615804150020967773253499055864326275653054448958/46246699280147178528562570956710822631670583595830707086132626125)
(85193994152921271065969293360851124626220980432286048423552715369379112/244361136025890562506966187225631795417302600691761, 18739528658863775074297736695716000874722549167274792308600754452542341362965561979819703372650952560211804/3819866659621395110807040040475891007912687252249634635819937428970334308009)
(2320275699655255782409662744497366071475332/14932546586776922703601, 18179120493512889642240103669628596398852593942154837344552401476/1824739265620402652758713469115849)
(-3211316425312668368949313097404590581/45332520010093801, 145860138042374690280330853933735499696501346136050607428/9651943986478595068850549)
(160366373609129592945506117677451266/12601200733489, 64106003120916324501501010658826842032357894534967886/44731956584151721513)
(151384140453037052548464511/466489, 1747178202997412131459483428277595353746/318611987)
(-4838530108259685535798099597686474691352033892743875688822883095093/6223062878974692306669298849200109790480589481, 6491765203971594248570719276675585008277506494542689614106230879131382009406198163830483291669627084/490914979139172623729182456029361004848067114354818343061044751433621)
(10550057603521857345543325/24964, 14548766259577022674390285092394276851/3944312)

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