curve #4644

y² + xy + y = x³ − 3494080778151482612032136346251999x + 79544281860769357174452982382959803171564819020966

a-invariants: [1, 0, 1, -3494080778151482612032136346251999, 79544281860769357174452982382959803171564819020966]
c-invariants: [167715877351271165377542544620095929, -68726259527704724850301192805784018006545820564258733]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/3ℤ
conductor (N): 2375058682479802063668459948953732228379612270
discriminant (Δ): -3288957625062392082778626427742638161908647190096449186758620057609918487960442920570688144962420900
Faltings height: 18.0322
naive height: 243.3239
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 31, 151, 157, 167, 173, 257, 269, 2835823128719620893424561
regulator: 327211501580996.44033190877465696494602871082987477291504582580
submitted by: Maksym Voznyy
submitted at: 2026-10-19 21:57:53 UTC
last updated: 2026-10-19 21:57:53 UTC

Witness: 12 independent points log in to add more points →

(349321523094402491776676412759/4105830901225, -165999589542599064010064550266171639183511722/8319583567688699125)
(38110109742284140819830490581685425153099/1092512092852104943708804, -373053466232255973550909098333954549013574551777951900196743/1141929728180295827990922275093353592)
(31729189885354635383391/776161, -1532582595107330926342022030805598/683797841)
(23080590753901484373933/687241, -159031580094525796857131160666338/569722789)
(69919826019103929556470036103243148239925187165/2154727875981788344636012698529, -1820980978545508249130123744333228398079411273942944355479506149557364/3162923189312641083956341069446088809418125583)
(124830057512435557100094536552565924714242358881947411834701/6141862884214785463158267151374518578706401, 62619608536339658896405605005336468459504176784549155274648586897875743540181892165857612/15221244952345867981773533544356131165919758617649153183121138351)
(762811364565491140982065632958507361460/22746203620373221000321, -991453521861682035075586714632447677644723187561331667202/3430547079899434529421551190130369)
(812076460652844040863677918637/22415566002064, -75709249919462478483896150510846103222117449/106126676561300024512)
(9242717741287208456487/24964, -877893323767517843093557513178749/3944312)
(6271869773583154227458767218818813220557436/11461969651044622230428209, 15619001331024413218490484523026207522529221948618815168571447674/38805106644037388932217167713235636823)
(8654704967459850236/289, -6525485762443353806547239946/4913)
(2910922194929418804046618464/80609998561, -15497299627748084959682416987697794711522/22886710181440559)

Commentary

t = 2134/1363 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec

last edited by Maksym Voznyy at 2026-10-19 21:57:53 UTC · history