curve #1979

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y² + xy = x³ − 41545775121470976885288990601680x + 102552718345786726027737698771599144365936490752

a-invariants: [1, 0, 0, -41545775121470976885288990601680, 102552718345786726027737698771599144365936490752]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 2697622583381105681131076542353138361974945693546038735875338834093414990
discriminant (Δ): 46079315620395329121871377851226942840351517866631913610323287674725919782619583428018240000000
Faltings height: 17.0050
naive height: 230.0266
primes of bad reduction: 2, 3, 5, 11, 19, 43, 61, 73, 107, 1741, 50671, 7825439, 30418777953084863230631583963046870732116440401
regulator: 338299794007732426262.2257111572744102121699885315272154627471582587617468792482434
submitted by: Ritik Jain
submitted at: 2026-09-25 23:05:48 UTC
last updated: 2026-09-25 23:05:48 UTC

Witness: 22 independent points log in to add more points →

(106450266864358564384/6561, -1022176807994700678448980039952/531441)
(112605732902957062/9, -33521123182554785126071078/27)
(64056928528309734, -16133363542335673635779682)
(-33325803420732837234/4489, -12844091320784425584418062636/300763)
(850121029621924623/4, 783472289304506741227273005/8)
(3971739631625578584/961, -1131238503466134723843594552/29791)
(226356463694430041892/97969, -4215179836952797452718782768768/30664297)
(3443259362868144, -17978956893394766929872)
(1391570399798951616/289, 584322502047108979130687664/4913)
(892812429748668534, 843585400143129996335796348)
(-2200797498750432, 428166992397925557352176)
(246942592761399744, -122672578552703194758587472)
(96459438582498851/4, 28981771877000528512225099/8)
(-41669974946840384/9, -11942941819721729314130384/27)
(10526333560021756368, 34151958209344596859007364096)
(24450612786322371/4, 2219826440797756318680039/8)
(658813342412485894111235896691537464/38765372294874679281, -500789882422930843654598491367466609620922839945827088/241360356591429278748237529929)
(88430379073019211215189521087824/153592594521205921, 16899892120052823262424251035932723894989182711168/60194306456470378905862031)
(-149922150607577675723200324668/25736921946649, 50043326704320035026670510259970556693555628/130567445732096000893)
(-4115285060397404968278734657300881376364/573690195259289030321569, 77066296057107429239540548592073413715899025690456850608384/434526373843766612656934045960416753)
(-159383643499252444007904/22118209, 17328493079888935298445753824080656/104021936927)
(-34273308069374132197025849166102144/5064160037562863689, 3094621748970421246540536621317237320477447804629744/11396228086037019001090370363)

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