curve #4601

y² + xy = x³ − 226050204081195740344480445x + 1307231167270120936892159837761138919025

a-invariants: [1, 0, 0, -226050204081195740344480445, 1307231167270120936892159837761138919025]
c-invariants: [10850409795897395536535061361, -1129447728521400765089519945918928828629641]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 26303332385145147029931058721365470
discriminant (Δ): 1031068053656890238467237649570324833864386035365113352863466139256000000000000
Faltings height: 13.8989
naive height: 193.6620
primes of bad reduction: 2, 3, 5, 7, 11, 13, 41, 47, 71, 79, 83, 88760043951110467511
regulator: 54476736173.07335766364178403751151980095409767524304436299
submitted by: Maksym Voznyy
submitted at: 2026-10-18 22:54:32 UTC
last updated: 2026-10-18 22:54:32 UTC

Witness: 10 independent points log in to add more points →

(30873006960658240/3481, 29085719107485674750795/205379)
(20251377161556316162/2247001, 4760587481697251718848587613/3368254499)
(17980579292290, -55279851432005824145)
(22623488251907410/529, 3215835851873355943989785/12167)
(1869179367467405085085210/209345596849, -80562924965504361832597810164557015/95784612419082007)
(27184800095113842887650/72471169, -4478633084199591299280816472911985/616947061697)
(370878909627694930/38809, 33973985053317582490497875/7645373)
(255930278253763481410/23746129, 1282625373350955707047871844535/115714886617)
(3009776784184520702994061/316343253136, 750100501569274062482000331293225293/177925364666824384)
(710721721105429810/80089, -6074519685728176484308115/22665187)

Commentary

t = 127/373 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 2026-10-18 22:54:32 UTC · history