curve #4637

y² + xy = x³ − 1405739329657645007269507360x + 20284293616725134193874411080402881561600

a-invariants: [1, 0, 0, -1405739329657645007269507360, 20284293616725134193874411080402881561600]
c-invariants: [67475487823566960348936353281, -17525629684850617156739226523908613073752321]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 3993916479095036308148774870430
discriminant (Δ): 37181709844539827546864677898707222311927850719440819047097468658319884288000000
Faltings height: 14.2924
naive height: 199.1447
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 41, 71, 331, 887755717, 5361446437
regulator: 93901953813.85403100073069416530019163953718833010792539710
submitted by: Maksym Voznyy
submitted at: 2026-10-19 09:07:34 UTC
last updated: 2026-10-19 09:07:34 UTC

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

(761806290754917440/10201, -593470490684663978255134880/1030301)
(1009439306729308758080/42680089, 4555143148775749356330591165280/278829021437)
(86880711206641175592205225280/3862461284582209, -1611443982545108958414482197745179484055520/240046959224498186224927)
(6426442537029041077280/285035689, 34412394181268097665033655602080/4812257537387)
(13236661497939512350880/1682209, -1522869803937516015199334412023680/2181825073)
(30888892804746428333120/279591841, 5149836138508027711728485144854240/4675055173361)
(78632150414449501375113680/2464639386889, -344121400615061121334834794395369144480/3869279272346618213)
(1053806213376974496131648/48181567009, -11456540726823621537198093864179936/10575998503176527)
(1760019215753690432/78961, -110931337709568094094029088/22188041)
(61951476670692364719680/2836308049, -91930456797420940955507816526880/151053257765593)

Commentary

t = 319/461 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 09:07:34 UTC · history