curve #4602

y² + xy = x³ − 195502573853583863408504480x + 1052086684085421050936509115038547174400

a-invariants: [1, 0, 0, -195502573853583863408504480, 1052086684085421050936509115038547174400]
c-invariants: [9384123544972025443608215041, -909002895049817864194461333431470171004161]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 2713500159794080585317568047438570
discriminant (Δ): 55735089022046527477386371369459756769961277836259210683757794428715008000000
Faltings height: 13.7812
naive height: 193.2265
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 37, 43, 109, 157, 469411, 16178695076899
regulator: 30521623461.99650946863390031281234987599995733942352326840
submitted by: Maksym Voznyy
submitted at: 2026-10-18 22:59:47 UTC
last updated: 2026-10-18 22:59:47 UTC

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

(2457782107090240/289, 10461980973246640849760/4913)
(22031913613141894423360/2469195481, -521328299276796741816331138240480/122696792646371)
(26575489077105559360/2550409, 49269439879634498778382209760/4073003173)
(315812906904185288602060/33599256601, -41270669163512376123811603515220880/6158777334219901)
(610435146233039252953240/15864158209, -449035364591171797363625123386379360/1998138318898177)
(27890915652859094080/3433609, 32959071188763310247844320/6362477477)
(713520898113951760/85849, 29033202906740132575727840/25153757)
(9088005102266104/289, -792209466783035926325344/4913)
(9863367640000, -9129118631680990880)
(1649731804202321560/192721, 203960093767226798787929080/84604519)

Commentary

t = 269/359 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 22:59:47 UTC · history