curve #4605

y² + xy = x³ − 7349376973374362592596305x + 7666427465337816486893078697173962025

a-invariants: [1, 0, 0, -7349376973374362592596305, 7666427465337816486893078697173962025]
c-invariants: [352770094721969404444622641, -6623793330052402599817702948464970123561]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 227330267084502693153717914909670
discriminant (Δ): 15306761109738019796410098450619478031029656894987770899017527971328000000
Faltings height: 13.0134
naive height: 183.3836
primes of bad reduction: 2, 3, 5, 7, 11, 13, 31, 107, 167, 179, 5881, 7666573, 1693302313
regulator: 135121848632.9305955892836954322529660778471185736103653718
submitted by: Maksym Voznyy
submitted at: 2026-10-18 23:22:46 UTC
last updated: 2026-10-18 23:22:46 UTC

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

(12076066220539690/7921, 51656109677383143253235/704969)
(7777617955195482890/7856809, 25693835644972542145871687465/22022635627)
(4774750648202811459770/95981209, 329453208157704507306710634576175/940327904573)
(-7411480436025666976774/4730550841, -1274123596667639263333879205261887/325362556293139)
(20583032271278223868610/12957496561, 23610078091115801757571439761045/1474964791035191)
(22519184257545657878090/14111776849, 77044416339634135359239975878915/1676380307223257)
(112572107744222479132730/73127517241, -557460217772098817049835141977025/19775216339828461)
(374262709475348699549/212343184, 1342581556450159688039517796031/3094264877248)
(4105783590567785930/2765569, -764771406090033832433240155/4599141247)
(-131012347422139510/82369, -92564997775228315229499515/23639903)

Commentary

t = 131/241 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 23:22:46 UTC · history