curve #4590

y² + xy + y = x³ − x² − 232527346414020761580752x + 43139664192317377855663276753728179

a-invariants: [1, -1, 1, -232527346414020761580752, 43139664192317377855663276753728179]
c-invariants: [11161312627872996555876081, -37272669862111988560467642630719704521]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 110901090159640526928003889351830
discriminant (Δ): 675625645889744332227226112360925940110869564263781929625242176000000
Faltings height: 12.1613
naive height: 173.0235
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 41, 43, 53, 59, 71, 317, 18379, 236164783
regulator: 212160252036.6263297289490752485230929514550740105674507037
submitted by: Maksym Voznyy
submitted at: 2026-10-18 15:04:13 UTC
last updated: 2026-10-18 15:04:13 UTC

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

(213400928388332834437/37933281, 3106318953654542732957098433039/233631077679)
(126422598382568133/418609, -5810658937004713852843537/270840023)
(13909954187031798757/7458361, 50292803962460446527558860371/20368783891)
(1491460286320293/4489, -15215604271393476980597/300763)
(705776949693731502273/2436705769, 1133473742054155774890084054547/120283106875147)
(22660656659798237077/34680321, -84251702972569390297258176511/204232410369)
(280398260414810673/76729, 147246134391771798238994473/21253933)
(2834391966434549949877/5800193281, 94952869547354012153477301332599/441736920087679)
(121755353860316629653/416690569, 101843470319606798297601249157/8505904584997)
(59346198879770509449/205951201, -23316953350642028352747996973/2955605685551)

Commentary

t = 75/157 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 15:04:13 UTC · history