curve #4588

y² + xy = x³ − 83988444309685736055608111x + 296413717732770620086157366281226224185

a-invariants: [1, 0, 0, -83988444309685736055608111, 296413717732770620086157366281226224185]
c-invariants: [4031445326864915330669189329, -256101452121119862922430261839975461479833]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 433617240451046823424614270
discriminant (Δ): -38588711019421717367543442093484784060359339961983062702483516103574094643200
Faltings height: 13.6404
naive height: 190.6928
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 31, 83, 193, 46411, 96469, 163477
regulator: 384430887.04259212732936148074068940777326907783434717002
submitted by: Maksym Voznyy
submitted at: 2026-10-18 14:10:25 UTC
last updated: 2026-10-18 14:10:25 UTC

Witness: 9 independent points log in to add more points →

(5789185340326, -2052237166951010051)
(2429212205321968918/292681, -2071053561328653175732134479/158340421)
(5266648644736, -400279169638395605)
(503344411278629758/109561, 99463231957754851042390711/36264691)
(429686976323571364/80089, 11057117426464697221867063/22665187)
(-4967498950345562129354/188692065769, 1416424326991173824201288893791951455/81965380373198603)
(-53126361192704522277410/14880828169, 42601155267291267706269882234128935/1815267585851803)
(677114861832118/841, -369325466255380897772431/24389)
(20974200288871408/3721, -327953814287400090609689/226981)

Commentary

t = 467/305 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 14:10:25 UTC · history