curve #4639

y² + xy = x³ − 4633074603274187127504705x + 3841024406642870375074093594635206025

a-invariants: [1, 0, 0, -4633074603274187127504705, 3841024406642870375074093594635206025]
c-invariants: [222387580957160982120225841, -3318645087339773585435452607237998344361]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 305531675428447570189919539286670
discriminant (Δ): -8653062483403419430722074086994215860278532641502956844450678661632000000
Faltings height: 12.9262
naive height: 182.0008
primes of bad reduction: 2, 3, 5, 7, 13, 31, 53, 59, 71, 103, 149, 265718861, 3987491731
regulator: 180166793913.2215501571147720429338973901922537070778846470
submitted by: Maksym Voznyy
submitted at: 2026-10-19 09:18:40 UTC
last updated: 2026-10-19 09:18:40 UTC

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

(167906719711852410/121801, 11554010739585700431125655/42508549)
(-275160045403265700/157609, -160849275348108442041228435/62570773)
(82970187915799769610/74666881, -164264546226939900956690986005/645196518721)
(147168717202173090/117649, 2157665762666593242738165/40353607)
(6111714389141562678010/5994011241, -195262893324859705390125701023705/464062344289461)
(2962510499506602458010/2622566521, -29684165159061559471803837611055/134304254106931)
(42951193691132458769790/9821404609, 7979991588556130462186263432060065/973330660965727)
(82372433014252560/32041, 17130754304490654022609455/5735339)
(-2337463598027190/961, -25279245192859199849355/29791)
(3216316104524293168890/2855512969, 34634244476649600696162790844535/152590046524453)

Commentary

t = 799/181 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 09:18:40 UTC · history