curve #4739

y² = x³ − 5390481963

a-invariants: [0, 0, 0, 0, -5390481963]
c-invariants: [0, 4657376416032]
rank (lower bound): ≥ 5
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 1746516156012 ☆ record for cube-sum curves, rank ≥ 5
discriminant (Δ): -12552751782761040015408 ☆ record for cube-sum curves, rank ≥ 5
Faltings height: 2.9192 ☆ record for cube-sum curves, rank ≥ 5
naive height: 58.3389 ☆ record for cube-sum curves, rank ≥ 5
primes of bad reduction: 2, 3, 19, 23, 97
regulator: 2844.52116748227855920035412401598547861879595846
submitted by: David Renshaw
submitted at: 2026-10-20 21:27:30 UTC
last updated: 2026-10-20 21:27:30 UTC

Witness: 5 independent points log in to add more points →

(1843, 29488)
(3439, 187834)
(6499, 518756)
(7663, 666778)
(21679, 3191126)

Commentary

Cube-sum curve x^3 + y^3 = 763002 (Weierstrass model y^2 = x^3 - 432*763002^2). Source: Elkies & Rogers, 'Elliptic Curves x^3+y^3=k of High Rank', ANTS-VI (LNCS 3076, 2004), arXiv:math/0403116, https://arxiv.org/abs/math/0403116.

last edited by David Renshaw at 2026-10-20 21:27:30 UTC · history