curve #4740

y² = x³ − 8130418443

a-invariants: [0, 0, 0, 0, -8130418443]
c-invariants: [0, 7024681534752]
rank (lower bound): ≥ 4
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 10840557924 ☆ record for cube-sum curves, rank ≥ 4
discriminant (Δ): -28556800153174603115568
Faltings height: 2.9877
naive height: 59.1609
primes of bad reduction: 2, 3, 7, 37, 67
regulator: 121.6464884678868112967982793014298781681883982
submitted by: David Renshaw
submitted at: 2026-10-20 21:27:34 UTC
last updated: 2026-10-20 21:27:34 UTC

Witness: 4 independent points log in to add more points →

(2479, 84286)
(17353/4, 2169125/8)
(52059/25, 3748248/125)
(96681/4, 30052917/8)

Commentary

Cube-sum curve x^3 + y^3 = 34706 (Weierstrass model y^2 = x^3 - 432*34706^2). 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 21:27:34 UTC · history