curve #4741

y² + y = x³ − 1617296497567

a-invariants: [0, 0, 1, 0, -1617296497567]
c-invariants: [0, 1397344173897672]
rank (lower bound): ≥ 5
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 6469185990267
discriminant (Δ): -1129959919170004286305744803
Faltings height: 3.8699
naive height: 69.7467
primes of bad reduction: 3, 7, 11, 13, 163
regulator: 3162.06878377157304964677524450190907953802342005
submitted by: David Renshaw
submitted at: 2026-10-20 21:27:37 UTC
last updated: 2026-10-20 21:27:37 UTC

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

(12103, 394439)
(14833, 1283054)
(15379, 1421283)
(27547, 4391627)
(45409, 9592446)

Commentary

Cube-sum curve x^3 + y^3 = 489489 (Weierstrass model y^2 = x^3 - 432*489489^2). 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 21:27:38 UTC · history