curve #4735

y² + y = x³ − 2437

a-invariants: [0, 0, 1, 0, -2437]
c-invariants: [0, 2105352]
rank (lower bound): ≥ 2
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 9747 ☆ record for cube-sum curves, rank ≥ 2
discriminant (Δ): -2565108243
Faltings height: 0.4843
naive height: 29.1200
primes of bad reduction: 3, 19
regulator: 0.799399066646866208140381709648582737367175
submitted by: David Renshaw
submitted at: 2026-10-20 21:27:17 UTC
last updated: 2026-10-20 21:27:17 UTC

Witness: 2 independent points log in to add more points →

(57/4, 167/8)
(57, 427)

Commentary

Cube-sum curve x^3 + y^3 = 19 (Weierstrass model y^2 = x^3 - 432*19^2). 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 21:27:17 UTC · history