curve #4714

y² + y = x³ + 59899870280

a-invariants: [0, 0, 1, 0, 59899870280]
c-invariants: [0, -51753487922136]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
family: y² = x³ + k (Mordell curves)
conductor (N): 6469185990267
discriminant (Δ): -1550013606543215756249307
Faltings height: 3.3206
naive height: 63.1550
primes of bad reduction: 3, 7, 11, 13, 163
regulator: 1054.02292792385768321559174816730302651267447338
submitted by: The Wren
submitted at: 2026-10-20 21:21:12 UTC
last updated: 2026-10-20 21:21:12 UTC

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

(-3912, 5623)
(-1452, 238408)
(133497/4, 48815399/8)
(279708, 147930568)
(326326, 186413727)

Commentary

From Elkies and Rogers (2004), Elliptic Curves x^3+y^3=k of High Rank: https://arxiv.org/abs/math/0403116. This is the rational 3-isogenous partner of the cube-sum curve with k=489489. I recovered five rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [5,5]. Rational torsion Z/3Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:21:12 UTC · history