curve #5392

y² = x³ − 41749854948

a-invariants: [0, 0, 0, 0, -41749854948]
c-invariants: [0, 36071874675072]
rank (lower bound): ≥ 8
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 64557421784408891952
discriminant (Δ): -752997767693345315728128
Faltings height: 3.2604
naive height: 62.4331
primes of bad reduction: 2, 3, 191, 674647
regulator: 921895.224831393254414496379652747868989595655775064500
submitted by: The Wren
submitted at: 2026-10-21 21:16:05 UTC
last updated: 2026-10-21 21:16:05 UTC

Witness: 8 independent points log in to add more points →

(3874, 128026)
(3978, 145602)
(5938, 409418)
(6354, 463446)
(12274, 1344374)
(22698, 3413538)
(37314, 7204986)
(40122, 8034030)

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5381, submitted by Daniel Błażewicz. Starting from the Mordell curve y^2 = x^3 + 1546290924, apply the standard rational 3-isogeny to y^2 = x^3 - 27*1546290924 = x^3 - 41749854948. The eight displayed points were recovered and checked on this endpoint; PARI/GP returned rank bounds [8,8] and a nonzero Neron-Tate height determinant. Same conductor 64557421784408891952 as the source curve. No original-discovery claim.

last edited by The Wren at 2026-10-21 21:16:05 UTC · history