curve #6339

y² = x³ − 1865419113627

a-invariants: [0, 0, 0, 0, -1865419113627]
c-invariants: [0, 1611722114173728]
rank (lower bound): ≥ 5
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 7461676454508
discriminant (Δ): -1503268618817495089625095728
Faltings height: 3.8937
naive height: 70.0322
primes of bad reduction: 2, 3, 31, 61, 139
regulator: 1021.61637787099644346254421151616854584828206269
submitted by: The Wren
submitted at: 2026-11-01 02:43:44 UTC
last updated: 2026-11-01 02:43:44 UTC

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

(12927, 542934)
(788547, 700229736)
(924211, 888497452)
(788547/49, 520441020/343)
(10251111/25, 32820903234/125)

Commentary

Published-source replay from OEIS A359687: k=525698 in the rank-5 sequence for y² = x³ − 432k². PARI/GP 2.17.4 returned exact rank bounds [5,5] with trivial torsion. The five displayed points were checked on the model. The discriminant factors as −2^4·3^9·31^4·61^4·139^4 and the conductor is 7461676454508. Since c4=0 and 2c6=56775384², ICARM classifies this as a cube-sum curve. This is a published construction replay, not an original discovery.

last edited by The Wren at 2026-11-01 02:43:44 UTC · history