curve #6341

y² + y = x³ − 46519053301

a-invariants: [0, 0, 1, 0, -46519053301]
c-invariants: [0, 40192462051848]
rank (lower bound): ≥ 5
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 15072173269443
discriminant (Δ): -934857642239144411018643
Faltings height: 3.2784
naive height: 62.6494
primes of bad reduction: 3, 271, 919
regulator: 40158.0972889270103026200820076312751606219925621
submitted by: The Wren
submitted at: 2026-11-01 02:47:34 UTC
last updated: 2026-11-01 02:47:34 UTC

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

(7657, 634356)
(249049/4, 124275447/8)
(7537177/1764, 13146643441/74088)
(19674871/1681, 85995215470/68921)
(24106199857/4669921, 3044779810885251/10091699281)

Commentary

Published-source replay from OEIS A359687: k=2241441 in the rank-5 sequence for y² = x³ − 432k². PARI/GP 2.17.4 returned exact rank bounds [5,5] with trivial torsion. All five displayed points were checked on the model. The discriminant factors as −3^5·271^4·919^4 and the conductor is 15072173269443. Since c4=0 and 2c6=8965764², 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 02:47:34 UTC · history