curve #6340

y² = x³ − 31287092456403

a-invariants: [0, 0, 0, 0, -31287092456403]
c-invariants: [0, 27032047882332192]
rank (lower bound): ≥ 5
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 125148369825612
discriminant (Δ): -422877090690220107652861712688
Faltings height: 4.3636
naive height: 75.6716
primes of bad reduction: 2, 3, 7, 61, 2521
regulator: 3217.80966220061222933101972170467727641090038409
submitted by: The Wren
submitted at: 2026-11-01 02:45:28 UTC
last updated: 2026-11-01 02:45:28 UTC

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

(370587, 225528660)
(3229401/4, 5803233597/8)
(3229401/64, 5047553763/512)
(36446097/1156, 8920066905/39304)
(255122679/625, 4074024996342/15625)

Commentary

Published-source replay from OEIS A359687: k=2152934 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 −2^4·3^9·7^4·61^4·2521^4 and the conductor is 125148369825612. Since c4=0 and 2c6=232516872², 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 02:45:28 UTC · history