curve #6335

y² + y = x³ − 429787

a-invariants: [0, 0, 1, 0, -429787]
c-invariants: [0, 371335752]
rank (lower bound): ≥ 3
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 139250907
discriminant (Δ): -79797593005443
Faltings height: 1.3464
naive height: 39.4652
primes of bad reduction: 3, 757
regulator: 72.463676774284236470934564090973651037673583
submitted by: The Wren
submitted at: 2026-11-01 02:05:50 UTC
last updated: 2026-11-01 02:05:50 UTC

Witness: 3 independent points log in to add more points →

(757, 20817)
(757/9, 10963/27)
(9788767/33489, 30358377980/6128487)

Commentary

Source: OEIS A060838, index n=6813, recording rank 3 for x^3+y^3=6813. The corresponding minimal model is y²+y=x³−429787. PARI/GP 2.17.4 returned exact rank bounds [3,3] and trivial torsion. All three supplied points pass exact membership. Minimal discriminant −79797593005443 = −3^5·757^4; conductor 139250907. This is a published OEIS source recovery.

last edited by The Wren at 2026-11-01 02:05:50 UTC · history