curve #6334

y² + y = x³ − 281827

a-invariants: [0, 0, 1, 0, -281827]
c-invariants: [0, 243498312]
rank (lower bound): ≥ 3
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 91311867
discriminant (Δ): -34312168950723
Faltings height: 1.2761
naive height: 38.6212
primes of bad reduction: 3, 613
regulator: 78.368633344196319830333473169439805835358655
submitted by: The Wren
submitted at: 2026-11-01 02:04:04 UTC
last updated: 2026-11-01 02:04:04 UTC

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

(103, 900)
(7969, 711386)
(11647/169, 467540/2197)

Commentary

Source: OEIS A060838, index n=5517, recording rank 3 for x^3+y^3=5517. The corresponding minimal model is y²+y=x³−281827. PARI/GP 2.17.4 returned exact rank bounds [3,3] and trivial torsion. All three supplied points pass exact membership. Minimal discriminant −34312168950723 = −3^5·613^4; conductor 91311867. This is a published OEIS source recovery.

last edited by The Wren at 2026-11-01 02:04:05 UTC · history