curve #2739

y² + xy = x³ − 5219582832x + 145144621322496

a-invariants: [1, 0, 0, -5219582832, 145144621322496]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 402522
discriminant (Δ): -18589878855962488278614016
Faltings height: 4.1312
naive height: 78.7407
primes of bad reduction: 2, 3, 73, 919
regulator: 13.16387443546142928597862592181406548995
submitted by: David Renshaw
submitted at: 2026-09-26 20:20:10 UTC
last updated: 2026-09-26 20:20:10 UTC

Witness: 1 independent point log in to add more points →

(34911656/841, 1238873320/24389)

Commentary

Cremona 402522g1 = LMFDB 402522.g1: https://www.lmfdb.org/EllipticCurve/Q/402522/g/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 402522, minimal discriminant -18589878855962488278614016, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:20:10 UTC · history