curve #2864

y² + xy = x³ − 494845990x + 4236906928100

a-invariants: [1, 0, 0, -494845990, 4236906928100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/10ℤ
conductor (N): 61770
discriminant (Δ): 1631134479352924800000
Faltings height: 3.4898
naive height: 71.6729
primes of bad reduction: 2, 3, 5, 29, 71
regulator: 5.537035265245930647452161041396821899796
submitted by: David Renshaw
submitted at: 2026-09-26 20:25:52 UTC
last updated: 2026-09-26 20:25:52 UTC

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

(-14158, 2906222)

Commentary

Cremona 61770bi2 = LMFDB 61770.be2: https://www.lmfdb.org/EllipticCurve/Q/61770/be/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 61770, minimal discriminant 1631134479352924800000, torsion ℤ/10ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:25:52 UTC · history