curve #2856

y² + xy = x³ − 30845990x + 66567728100

a-invariants: [1, 0, 0, -30845990, 66567728100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/10ℤ
conductor (N): 61770
discriminant (Δ): -36104958351360000000000
Faltings height: 3.1432
naive height: 63.3662
primes of bad reduction: 2, 3, 5, 29, 71
regulator: 2.768517632622965323726080520698410949898
submitted by: David Renshaw
submitted at: 2026-09-26 20:25:33 UTC
last updated: 2026-09-26 20:25:33 UTC

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

(2580, 63210)

Commentary

Cremona 61770bi1 = LMFDB 61770.be3: https://www.lmfdb.org/EllipticCurve/Q/61770/be/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 61770, minimal discriminant -36104958351360000000000, torsion ℤ/10ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:25:33 UTC · history