curve #3306

y² + xy + y = x³ + x² − 2460x + 45949

a-invariants: [1, 1, 1, -2460, 45949]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/5ℤ
conductor (N): 862
discriminant (Δ): -451936256
Faltings height: 0.6432
naive height: 35.0379
primes of bad reduction: 2, 431
regulator: 2.137778577888988860281515907617440528250
submitted by: David Renshaw
submitted at: 2026-09-26 20:55:00 UTC
last updated: 2026-09-26 20:55:00 UTC

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

(23, 35)

Commentary

Cremona 862e1 = LMFDB 862.d1: https://www.lmfdb.org/EllipticCurve/Q/862/d/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 862, minimal discriminant -451936256, torsion ℤ/5ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:55:00 UTC · history