curve #2787

y² + xy + y = x³ − 222x − 1220

a-invariants: [1, 0, 1, -222, -1220]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 8502
discriminant (Δ): 72284004
Faltings height: 0.2606
naive height: 27.8152
primes of bad reduction: 2, 3, 13, 109
regulator: 3.41755890818183821563630896792156575209707
submitted by: David Renshaw
submitted at: 2026-09-26 20:22:25 UTC
last updated: 2026-09-26 20:22:25 UTC

Witness: 2 independent points log in to add more points →

(19, 29)
(-8, 11)

Commentary

Cremona 8502b2 = LMFDB 8502.b2: https://www.lmfdb.org/EllipticCurve/Q/8502/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 8502, minimal discriminant 72284004, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:22:25 UTC · history