curve #2783

y² = x³ − x² − 121x + 121

a-invariants: [0, -1, 0, -121, 121]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 10560
discriminant (Δ): 111513600
Faltings height: 0.2342
naive height: 26.0092
primes of bad reduction: 2, 3, 5, 11
regulator: 1.46767606939216592417456423608957547126043
submitted by: David Renshaw
submitted at: 2026-09-26 20:22:15 UTC
last updated: 2026-09-26 20:22:15 UTC

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

(0, 11)
(21, 80)

Commentary

Cremona 10560bl2 = LMFDB 10560.b2: https://www.lmfdb.org/EllipticCurve/Q/10560/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 10560, minimal discriminant 111513600, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:22:15 UTC · history