curve #2736

y² + xy = x³ − 1080971082x + 13678914712356

a-invariants: [1, 0, 0, -1080971082, 13678914712356]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 118698
discriminant (Δ): 5481890282879036260614144
Faltings height: 3.8310
naive height: 74.0170
primes of bad reduction: 2, 3, 73, 271
regulator: 5.522076526356417137934621997165685294596
submitted by: David Renshaw
submitted at: 2026-09-26 20:20:00 UTC
last updated: 2026-09-26 20:20:00 UTC

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

(53556, 10432614)

Commentary

Cremona 118698i1 = LMFDB 118698.f3: https://www.lmfdb.org/EllipticCurve/Q/118698/f/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 118698, minimal discriminant 5481890282879036260614144, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

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