curve #2729

y² + xy + y = x³ − x² + 9555583x + 26802839441

a-invariants: [1, -1, 1, 9555583, 26802839441]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 417690
discriminant (Δ): -366241548885849000000000
Faltings height: 3.2043
naive height: 61.5469
primes of bad reduction: 2, 3, 5, 7, 13, 17
regulator: 2.144954042440379449187235777052255795846
submitted by: David Renshaw
submitted at: 2026-09-26 20:19:40 UTC
last updated: 2026-09-26 20:19:40 UTC

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

(4681, 414894)

Commentary

Cremona 417690cy2 = LMFDB 417690.cy3: https://www.lmfdb.org/EllipticCurve/Q/417690/cy/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 417690, minimal discriminant -366241548885849000000000, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:19:40 UTC · history