curve #2437

y² + xy + y = x³ − 49464345473x + 4233869458720256

a-invariants: [1, 0, 1, -49464345473, 4233869458720256]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 133996170
discriminant (Δ): 1734342836883363856632353062500
Faltings height: 4.8231
naive height: 85.4872
primes of bad reduction: 2, 3, 5, 7, 11, 19, 43, 71
regulator: 3.682082420219659987193425674106410935731
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:33 UTC
last updated: 2026-09-26 20:01:33 UTC

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

(-248295, 34882552)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=19; A=(3q-p)(p+q)^3=8875, B=-(p+3q)(p-q)^3=1545291. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 20:01:33 UTC · history