curve #2255

y² + xy + y = x³ − 92068659682814x + 340027902657950559536

a-invariants: [1, 0, 1, -92068659682814, 340027902657950559536]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5232570630
discriminant (Δ): 294042958254359871457597048359139406400
Faltings height: 6.6021
naive height: 108.0743
primes of bad reduction: 2, 3, 5, 7, 29, 47, 101, 181
regulator: 5.746426042496760396031564833649876239828
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:05 UTC
last updated: 2026-09-26 19:50:05 UTC

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

(5667789, 519924733)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=47; A=(3q-p)(p+q)^3=62083, B=-(p+3q)(p-q)^3=66508803. 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 19:50:05 UTC · history