curve #2439

y² + xy = x³ − 70630086715x + 7224747469574225

a-invariants: [1, 0, 0, -70630086715, 7224747469574225]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 134646330
discriminant (Δ): 1007023555175728077982449000000
Faltings height: 4.8638
naive height: 86.5558
primes of bad reduction: 2, 3, 5, 7, 13, 31, 37, 43
regulator: 2.264886906101502460590700445621814934654
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:40 UTC
last updated: 2026-09-26 20:01:40 UTC

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

(-172310, 119580985)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=2; A=(3q-p)(p+q)^3=-1843625, B=-(p+3q)(p-q)^3=-1838889. 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 20:01:40 UTC · history