curve #2627

y² + xy + y = x³ − x² − 381896194388x + 90581601506435831

a-invariants: [1, -1, 1, -381896194388, 90581601506435831]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 114504390
discriminant (Δ): 20078388500331509364865963932417600
Faltings height: 5.4477
naive height: 91.6188
primes of bad reduction: 2, 3, 5, 7, 11, 13, 31, 41
regulator: 17.6407779770580377745836013179429869187130
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:37 UTC
last updated: 2026-09-26 20:13:37 UTC

Witness: 2 independent points log in to add more points →

(-501549, 395163061)
(-441185/4, 2899947651/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-15, q=26; A=(3q-p)(p+q)^3=123783, B=-(p+3q)(p-q)^3=4342023. 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 20:13:38 UTC · history