curve #2618

y² + xy = x³ − 1428815007255x + 656692442010074025

a-invariants: [1, 0, 0, -1428815007255, 656692442010074025]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 339664710
discriminant (Δ): 386488890398721590182824502689000000
Faltings height: 5.7395
naive height: 95.5772
primes of bad reduction: 2, 3, 5, 7, 11, 19, 71, 109
regulator: 15.5609808921838610719571528422646905969420
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:05 UTC
last updated: 2026-09-26 20:13:05 UTC

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

(-1355808, 319464141)
(-1069038, 981558717)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=30; A=(3q-p)(p+q)^3=145079, B=-(p+3q)(p-q)^3=8353079. 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 20:13:05 UTC · history