curve #2286

y² + xy = x³ − 2304805431506x + 1258285411882678020

a-invariants: [1, 0, 0, -2304805431506, 1258285411882678020]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 13123110
discriminant (Δ): 99600875678758534460958087078183014400
Faltings height: 6.0372
naive height: 97.0117
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23
regulator: 4.834209349265429143210891660190634536739
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:07 UTC
last updated: 2026-09-26 19:52:07 UTC

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

(568408, 362842846)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=36; A=(3q-p)(p+q)^3=1472207, B=-(p+3q)(p-q)^3=11176655. 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 19:52:07 UTC · history