curve #2369

y² + xy = x³ − 1361827899240x + 611684340535425600

a-invariants: [1, 0, 0, -1361827899240, 611684340535425600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 535931970
discriminant (Δ): 2985878750586876564479309376000000
Faltings height: 5.5789
naive height: 95.4331
primes of bad reduction: 2, 3, 5, 7, 17, 23, 61, 107
regulator: 5.058162919636335468170825733065142358062
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:18 UTC
last updated: 2026-09-26 19:57:18 UTC

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

(-1232550, 646945140)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=28; A=(3q-p)(p+q)^3=13375, B=-(p+3q)(p-q)^3=8091711. 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 19:57:18 UTC · history