curve #2420

y² + xy + y = x³ − 533448389799x + 149963725551109366

a-invariants: [1, 0, 1, -533448389799, 149963725551109366]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 51299430
discriminant (Δ): 16850075155527464897776105112100
Faltings height: 5.2840
naive height: 92.6215
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 43
regulator: 4.300992091174344675649658109003056661621
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:29 UTC
last updated: 2026-09-26 20:00:29 UTC

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

(-663367, 460676568)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-26, q=23; A=(3q-p)(p+q)^3=-2565, B=-(p+3q)(p-q)^3=5058907. 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 20:00:29 UTC · history