curve #2330

y² + xy = x³ − 501215063971x + 40447235690448065

a-invariants: [1, 0, 0, -501215063971, 40447235690448065]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2026094070
discriminant (Δ): 7351720584302772926129722517299022400
Faltings height: 5.7656
naive height: 92.4345
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 53, 67
regulator: 9.167934663419349631959643723994229442238
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:51 UTC
last updated: 2026-09-26 19:54:51 UTC

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

(-428944, 420354689)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=14; A=(3q-p)(p+q)^3=-5635305, B=-(p+3q)(p-q)^3=-3308393. 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 19:54:51 UTC · history