curve #2355

y² + xy + y = x³ − 249514028783x + 44109943159425806

a-invariants: [1, 0, 1, -249514028783, 44109943159425806]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 389511210
discriminant (Δ): 153642060726318360405688630950562500
Faltings height: 5.4915
naive height: 90.3419
primes of bad reduction: 2, 3, 5, 11, 19, 23, 37, 73
regulator: 2.928240312629879937880687985959094095738
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:25 UTC
last updated: 2026-09-26 19:56:25 UTC

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

(-516360, 188069842)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-46, q=9; A=(3q-p)(p+q)^3=-3697669, B=-(p+3q)(p-q)^3=-3161125. 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 19:56:25 UTC · history