curve #2335

y² + xy + y = x³ − 507355385373x + 138221603418250756

a-invariants: [1, 0, 1, -507355385373, 138221603418250756]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1436064630
discriminant (Δ): 104821245954432716278048659743062500
Faltings height: 5.5513
naive height: 92.4710
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 29, 97
regulator: 2.318059367775337638824362865923033584701
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:10 UTC
last updated: 2026-09-26 19:55:10 UTC

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

(-742705, 324952752)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=21; A=(3q-p)(p+q)^3=-213109, B=-(p+3q)(p-q)^3=4824875. 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 19:55:10 UTC · history