curve #2322

y² + xy + y = x³ − 605383380004x + 155818881509261906

a-invariants: [1, 0, 1, -605383380004, 155818881509261906]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 397687290
discriminant (Δ): 3710686708255786319517365400255363600
Faltings height: 5.7410
naive height: 93.0010
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 41
regulator: 3.701588642692950780251210321794498908615
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:20 UTC
last updated: 2026-09-26 19:54:20 UTC

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

(262969, 121551923)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-52, q=11; A=(3q-p)(p+q)^3=-5858285, B=-(p+3q)(p-q)^3=-4750893. 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 19:54:20 UTC · history