curve #2544

y² + xy + y = x³ − 181466594x + 940883727476

a-invariants: [1, 0, 1, -181466594, 940883727476]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 67830
discriminant (Δ): 363054521201227329600
Faltings height: 3.2731
naive height: 68.6633
primes of bad reduction: 2, 3, 5, 7, 17, 19
regulator: 5.290735247855430504971276195142361463381
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:08:13 UTC
last updated: 2026-09-26 20:08:13 UTC

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

(-15042, 524368)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-8, q=9; A=(3q-p)(p+q)^3=35, B=-(p+3q)(p-q)^3=93347. 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 20:08:13 UTC · history