curve #2628

y² + xy = x³ − 338846767400x + 73590716294760000

a-invariants: [1, 0, 0, -338846767400, 73590716294760000]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 329261790
discriminant (Δ): 150408294381649658861227708416000000
Faltings height: 5.5210
naive height: 91.2600
primes of bad reduction: 2, 3, 5, 11, 13, 23, 47, 71
regulator: 6.54955670822685879320993548727078239644690
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:41 UTC
last updated: 2026-09-26 20:13:41 UTC

Witness: 2 independent points log in to add more points →

(-655280, 119736280)
(-578000, 276592600)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=8; A=(3q-p)(p+q)^3=-4211649, B=-(p+3q)(p-q)^3=-3826625. 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 20:13:41 UTC · history