curve #2629

y² + xy = x³ − 505214787431x + 138196766435339145

a-invariants: [1, 0, 0, -505214787431, 138196766435339145]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 800597490
discriminant (Δ): 2438889006691467873817603822785600
Faltings height: 5.4129
naive height: 92.4584
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 29, 37
regulator: 11.4465933123462019421592452756936251223194
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:45 UTC
last updated: 2026-09-26 20:13:45 UTC

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

(-808014, 137794029)
(-496472, 516629101)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=22; A=(3q-p)(p+q)^3=-32585, B=-(p+3q)(p-q)^3=4908087. 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 20:13:45 UTC · history