curve #2636

y² + xy = x³ − 95639147386x + 6422137511474660

a-invariants: [1, 0, 0, -95639147386, 6422137511474660]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 77008470
discriminant (Δ): 38169594995437255265353580779929600
Faltings height: 5.3341
naive height: 87.4651
primes of bad reduction: 2, 3, 5, 7, 11, 17, 37, 53
regulator: 13.5273967452256298857202996784051452730323
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:14:20 UTC
last updated: 2026-09-26 20:14:20 UTC

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

(-337384, 17066930)
(-229996, 127599926)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=16; A=(3q-p)(p+q)^3=-787185, B=-(p+3q)(p-q)^3=1637647. 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 20:14:20 UTC · history