curve #2625

y² + xy = x³ − 424996114390x + 102648347093560100

a-invariants: [1, 0, 0, -424996114390, 102648347093560100]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 799880430
discriminant (Δ): 361014981697392143000683669056000000
Faltings height: 5.5871
naive height: 91.9396
primes of bad reduction: 2, 3, 5, 17, 19, 23, 37, 97
regulator: 14.5974614423817544652994290085281755544436
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:30 UTC
last updated: 2026-09-26 20:13:30 UTC

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

(-2807005/4, 1884240355/8)
(299180, 47570810)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=20; A=(3q-p)(p+q)^3=-476561, B=-(p+3q)(p-q)^3=4259439. 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 20:13:30 UTC · history