curve #2471

y² + xy = x³ − 32254873510x + 2229654167152100

a-invariants: [1, 0, 0, -32254873510, 2229654167152100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 7752570
discriminant (Δ): 30641392183312533159936000000
Faltings height: 4.6362
naive height: 84.2044
primes of bad reduction: 2, 3, 5, 7, 19, 29, 67
regulator: 3.544234449999414526797926631828502525826
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:03:40 UTC
last updated: 2026-09-26 20:03:40 UTC

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

(-176020, 49621130)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=16; A=(3q-p)(p+q)^3=-1809, B=-(p+3q)(p-q)^3=1243375. 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 20:03:40 UTC · history