curve #2508

y² + xy = x³ − 94817916x − 164841058800

a-invariants: [1, 0, 0, -94817916, -164841058800]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1111110
discriminant (Δ): 42819662302946934947942400
Faltings height: 3.6133
naive height: 66.7160
primes of bad reduction: 2, 3, 5, 7, 11, 13, 37
regulator: 2.733043379245865586479501181347058123854
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:57 UTC
last updated: 2026-09-26 20:05:57 UTC

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

(-8400, 201540)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=12; A=(3q-p)(p+q)^3=49247, B=-(p+3q)(p-q)^3=76895. 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 20:05:57 UTC · history