curve #2456

y² + xy + y = x³ − 5555665284x − 1434733352654

a-invariants: [1, 0, 1, -5555665284, -1434733352654]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 31141110
discriminant (Δ): 10973698471681467170217417248400
Faltings height: 4.6456
naive height: 78.9279
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 61
regulator: 3.780404100927617800955324363550489997307
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:42 UTC
last updated: 2026-09-26 20:02:42 UTC

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

(-295813/4, 18129999/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=11; A=(3q-p)(p+q)^3=-299693, B=-(p+3q)(p-q)^3=296595. 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 20:02:42 UTC · history