curve #2476

y² + xy = x³ − 2227866201x − 29639429660295

a-invariants: [1, 0, 0, -2227866201, -29639429660295]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5649270
discriminant (Δ): 328191465200032067097457857600
Faltings height: 4.3718
naive height: 76.1865
primes of bad reduction: 2, 3, 5, 11, 17, 19, 53
regulator: 4.855188290216240635647014614161408984033
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:03:59 UTC
last updated: 2026-09-26 20:03:59 UTC

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

(-24352, 3201611)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=18; A=(3q-p)(p+q)^3=270215, B=-(p+3q)(p-q)^3=363527. 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 20:03:59 UTC · history