curve #2272

y² + xy = x³ − 10502345090210x + 13097185557382796100

a-invariants: [1, 0, 0, -10502345090210, 13097185557382796100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 104537730
discriminant (Δ): 33973619003310076646916096000000000000
Faltings height: 6.1857
naive height: 101.5615
primes of bad reduction: 2, 3, 5, 11, 43, 53, 139
regulator: 3.988424312772213316800969556586150259730
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:10 UTC
last updated: 2026-09-26 19:51:10 UTC

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

(1846300, 19518190)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-43, q=32; A=(3q-p)(p+q)^3=-185009, B=-(p+3q)(p-q)^3=22359375. 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 19:51:10 UTC · history