curve #2218

y² + xy + y = x³ − 150610707827884x + 711407600698698648746

a-invariants: [1, 0, 1, -150610707827884, 711407600698698648746]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 11133712590
discriminant (Δ): 13471532683715201824250721096608560449600
Faltings height: 6.7893
naive height: 109.5508
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 113, 193
regulator: 3.622230526055361416812335953414398278163
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:48 UTC
last updated: 2026-09-26 19:47:48 UTC

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

(7183993, 427063943)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=51; A=(3q-p)(p+q)^3=256883, B=-(p+3q)(p-q)^3=85153523. 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 19:47:48 UTC · history