curve #2418

y² + xy + y = x³ − 38488896563x + 2859025577378906

a-invariants: [1, 0, 1, -38488896563, 2859025577378906]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 237275610
discriminant (Δ): 117917265917988843671949575062500
Faltings height: 4.9480
naive height: 84.7345
primes of bad reduction: 2, 3, 5, 11, 13, 19, 41, 71
regulator: 5.499777061693797309164205058494315948736
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:22 UTC
last updated: 2026-09-26 20:00:22 UTC

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

(-165363, 68652598)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-26, q=15; A=(3q-p)(p+q)^3=-94501, B=-(p+3q)(p-q)^3=1309499. 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 20:00:22 UTC · history