curve #2252

y² + xy = x³ − 18000516503201x + 29382836800461732105

a-invariants: [1, 0, 0, -18000516503201, 29382836800461732105]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 510728790
discriminant (Δ): 312418944674606368957383970520306702400
Faltings height: 6.3407
naive height: 103.1779
primes of bad reduction: 2, 3, 5, 11, 13, 17, 47, 149
regulator: 3.975085028077402128395121491014885166634
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:54 UTC
last updated: 2026-09-26 19:49:54 UTC

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

(2392648, 105032851)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=34; A=(3q-p)(p+q)^3=-327353, B=-(p+3q)(p-q)^3=29229255. 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 19:49:54 UTC · history