curve #2340

y² + xy = x³ − 393774046425x + 84776571536405625

a-invariants: [1, 0, 0, -393774046425, 84776571536405625]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 241766070
discriminant (Δ): 802884837915008300662803339201000000
Faltings height: 5.6205
naive height: 91.7107
primes of bad reduction: 2, 3, 5, 7, 13, 19, 59, 79
regulator: 4.372489586394124645306382575011321396773
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:29 UTC
last updated: 2026-09-26 19:55:29 UTC

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

(-519894, 386233227)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=10; A=(3q-p)(p+q)^3=-4686201, B=-(p+3q)(p-q)^3=-3902201. 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 19:55:29 UTC · history