curve #2392

y² + xy = x³ − 76184850960x + 7565977046073600

a-invariants: [1, 0, 0, -76184850960, 7565977046073600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 58702530
discriminant (Δ): 3570508003350887533497286656000000
Faltings height: 5.1844
naive height: 86.7829
primes of bad reduction: 2, 3, 5, 17, 31, 47, 79
regulator: 7.691755735683768983705320642413298964212
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:43 UTC
last updated: 2026-09-26 19:58:43 UTC

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

(-316320, 3944880)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=16; A=(3q-p)(p+q)^3=-266625, B=-(p+3q)(p-q)^3=1764991. 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 19:58:43 UTC · history