curve #2387

y² + xy = x³ − 86548536190x − 174819801715900

a-invariants: [1, 0, 0, -86548536190, -174819801715900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 243259170
discriminant (Δ): 41478300155422237766151721536000000
Faltings height: 5.3320
naive height: 87.1655
primes of bad reduction: 2, 3, 5, 7, 11, 31, 43, 79
regulator: 7.121397448390479105885124432017391851090
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:23 UTC
last updated: 2026-09-26 19:58:23 UTC

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

(-8554, 23771702)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-43, q=12; A=(3q-p)(p+q)^3=-2353489, B=-(p+3q)(p-q)^3=-1164625. 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 19:58:23 UTC · history