curve #2414

y² + xy = x³ − 43459957946x + 1980891342208740

a-invariants: [1, 0, 0, -43459957946, 1980891342208740]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 85278270
discriminant (Δ): 3558345449879542067954509735526400
Faltings height: 5.1365
naive height: 85.0989
primes of bad reduction: 2, 3, 5, 7, 11, 19, 29, 67
regulator: 4.782240664780350872678140721593953835782
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:07 UTC
last updated: 2026-09-26 20:00:07 UTC

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

(47806, 3511864)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-5, q=24; A=(3q-p)(p+q)^3=528143, B=-(p+3q)(p-q)^3=1634063. 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 20:00:08 UTC · history