curve #2388

y² + xy + y = x³ − x² − 82811204123x + 7954502395245131

a-invariants: [1, -1, 1, -82811204123, 7954502395245131]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 117810
discriminant (Δ): 9010945022845577916088355232153600
Faltings height: 5.2408
naive height: 87.0331
primes of bad reduction: 2, 3, 5, 7, 11, 17
regulator: 4.389108076187385496103875540777356441592
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:27 UTC
last updated: 2026-09-26 19:58:27 UTC

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

(-284277, 92458810)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-33, q=16; A=(3q-p)(p+q)^3=-397953, B=-(p+3q)(p-q)^3=1764735. 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 19:58:27 UTC · history