curve #2522

y² + xy = x³ − x² − 1360319310x + 19311544570500

a-invariants: [1, -1, 0, -1360319310, 19311544570500]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 159390
discriminant (Δ): 33724788611007717392400
Faltings height: 3.7425
naive height: 74.7066
primes of bad reduction: 2, 3, 5, 7, 11, 23
regulator: 8.151990551601195677289555773077041518715
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:06:50 UTC
last updated: 2026-09-26 20:06:50 UTC

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

(-15680, 6072990)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=11; A=(3q-p)(p+q)^3=-45, B=-(p+3q)(p-q)^3=255507. 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 20:06:50 UTC · history