curve #2319

y² + xy = x³ − 3590508384596x + 2618588957907876240

a-invariants: [1, 0, 0, -3590508384596, 2618588957907876240]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3116190
discriminant (Δ): 199850251649122942309906608291840000
Faltings height: 5.8579
naive height: 98.3415
primes of bad reduction: 2, 3, 5, 7, 11, 19, 71
regulator: 6.117010915949899256417809386516737805451
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:09 UTC
last updated: 2026-09-26 19:54:09 UTC

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

(-2167544, 467471980)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=32; A=(3q-p)(p+q)^3=41503, B=-(p+3q)(p-q)^3=13148703. 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 19:54:09 UTC · history