curve #2372

y² + xy = x³ − 128299393926x + 7021987582561380

a-invariants: [1, 0, 0, -128299393926, 7021987582561380]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 373557030
discriminant (Δ): 113860489868342159435706310742937600
Faltings height: 5.4201
naive height: 88.3465
primes of bad reduction: 2, 3, 5, 7, 11, 23, 79, 89
regulator: 4.232938934346843054712193851914471842980
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:28 UTC
last updated: 2026-09-26 19:57:28 UTC

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

(-379236, 33895290)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-5, q=28; A=(3q-p)(p+q)^3=1082863, B=-(p+3q)(p-q)^3=2839023. 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 19:57:28 UTC · history