curve #2371

y² + xy = x³ − 133260875650x + 18396163109922500

a-invariants: [1, 0, 0, -133260875650, 18396163109922500]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 152041890
discriminant (Δ): 5259410333280469769930182656000000
Faltings height: 5.2618
naive height: 88.4603
primes of bad reduction: 2, 3, 5, 7, 11, 13, 61, 83
regulator: 1.957053754638464229283512176264885915839
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:25 UTC
last updated: 2026-09-26 19:57:25 UTC

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

(-247450, 190438850)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-11, q=24; A=(3q-p)(p+q)^3=182351, B=-(p+3q)(p-q)^3=2615375. 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 19:57:25 UTC · history