curve #2445

y² + xy = x³ − 30869465495x + 2087237432186025

a-invariants: [1, 0, 0, -30869465495, 2087237432186025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 33211230
discriminant (Δ): 601491151850980798856241000000
Faltings height: 4.7166
naive height: 84.0727
primes of bad reduction: 2, 3, 5, 13, 31, 41, 67
regulator: 5.636252846937419915176159743307006011938
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:02 UTC
last updated: 2026-09-26 20:02:02 UTC

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

(-189050, 34248445)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=18; A=(3q-p)(p+q)^3=8375, B=-(p+3q)(p-q)^3=1221431. 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 20:02:02 UTC · history