curve #2496

y² + xy + y = x³ − x² − 600507338x + 3379679233481

a-invariants: [1, -1, 1, -600507338, 3379679233481]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1531530
discriminant (Δ): 8925131104306733707701710400
Faltings height: 4.0631
naive height: 72.2535
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17
regulator: 3.212817863229253552473511416555823385869
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:12 UTC
last updated: 2026-09-26 20:05:12 UTC

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

(-25515, 1458607)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-3, q=14; A=(3q-p)(p+q)^3=59895, B=-(p+3q)(p-q)^3=191607. 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 20:05:13 UTC · history