curve #2608

y² + xy + y = x³ − 5021452375364x + 4329306215567414786

a-invariants: [1, 0, 1, -5021452375364, 4329306215567414786]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1313836590
discriminant (Δ): 6482787457546589305113119160368193600
Faltings height: 6.0200
naive height: 99.3478
primes of bad reduction: 2, 3, 5, 11, 23, 29, 47, 127
regulator: 40.8161357598636249480470602557701809313496
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:27 UTC
last updated: 2026-09-26 20:12:27 UTC

Witness: 2 independent points log in to add more points →

(1263828, 40816213)
(1432689, 274713127)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=29; A=(3q-p)(p+q)^3=-169037, B=-(p+3q)(p-q)^3=15439923. 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 20:12:27 UTC · history