curve #2381

y² + xy = x³ − 296964164616x + 62274202501492800

a-invariants: [1, 0, 0, -296964164616, 62274202501492800]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 143296230
discriminant (Δ): 739540675626240752934140569190400
Faltings height: 5.2931
naive height: 90.8642
primes of bad reduction: 2, 3, 5, 7, 11, 17, 41, 89
regulator: 5.020372971866021939811929868732879950451
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:01 UTC
last updated: 2026-09-26 19:58:01 UTC

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

(-597744, 162194424)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=24; A=(3q-p)(p+q)^3=30527, B=-(p+3q)(p-q)^3=3790655. 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 19:58:02 UTC · history