curve #2344

y² + xy + y = x³ − x² − 354601482647x + 80603184624262319

a-invariants: [1, -1, 1, -354601482647, 80603184624262319]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 21145410
discriminant (Δ): 47012853349819651977318182976000000
Faltings height: 5.4734
naive height: 91.3964
primes of bad reduction: 2, 3, 5, 11, 13, 31, 53
regulator: 6.080843701459796392805716970875460082577
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:43 UTC
last updated: 2026-09-26 19:55:43 UTC

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

(375787, 20196886)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-33, q=20; A=(3q-p)(p+q)^3=-204321, B=-(p+3q)(p-q)^3=4019679. 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 19:55:43 UTC · history