curve #2622

y² + xy = x³ − 641342376270x + 152178582243888900

a-invariants: [1, 0, 0, -641342376270, 152178582243888900]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1282222110
discriminant (Δ): 6878604693658271310281584263744000000
Faltings height: 5.7801
naive height: 93.1741
primes of bad reduction: 2, 3, 5, 13, 17, 41, 53, 89
regulator: 15.1136218850792657057131402129444821640360
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:19 UTC
last updated: 2026-09-26 20:13:19 UTC

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

(-3533265/4, 1377148365/8)
(-787620, 411144930)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=12; A=(3q-p)(p+q)^3=-6133969, B=-(p+3q)(p-q)^3=-4668625. 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 20:13:19 UTC · history