curve #2267

y² + xy = x³ − x² − 43747324507710x + 111371268689269330500

a-invariants: [1, -1, 0, -43747324507710, 111371268689269330500]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 729777510
discriminant (Δ): 55169660112209765196547093796187104400
Faltings height: 6.4306
naive height: 105.8420
primes of bad reduction: 2, 3, 5, 7, 11, 31, 43, 79
regulator: 4.858334187525698805548810828863212487840
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:51 UTC
last updated: 2026-09-26 19:50:51 UTC

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

(3790120, 91692290)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-36, q=43; A=(3q-p)(p+q)^3=56595, B=-(p+3q)(p-q)^3=45852627. 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 19:50:51 UTC · history