curve #2262

y² + xy = x³ − x² − 6558286225374x + 5263235622988902468

a-invariants: [1, -1, 0, -6558286225374, 5263235622988902468]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 806318370
discriminant (Δ): 6085965335170021953673721901705182250000
Faltings height: 6.3507
naive height: 100.1489
primes of bad reduction: 2, 3, 5, 11, 13, 31, 43, 47
regulator: 4.492565225386501815887234932263981963777
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:32 UTC
last updated: 2026-09-26 19:50:32 UTC

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

(3641703/4, 1731298647/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=43; A=(3q-p)(p+q)^3=4200531, B=-(p+3q)(p-q)^3=19465875. 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 19:50:32 UTC · history