curve #2336

y² + xy + y = x³ − 457168669273x − 85469569045618744

a-invariants: [1, 0, 1, -457168669273, -85469569045618744]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 941964870
discriminant (Δ): 2959403927812227512885815321568062500
Faltings height: 5.7053
naive height: 92.1586
primes of bad reduction: 2, 3, 5, 7, 11, 37, 103, 107
regulator: 3.997576521405442707225968195138943910694
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:14 UTC
last updated: 2026-09-26 19:55:14 UTC

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

(-503780, 130583927)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-2, q=35; A=(3q-p)(p+q)^3=3845259, B=-(p+3q)(p-q)^3=5217259. 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 19:55:14 UTC · history