curve #2346

y² + xy = x³ − 302913224516x + 37934817438378000

a-invariants: [1, 0, 0, -302913224516, 37934817438378000]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 104747370
discriminant (Δ): 1157160357150979734413607878672486400
Faltings height: 5.6195
naive height: 90.9237
primes of bad reduction: 2, 3, 5, 7, 13, 17, 37, 61
regulator: 7.645505043533549969247661953950982885838
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:51 UTC
last updated: 2026-09-26 19:55:51 UTC

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

(-453756, 286509420)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=12; A=(3q-p)(p+q)^3=-4305505, B=-(p+3q)(p-q)^3=-2950753. 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 19:55:51 UTC · history