curve #2292

y² + xy = x³ − 2689929469955x + 1696239617077121025

a-invariants: [1, 0, 0, -2689929469955, 1696239617077121025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3850056210
discriminant (Δ): 2705802207959509929427123527561000000
Faltings height: 5.8994
naive height: 97.4752
primes of bad reduction: 2, 3, 5, 7, 11, 13, 41, 53, 59
regulator: 4.524522635393163085618970838097464351726
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:29 UTC
last updated: 2026-09-26 19:52:29 UTC

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

(3890575/4, 54150785/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-59, q=6; A=(3q-p)(p+q)^3=-11463529, B=-(p+3q)(p-q)^3=-11259625. 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 19:52:29 UTC · history