curve #2367

y² + xy + y = x³ − x² − 159795389912x + 22624696858604699

a-invariants: [1, -1, 1, -159795389912, 22624696858604699]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 92866410
discriminant (Δ): 40009542724567971030014015841000000
Faltings height: 5.3796
naive height: 89.0051
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 29
regulator: 3.814037730988907007502051122085657608935
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:10 UTC
last updated: 2026-09-26 19:57:10 UTC

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

(-450681, 55920553)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-9, q=26; A=(3q-p)(p+q)^3=427431, B=-(p+3q)(p-q)^3=2958375. 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 19:57:11 UTC · history