curve #2254

y² + xy = x³ − 10154535135795x + 12194281601397893025

a-invariants: [1, 0, 0, -10154535135795, 12194281601397893025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 16059825210
discriminant (Δ): 2774535979084538593013300527768881000000
Faltings height: 6.3532
naive height: 101.4604
primes of bad reduction: 2, 3, 5, 11, 13, 23, 37, 53, 83
regulator: 8.424878144590969797533622978624002931359
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:01 UTC
last updated: 2026-09-26 19:50:01 UTC

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

(8251635/4, 1264284315/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=30; A=(3q-p)(p+q)^3=-1739881, B=-(p+3q)(p-q)^3=21156119. 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 19:50:01 UTC · history