curve #2234

y² + xy + y = x³ − 45709062304588x + 118921842584777888906

a-invariants: [1, 0, 1, -45709062304588, 118921842584777888906]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 516546030
discriminant (Δ): 2530969408176967437774602457405456000000
Faltings height: 6.5501
naive height: 105.9736
primes of bad reduction: 2, 3, 5, 7, 11, 13, 103, 167
regulator: 2.962632810973851007154771812724736593306
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:47 UTC
last updated: 2026-09-26 19:48:47 UTC

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

(3835825, 166896887)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-32, q=45; A=(3q-p)(p+q)^3=366899, B=-(p+3q)(p-q)^3=47022899. 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 19:48:47 UTC · history