curve #2231

y² + xy = x³ − 292294069252681x + 1923435274267657789145

a-invariants: [1, 0, 0, -292294069252681, 1923435274267657789145]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 4791954090
discriminant (Δ): 3951509319270662975179249328801517441600
Faltings height: 6.8691
naive height: 111.5399
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 47, 101
regulator: 4.026350361014473885050469854336068767627
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:36 UTC
last updated: 2026-09-26 19:48:36 UTC

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

(9824348, 242540801)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=54; A=(3q-p)(p+q)^3=71687, B=-(p+3q)(p-q)^3=118484615. 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 19:48:36 UTC · history