curve #2431

y² + xy = x³ − 23224950461x + 1329595722561585

a-invariants: [1, 0, 0, -23224950461, 1329595722561585]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 34204170
discriminant (Δ): 38057427847530682422512040360000
Faltings height: 4.8395
naive height: 83.2191
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 67
regulator: 2.502382391247586450256387378321828118722
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:11 UTC
last updated: 2026-09-26 20:01:11 UTC

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

(-160526, 30432871)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=14; A=(3q-p)(p+q)^3=-89177, B=-(p+3q)(p-q)^3=1008423. 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 20:01:11 UTC · history