curve #2633

y² + xy = x³ − 179291378246x + 29073850535056740

a-invariants: [1, 0, 0, -179291378246, 29073850535056740]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 159206190
discriminant (Δ): 3692006737958854077154821675417600
Faltings height: 5.2819
naive height: 89.3504
primes of bad reduction: 2, 3, 5, 11, 13, 17, 37, 59
regulator: 10.4508497223344765402494959796681330748769
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:14:10 UTC
last updated: 2026-09-26 20:14:10 UTC

Witness: 2 independent points log in to add more points →

(-442484, 147776650)
(-344804, 223556794)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=24; A=(3q-p)(p+q)^3=113135, B=-(p+3q)(p-q)^3=2988527. 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 20:14:10 UTC · history