curve #2328

y² + xy = x³ − 518799380331x + 23028196154645745

a-invariants: [1, 0, 0, -518799380331, 23028196154645745]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1995570330
discriminant (Δ): 8707633958506144216344109899620558400
Faltings height: 5.7782
naive height: 92.5380
primes of bad reduction: 2, 3, 5, 13, 17, 29, 97, 107
regulator: 8.310194698188559622794540624368037838763
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:41 UTC
last updated: 2026-09-26 19:54:41 UTC

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

(-739602, 46876521)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-5, q=34; A=(3q-p)(p+q)^3=2609623, B=-(p+3q)(p-q)^3=5753943. 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 19:54:42 UTC · history