curve #2284

y² + xy = x³ − 2422468397196x + 871987699874244240

a-invariants: [1, 0, 0, -2422468397196, 871987699874244240]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1744839030
discriminant (Δ): 581340827761676821185943652315489894400
Faltings height: 6.1383
naive height: 97.1610
primes of bad reduction: 2, 3, 5, 11, 17, 31, 79, 127
regulator: 5.042820133546306346510317216831102989391
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:59 UTC
last updated: 2026-09-26 19:51:59 UTC

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

(-6766461/4, 2882437875/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-55, q=24; A=(3q-p)(p+q)^3=-3783457, B=-(p+3q)(p-q)^3=8381663. 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 19:51:59 UTC · history