curve #2301

y² + xy = x³ − 1328762216716x + 583220985773421200

a-invariants: [1, 0, 0, -1328762216716, 583220985773421200]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 265887930
discriminant (Δ): 3205334186424752223554818399803801600
Faltings height: 5.8149
naive height: 95.3594
primes of bad reduction: 2, 3, 5, 7, 11, 31, 47, 79
regulator: 3.477084356647905981629288612111595254060
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:04 UTC
last updated: 2026-09-26 19:53:04 UTC

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

(563048, 116180276)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-55, q=8; A=(3q-p)(p+q)^3=-8202017, B=-(p+3q)(p-q)^3=-7751457. 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 19:53:05 UTC · history