curve #2329

y² + xy = x³ − 759852581620x + 254516108830240400

a-invariants: [1, 0, 0, -759852581620, 254516108830240400]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 265740090
discriminant (Δ): 93814415562271305361302190656000000
Faltings height: 5.5995
naive height: 93.6828
primes of bad reduction: 2, 3, 5, 7, 11, 17, 67, 101
regulator: 3.417665943262956892230063750895796366118
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:47 UTC
last updated: 2026-09-26 19:54:47 UTC

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

(-291940, 672057980)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=28; A=(3q-p)(p+q)^3=134431, B=-(p+3q)(p-q)^3=6105375. 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 19:54:48 UTC · history