curve #2323

y² + xy = x³ − 6935189822495x + 7029661714398416025

a-invariants: [1, 0, 0, -6935189822495, 7029661714398416025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 990057390
discriminant (Δ): 116070306789521462285350380609000000
Faltings height: 5.9536
naive height: 100.3165
primes of bad reduction: 2, 3, 5, 7, 17, 29, 73, 131
regulator: 5.398386700326546965333426124121079437908
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:23 UTC
last updated: 2026-09-26 19:54:23 UTC

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

(1469380, 107609455)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=34; A=(3q-p)(p+q)^3=16375, B=-(p+3q)(p-q)^3=18253431. 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 19:54:23 UTC · history