curve #2326

y² + xy = x³ − 593477041221x − 172826369313982335

a-invariants: [1, 0, 0, -593477041221, -172826369313982335]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 97154970
discriminant (Δ): 474636257147066139268781479563585600
Faltings height: 5.6362
naive height: 92.9414
primes of bad reduction: 2, 3, 5, 11, 37, 73, 109
regulator: 6.445494762490764395647533450701182203016
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:34 UTC
last updated: 2026-09-26 19:54:34 UTC

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

(-1882449/4, 380679273/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-55, q=18; A=(3q-p)(p+q)^3=-5521177, B=-(p+3q)(p-q)^3=-389017. 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 19:54:34 UTC · history