curve #2419

y² + xy = x³ − 175384481545x + 28269354518248025

a-invariants: [1, 0, 0, -175384481545, 28269354518248025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 42372330
discriminant (Δ): 29798193820909032874996641000000
Faltings height: 5.1104
naive height: 89.2843
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 83
regulator: 1.997911245119120524433475495483245970218
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:25 UTC
last updated: 2026-09-26 20:00:25 UTC

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

(-465010, 96533255)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=22; A=(3q-p)(p+q)^3=10375, B=-(p+3q)(p-q)^3=2906631. 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 20:00:26 UTC · history