curve #2332

y² + xy = x³ − 489742284840x + 115540553004033600

a-invariants: [1, 0, 0, -489742284840, 115540553004033600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1007877990
discriminant (Δ): 1750622134772764855702461178944000000
Faltings height: 5.6818
naive height: 92.3650
primes of bad reduction: 2, 3, 5, 7, 19, 41, 61, 101
regulator: 5.358178122997071390059454623095015945264
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:59 UTC
last updated: 2026-09-26 19:54:59 UTC

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

(550770, 113214810)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=20; A=(3q-p)(p+q)^3=-935361, B=-(p+3q)(p-q)^3=4312639. 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 19:54:59 UTC · history