curve #2500

y² + xy = x³ − x² − 2245670064x + 40961041011648

a-invariants: [1, -1, 0, -2245670064, 40961041011648]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 14490
discriminant (Δ): 6692612332320140625000000
Faltings height: 3.9585
naive height: 76.2104
primes of bad reduction: 2, 3, 5, 7, 23
regulator: 7.270851926088596506706943819743303853167
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:05:27 UTC
last updated: 2026-09-26 20:05:27 UTC

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

(-130557/4, 71454477/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-24, q=1; A=(3q-p)(p+q)^3=-328509, B=-(p+3q)(p-q)^3=-328125. 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 20:05:28 UTC · history