curve #2460

y² + xy + y = x³ − x² − 7495963367x + 248904729248159

a-invariants: [1, -1, 1, -7495963367, 248904729248159]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 155610
discriminant (Δ): 192891074497744896000000000000
Faltings height: 4.4745
naive height: 79.8265
primes of bad reduction: 2, 3, 5, 7, 13, 19
regulator: 2.214500876940768837982944054029164152594
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:57 UTC
last updated: 2026-09-26 20:02:57 UTC

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

(-86933, 15649966)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-9, q=16; A=(3q-p)(p+q)^3=19551, B=-(p+3q)(p-q)^3=609375. 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 20:02:57 UTC · history