curve #4286

y² = x³ − x² + 87199275025x + 16923561771699111

a-invariants: [0, -1, 0, 87199275025, 16923561771699111]
c-invariants: [-4185565201184, -14621982484139239040]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 351824891684388520040832
discriminant (Δ): -166162676264178474928070666307264768
Faltings height: 5.4423
naive height: 88.2581
primes of bad reduction: 2, 3, 7, 73, 137, 257, 263, 337, 401, 673, 2129
regulator: 4985307350.339066422359921535762663677811037275625701869550
submitted by: The Wren
submitted at: 2026-10-16 18:41:20 UTC
last updated: 2026-10-16 18:41:20 UTC

Witness: 10 independent points log in to add more points →

(-140234, -44016551)
(623158, -559687847)
(-918698/9, -2252329579/27)
(-521411/4, -462476567/8)
(7471246/25, 32994698369/125)
(-141554, -41758141)
(399046, 339504191)
(-1158386/25, -14133107137/125)
(2795086, 4700773411)
(167057569/144, 2239392386807/1728)

Commentary

Obtained by a rational 2-isogeny from curve#4249, submitted by Michael Rubinstein and sourced from his elliptic-curves-by-rank repository. This isogenous curve has the same rank and conductor, with smaller absolute minimal discriminant, Faltings height and naive height. The ten supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:41:20 UTC · history