curve #4292

y² = x³ + x² − 44585x + 3582439

a-invariants: [0, 1, 0, -44585, 3582439]
c-invariants: [2140096, -3108067840]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 846118016
discriminant (Δ): 81931299725312
Faltings height: 1.4955
naive height: 43.7291
primes of bad reduction: 2, 17, 89, 257
regulator: 4149.43872121831048163514530104100370509767567199
submitted by: The Wren
submitted at: 2026-10-16 18:55:40 UTC
last updated: 2026-10-16 18:55:40 UTC

Witness: 5 independent points log in to add more points →

(234, -2453)
(474, -9443)
(573/4, 3157/8)
(1378/9, 16397/27)
(4909/36, -51533/216)

Commentary

Obtained by a rational 2-isogeny from curve#4040, submitted by NDElkies. This isogenous curve has the same rank and conductor. The five supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:55:40 UTC · history