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curve #1332

y² = x³ + x² − 4689225x + 6792889159

a-invariants: [0, 1, 0, -4689225, 6792889159]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 49159219350656
discriminant (Δ): -13344020757175024672768
Faltings height: 2.9395
naive height: 58.8019
primes of bad reduction: 2, 23, 31, 41, 47, 71, 127
regulator: 2176.928408997516646656741273833489348309718435246452
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:33:40 UTC
last updated: 2026-09-24 17:33:40 UTC

Witness: 7 independent points log in to add more points →

(1715, 61628)
(3135, -151372)
(-145, -86428)
(23066/25, -7129039/125)
(351, 72044)
(75231/49, 19448036/343)
(863, -58220)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:33:40 UTC · history

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