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curve #1662

y² + xy = x³ − 8232229763615x + 11525150347009627449

a-invariants: [1, 0, 0, -8232229763615, 11525150347009627449]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 49410615496242
discriminant (Δ): -21676895546976042954849194709470003892576
Faltings height: 6.4509
naive height: 101.3053
primes of bad reduction: 2, 3, 7, 11, 13, 193, 42626299
regulator: 1952.41476558676288932836390707066407473643075073
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:38:19 UTC
last updated: 2026-09-25 02:38:19 UTC

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

(9709546, 29097793945)
(-819830, 4210297597)
(6058099/4, 12721812875/8)
(561341506/25, -13198865777911/125)
(732278074/225, 14785291740263/3375)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:38:19 UTC · history

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