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curve #1313

y² = x³ − 2092695843x + 6682415701858

a-invariants: [0, 0, 0, -2092695843, 6682415701858]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 4184222602320
discriminant (Δ): 567250088658803912967989760000
Faltings height: 4.3994
naive height: 75.9988
primes of bad reduction: 2, 3, 5, 23, 37, 73, 139, 673
regulator: 1725.3183440870985606751007547973300961796728954956
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:30:26 UTC
last updated: 2026-09-24 17:30:26 UTC

Witness: 6 independent points log in to add more points →

(-18066, 6212300)
(2009, 1576800)
(-20767, 6417576)
(1535009, 1900963800)
(-41791, 4599000)
(45759, 2595550)

Commentary

Torsion Z/2+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 17:30:26 UTC · history

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