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curve #3441

y² + xy = x³ − x² − 6472503x + 2938419085

a-invariants: [1, -1, 0, -6472503, 2938419085]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6485495346
discriminant (Δ): 13627974562088001747984
Faltings height: 2.9423
naive height: 58.6628
primes of bad reduction: 2, 3, 11, 37, 67, 73, 181
regulator: 171.459265973120850072624822581148785588704636638
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:34:09 UTC
last updated: 2026-09-27 05:34:09 UTC

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

(-2203, 81737)
(8354, 725093)
(2582, 57317)
(-2158, 83861)
(-1942, 91421)

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 2026-09-27 05:34:09 UTC · history

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