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curve #3448

y² + xy + y = x³ − 40932715x + 100783384482

a-invariants: [1, 0, 1, -40932715, 100783384482]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 16619239546
discriminant (Δ): 1016533506829348089764
Faltings height: 3.0499
naive height: 64.1959
primes of bad reduction: 2, 7, 13, 41, 373, 853
regulator: 139.244160847199024580008046093179616019864034182
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:35:22 UTC
last updated: 2026-09-27 05:35:22 UTC

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

(2741, 94452)
(31585/9, 463756/27)
(2325, 133686)
(726, 266936)
(243609/25, 98385538/125)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:35:22 UTC · history

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