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curve #3445

y² + xy = x³ − 127702x + 333062436

a-invariants: [1, 0, 0, -127702, 333062436]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 8982023266
discriminant (Δ): -47791793129916146176
Faltings height: 2.4554
naive height: 52.7709
primes of bad reduction: 2, 31, 43, 47, 97, 739
regulator: 266.297500447367792597224662242623775452673386397
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:34:49 UTC
last updated: 2026-09-27 05:34:49 UTC

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

(380, 18234)
(192, 17670)
(-748, 3570)
(1884, 81402)
(-654, 12030)

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 05:34:49 UTC · history

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