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curve #1593

y² + xy = x³ − x² − 52251x + 2965013

a-invariants: [1, -1, 0, -52251, 2965013]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 19378602
discriminant (Δ): 5365499107798224
Faltings height: 1.7204
naive height: 44.2051
primes of bad reduction: 2, 3, 37, 53, 61
regulator: 18.80245307918824844115190745925822267433019643
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:24:00 UTC
last updated: 2026-09-25 01:24:00 UTC

Witness: 4 independent points log in to add more points →

(-206, 2329)
(-47, 2329)
(6154, 479329)
(-173, 2695)

Commentary

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

last edited by Michael Rubinstein at 2026-09-25 01:24:00 UTC · history

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