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curve #1476

y² + xy = x³ + 825604719750438x + 18741558140089346956644

a-invariants: [1, 0, 0, 825604719750438, 18741558140089346956644]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/9ℤ
conductor (N): 1581037158
discriminant (Δ): -187754354257661051435207917612407890833179672576
Faltings height: 7.7543
naive height: 116.0932
primes of bad reduction: 2, 3, 19, 23, 37, 43, 379
regulator: 188.774753849304110714665674141181445096085
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:20:19 UTC
last updated: 2026-09-25 00:20:19 UTC

Witness: 2 independent points log in to add more points →

(-10824589068/4489, 38910200885526546/300763)
(-117205625284552524/7758967225, -36308902188354108898598754/683448628014125)

Commentary

Torsion Z/9. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:20:19 UTC · history

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