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curve #1475

y² + xy = x³ − 2435722413012x + 1729624904757976464

a-invariants: [1, 0, 0, -2435722413012, 1729624904757976464]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/9ℤ
conductor (N): 129107622
discriminant (Δ): -367539430670886784942825009262673002496
Faltings height: 6.1196
naive height: 97.5120
primes of bad reduction: 2, 3, 7, 17, 19, 31, 307
regulator: 28.5650460036058241071047831109583803933327
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:19:19 UTC
last updated: 2026-09-25 00:19:19 UTC

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

(38381616/25, 158453296596/125)
(-2153530008/2209, -185023645097004/103823)

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 00:19:19 UTC · history

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