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curve #1710

y² = x³ − x² − 9700008x + 11577952512

a-invariants: [0, -1, 0, -9700008, 11577952512]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 97561200
discriminant (Δ): 534400975460880000000
Faltings height: 2.8220
naive height: 59.8765
primes of bad reduction: 2, 3, 5, 11, 19, 389
regulator: 19.31774278665198249970264276703804045409914864
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:13:58 UTC
last updated: 2026-09-25 06:13:58 UTC

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

(-3328, 83600)
(21752, 3176800)
(-1128, 145200)
(-2074, 150898)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:13:58 UTC · history

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