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curve #1569

y² = x³ − x² − 76509865360x + 27624835288496800

a-invariants: [0, -1, 0, -76509865360, 27624835288496800]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/8ℤ
conductor (N): 676608240
discriminant (Δ): -301008507504845269801122088394803200
Faltings height: 5.4914
naive height: 89.2381
primes of bad reduction: 2, 3, 5, 7, 11, 19, 41, 47
regulator: 188.10011583802142472399808927788575718725849
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:13:19 UTC
last updated: 2026-09-25 01:13:19 UTC

Witness: 3 independent points log in to add more points →

(2440722, 3792171262)
(1601603930/961, 63400933225410/29791)
(2725409641/2025, 140065216373764/91125)

Commentary

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:13:19 UTC · history

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