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curve #589

y² + xy + y = x³ − x² − 176907x + 16703700

a-invariants: [1, -1, 1, -176907, 16703700]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 234437475388446487
discriminant (Δ): 234437475388446487
Faltings height: 2.0322
naive height: 47.8637 ★ record for rank ≥ 9
primes of bad reduction: 607, 2503, 27983, 5514209
regulator: 132939.79467483175127387406107377816042819305510767506217
submitted by: Michael Rubinstein
submitted at: 2026-09-05 22:15:32 UTC
last updated: 2026-09-05 22:15:32 UTC

Witness: 9 independent points log in to add more points →

(-24, 4587)
(207/4, 21967/8)
(60, 2480)
(91, 1117)
(100, 24)
(362, -125)
(372, 1320)
(438, 4587)
(467, 5747)

Commentary

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

last edited by Michael Rubinstein at 2026-09-05 22:15:32 UTC · history

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