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curve #1696

y² + xy = x³ − 684686652908550x + 6895820505959439384132

a-invariants: [1, 0, 0, -684686652908550, 6895820505959439384132]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 23738634901410
discriminant (Δ): -4318502712231407284048071581232187500000
Faltings height: 7.0248
naive height: 114.0936
primes of bad reduction: 2, 3, 5, 11, 13, 29, 1609, 118589
regulator: 754.760621681424328655052719912899243283341186437
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:11:38 UTC
last updated: 2026-09-25 06:11:38 UTC

Witness: 5 independent points log in to add more points →

(60421791/4, 175731009/8)
(16799754, 11596639998)
(15573254, 3145647998)
(18811104, 25924385298)
(15268224, 1078349358)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:11:38 UTC · history

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