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curve #1665

y² + xy = x³ − 3206763812089675x + 73392260033241789280625

a-invariants: [1, 0, 0, -3206763812089675, 73392260033241789280625]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 971000491362330
discriminant (Δ): -216456788951741890686948267154616044897996800000
Faltings height: 7.8384
naive height: 118.8234
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 419, 1672421
regulator: 416.871182147234784329898053370540359857233255331
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:44:19 UTC
last updated: 2026-09-25 02:44:19 UTC

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

(-62298850, 177172285025)
(51885662, 216052111361)
(832698110, 23974246454465)
(100076990, 868730987585)
(-26943970, 374492432225)

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 02:44:19 UTC · history

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