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curve #1659

y² + xy + y = x³ + x² − 57864771939203375x + 5357620560533311846349685

a-invariants: [1, 1, 1, -57864771939203375, 5357620560533311846349685]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 2193031260769090
discriminant (Δ): -141178227814429087047677663071589553196236800000
Faltings height: 8.2301
naive height: 127.4043
primes of bad reduction: 2, 5, 7, 17, 23, 43, 1863380599
regulator: 2232.86410137533517998885098187419369445422139360
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:34:19 UTC
last updated: 2026-09-25 02:34:19 UTC

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

(135723739, 64393962130)
(598332123, 13598927452818)
(5005790143/36, 1388166522973/216)
(138219883, 14524026658)
(-173246117, 3191108573458)

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 02:34:19 UTC · history

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