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curve #1706

y² + xy = x³ − 336509320475x + 78387368402386641

a-invariants: [1, 0, 0, -336509320475, 78387368402386641]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 13977659094
discriminant (Δ): -215687879787042046738560291562487808
Faltings height: 5.5402
naive height: 91.3240
primes of bad reduction: 2, 3, 7, 47, 7080881
regulator: 104.8889767658643849958160555904724554405854319
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:13:18 UTC
last updated: 2026-09-25 06:13:18 UTC

Witness: 4 independent points log in to add more points →

(-477986, 360833521)
(93926590, 910232137009)
(2791366/9, 1671816595/27)
(39450784/169, 245909257021/2197)

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 06:13:18 UTC · history

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