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curve #1599

y² + xy + y = x³ − 325580x + 71396382

a-invariants: [1, 0, 1, -325580, 71396382]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 45171154
discriminant (Δ): 5004131178147164
Faltings height: 1.9192
naive height: 49.6937
primes of bad reduction: 2, 7, 29, 31, 37, 97
regulator: 24.96312278722465572203524594138566431947241180
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:25:00 UTC
last updated: 2026-09-25 01:25:00 UTC

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

(3187, 175625)
(-1317/4, 96955/8)
(-305, 12083)
(6000, 459738)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:25:00 UTC · history

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