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curve #1322

y² + xy + y = x³ − 5350645921x + 150644230655160

a-invariants: [1, 0, 1, -5350645921, 150644230655160]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 7213783166674
discriminant (Δ): 164475246006515136366543212
Faltings height: 4.1914
naive height: 78.8151
primes of bad reduction: 2, 7, 19, 157, 223, 239, 463
regulator: 3145.1448593110950993382518215182779709305679497384
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:31:58 UTC
last updated: 2026-09-24 17:31:58 UTC

Witness: 6 independent points log in to add more points →

(308401/25, 1161902034/125)
(264634, 131272870)
(37584, 1604615)
(4688435/121, 1601534784/1331)
(-24741, 16379420)
(138681, 45491468)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:31:58 UTC · history

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