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curve #1529

y² = x³ + 271284x + 104112016

a-invariants: [0, 0, 0, 271284, 104112016]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 614592
discriminant (Δ): -5960352223259394048
Faltings height: 2.2863
naive height: 50.4451
primes of bad reduction: 2, 3, 11, 97
regulator: 15.900517692749506778175591341174186380645455
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:50:30 UTC
last updated: 2026-09-25 00:50:30 UTC

Witness: 3 independent points log in to add more points →

(-160, 7524)
(-270, 3344)
(-259, 4059)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:50:30 UTC · history

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