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curve #1528

y² + xy + y = x³ + x² − 73063x + 7529156

a-invariants: [1, 1, 1, -73063, 7529156]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 608475
discriminant (Δ): 273887907890625
Faltings height: 1.6074
naive height: 45.2108
primes of bad reduction: 3, 5, 7, 19, 61
regulator: 6.1642687099657445652982842976115562302672377
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:50:20 UTC
last updated: 2026-09-25 00:50:20 UTC

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

(-196, 3888)
(-310, 867)
(-1145/4, 19191/8)

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 00:50:20 UTC · history

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