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curve #1583

y² = x³ + x² + 161x + 2097

a-invariants: [0, 1, 0, 161, 2097]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 5360768
discriminant (Δ): -2069256448
Faltings height: 0.4700 ☆ record for ℤ/2ℤ torsion, rank ≥ 4
naive height: 28.7679 ☆ record for ℤ/2ℤ torsion, rank ≥ 4
primes of bad reduction: 2, 7, 31, 193
regulator: 36.34230833061797125686507307561748351292926120
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:22:20 UTC
last updated: 2026-09-25 01:22:20 UTC

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

(-7, 26)
(-1, 44)
(-8, 19)
(9, 66)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:22:20 UTC · history

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