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curve #1272

y² = x³ − x² − 16025x + 731481

a-invariants: [0, -1, 0, -16025, 731481]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 232106304 ☆ record for ℤ/2ℤ torsion, rank ≥ 5
discriminant (Δ): 35606963884032
Faltings height: 1.3443
naive height: 40.6594 ☆ record for ℤ/2ℤ torsion, rank ≥ 5
primes of bad reduction: 2, 3, 17, 47, 89
regulator: 26.8540410689644495381685891911531519528800768633
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:16:38 UTC
last updated: 2026-09-24 17:16:38 UTC

Witness: 5 independent points log in to add more points →

(-37, 1128)
(245, 3384)
(104, 423)
(151, 1316)
(-131, 752)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:16:38 UTC · history

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