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curve #1286

y² + xy + y = x³ + x² − 10938250x + 3541708142

a-invariants: [1, 1, 1, -10938250, 3541708142]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 93288459615
discriminant (Δ): 78324630276055373534025
Faltings height: 3.0839
naive height: 60.2369
primes of bad reduction: 3, 5, 13, 29, 101, 233, 701
regulator: 604.766594789763208464514557260239389482205199978
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:25:50 UTC
last updated: 2026-09-24 17:25:50 UTC

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(3356, 66474)
(-7805/4, 1064909/8)
(-838, 110511)
(-1770, 132646)
(-2553, 123076)

Commentary

Torsion Z/2+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 17:25:50 UTC · history

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