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curve #1290

y² + xy = x³ − 31400288x + 238881825792

a-invariants: [1, 0, 0, -31400288, 238881825792]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 172725190950
discriminant (Δ): -22670975863542047109120000
Faltings height: 3.5487
naive height: 65.9216
primes of bad reduction: 2, 3, 5, 13, 17, 487, 823
regulator: 73.8892373357692399263690325632872614814876879579
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:26:31 UTC
last updated: 2026-09-24 17:26:31 UTC

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(-7808, 93664)
(21568, -3108320)
(-4952, -519968)
(-6278, 437404)
(4096, 421024)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:26:31 UTC · history

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