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curve #1344

y² + xy = x³ − x² − 48749704665x + 6287102302927625

a-invariants: [1, -1, 0, -48749704665, 6287102302927625]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 53077317663778110
discriminant (Δ): -9661140676486956250966727130893100
Faltings height: 5.2202
naive height: 86.2777
primes of bad reduction: 2, 3, 5, 17, 19, 37, 53, 71, 85711
regulator: 5101.827602183103667537251746717950257259561545478145
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:35:47 UTC
last updated: 2026-09-24 17:35:47 UTC

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(-63380, 95542195)
(260185, -106038800)
(1289710, 1444572925)
(436675, -261497075)
(-155282, 100640053)
(-214340, -82892525)
(76036, -54992231)

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 17:35:47 UTC · history

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