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curve #1275

y² + xy = x³ − x² − 483939x + 105674949

a-invariants: [1, -1, 0, -483939, 105674949]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 672899094
discriminant (Δ): 2440390822081590672
Faltings height: 2.2451
naive height: 50.8827
primes of bad reduction: 2, 3, 7, 37, 47, 83
regulator: 30.1965806036469267072453888660481211119369415346
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:19:03 UTC
last updated: 2026-09-24 17:19:03 UTC

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(978, 23325)
(243, -1665)
(537, 393)
(-345, 15387)
(222, 2913)

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 17:19:03 UTC · history

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