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curve #3505

y² + xy = x³ − x² − 67864923x − 24603903275

a-invariants: [1, -1, 0, -67864923, -24603903275]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 5037649974
discriminant (Δ): 19742090906990030918676624
Faltings height: 3.5435
naive height: 65.7127
primes of bad reduction: 2, 3, 7, 37, 47, 83, 277
regulator: 118.180183461319809084125619453703171974555209967
submitted by: Michael Rubinstein
submitted at: 2026-09-27 12:21:05 UTC
last updated: 2026-09-27 12:21:05 UTC

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

(154826, 60756773)
(-38374/25, 34544209/125)
(-2233, 341411)
(15218, 1562981)
(-7854, -150619)

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 2026-09-27 12:21:05 UTC · history

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