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curve #1725

y² + xy = x³ − 197121372350x + 33529918474699332

a-invariants: [1, 0, 0, -197121372350, 33529918474699332]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 55702677030
discriminant (Δ): 4529991596340935854559430000000000
Faltings height: 5.3023
naive height: 89.6349
primes of bad reduction: 2, 3, 5, 7, 11, 13, 59, 149, 211
regulator: 34.36416913838251283376164298649176469442133127
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:16:27 UTC
last updated: 2026-09-25 06:16:27 UTC

Witness: 4 independent points log in to add more points →

(162484, 76014778)
(-489596, 112857298)
(228004, -21053102)
(965251/4, -31025281/8)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:16:27 UTC · history

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