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curve #1717

y² + xy + y = x³ + x² − 51910272365425865x + 4552270631075057038390647

a-invariants: [1, 1, 1, -51910272365425865, 4552270631075057038390647]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 89136035982910
discriminant (Δ): 1602595440072470114110607290670770000000000
Faltings height: 7.9720
naive height: 127.0785
primes of bad reduction: 2, 5, 7, 19, 43, 89, 17512301
regulator: 2894.03282701628267585998460893429048348562901391
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:15:08 UTC
last updated: 2026-09-25 06:15:08 UTC

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

(103622607, 534602868696)
(131543577, -57552984)
(147204607, 317172270696)
(116233857, 298094288696)
(69108791803/529, 216979513532832/12167)

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 06:15:08 UTC · history

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