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curve #1655

y² + xy = x³ − 7881631206568850x + 269461137047295940522500

a-invariants: [1, 0, 0, -7881631206568850, 269461137047295940522500]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 1105763581495830
discriminant (Δ): -32320362261132738484994596912254690095923200000
Faltings height: 7.8685
naive height: 121.4246
primes of bad reduction: 2, 3, 5, 29, 37, 43, 798863999
regulator: 1522.42164025866631688577121936415544474032092715
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:29:27 UTC
last updated: 2026-09-25 02:29:27 UTC

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

(-100490690, 216148942000)
(72455740, 280627882750)
(5955259300/121, 36897787542650/1331)
(-154427025/4, 5747934193725/8)
(118761910852/2401, 2943797854544254/117649)

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 02:29:27 UTC · history

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