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curve #1707

y² + xy + y = x³ + x² − 2630963813x + 50707902137906

a-invariants: [1, 1, 1, -2630963813, 50707902137906]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 47961031575
discriminant (Δ): 54687177101664284845914140625
Faltings height: 4.2945
naive height: 76.6855
primes of bad reduction: 3, 5, 29, 181, 4201
regulator: 1208.91192820697404822057888501233539914351847463
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:13:28 UTC
last updated: 2026-09-25 06:13:28 UTC

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

(1482309/16, 1567499407/64)
(91155/4, 12776141/8)
(504, 7026982)
(-4580, 7918202)
(37470, 2157352)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:13:28 UTC · history

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