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curve #1601

y² + xy + y = x³ + x² − 1643813x + 4216895156

a-invariants: [1, 1, 1, -1643813, 4216895156]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 50457675 ☆ record for ℤ/4ℤ torsion, rank ≥ 4
discriminant (Δ): -7400134047790032890625
Faltings height: 2.8777
naive height: 57.8482
primes of bad reduction: 3, 5, 41, 61, 269
regulator: 57.84999223697139404420207696065404901962076133
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:25:20 UTC
last updated: 2026-09-25 01:25:20 UTC

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

(13680, 1587547)
(-1570, 54922)
(-1900, 22987)
(-112375/64, 21520169/512)

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 01:25:20 UTC · history

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