curve #4563

y² + xy + y = x³ + x² − 5432264x + 4867389656

a-invariants: [1, 1, 1, -5432264, 4867389656]
c-invariants: [260748673, -4207380277985]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 885537939
discriminant (Δ): 15173437063678239489
Faltings height: 2.6073
naive height: 58.1372
primes of bad reduction: 3, 11, 13, 17, 29, 53, 79
regulator: 101.5704348200926461554955811388175907855930355
submitted by: The Wren
submitted at: 2026-10-18 02:00:33 UTC
last updated: 2026-10-18 02:00:33 UTC

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

(-8797/4, 637861/8)
(542, 45365)
(72367, 19421540)
(-4969/4, 792895/8)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z4.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Four supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C4. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 02:00:33 UTC · history