curve #1777

y² + xy = x³ − 2564530435455464744050430x − 774033544664307864229665861908231100

a-invariants: [1, 0, 0, -2564530435455464744050430, -774033544664307864229665861908231100]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 132792596202630
discriminant (Δ): 820629260378340122534707714306737863072565546605087122793887672400100000000
Faltings height: 13.0705
naive height: 180.2251
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 47, 73, 149, 193
regulator: 1707.2111411137934742190002124525324629851573
submitted by: hdeping
submitted at: 2026-09-25 14:35:28 UTC
last updated: 2026-09-25 14:35:28 UTC

Witness: 3 independent points log in to add more points →

(-557806133900, 694922703833151730)
(-2287973216290310660/6265009, 5290514967596142058182262990/15681317527)
(3484671356493652101640/949687489, 183279040738711134507748125258310/29266519348513)

Commentary

Specialization t=47/18 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4). This is the Dujella (2001) rank-3 record curve, identified here as a specialization of the family.

last edited by hdeping at 2026-09-27 08:33:25 UTC · history