curve #5519

y² = x³ + x² − 4666505277842119264x + 3715583909827129765128856436

a-invariants: [0, 1, 0, -4666505277842119264, 3715583909827129765128856436]
c-invariants: [223992253336421724688, -3210264499434593637089862308800]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 250961682277448688
discriminant (Δ): 539617936470855180403400959802209725801417812733207527424
Faltings height: 9.6460
naive height: 140.5744
primes of bad reduction: 2, 3, 7, 13, 23, 29, 101, 103, 199, 41609
regulator: 42331.115709793722003713548159716075925823395086077
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 21:22:30 UTC
last updated: 2026-10-22 21:22:30 UTC

(-2481798550, 3272379829056)
(926716235, 13672028870136)
(996765242, 7382461065840)
(1027062383, 2489169822930)
(2321332367, 73428662844810)
(118633242394/81, 3471691135406480/729)

(u,v) = (20497,62721) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 6.

last edited by Daniel Błażewicz at 2026-10-22 21:22:30 UTC · history