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curve #5505

y² + xy = x³ − 26632386872980x + 46197780170860087952

a-invariants: [1, 0, 0, -26632386872980, 46197780170860087952]
c-invariants: [1278354569903041, -39914883985154970845089]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 9316295564730
discriminant (Δ): 286965746848684048890198562949660672160000
Faltings height: 6.6818
naive height: 104.3531
primes of bad reduction: 2, 3, 5, 7, 11, 127, 3583, 8863
regulator: 45735.2009285213307736544411847504448549233159907
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 20:04:08 UTC
last updated: 2026-10-22 20:04:08 UTC

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

(17891482, 72770585230)
(-215833813636/312481, 1400349298803653912/174676879)
(-150584/9, 184399308436/27)
(18465076/9, 11835020596/27)
(116762481248/29929, 6691980041688676/5177717)

Commentary

(u,v) = (6223,2640) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.

last edited by Daniel Błażewicz at 2026-10-22 20:04:08 UTC · history

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