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curve #5506

y² = x³ + x² − 17287140540804x − 5023901787982448544

a-invariants: [0, 1, 0, -17287140540804, -5023901787982448544]
c-invariants: [829782745958608, 4340646166120359790400]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 30542816147592
discriminant (Δ): 319732007783129977259105958306837886159104
Faltings height: 6.6543
naive height: 103.0566
primes of bad reduction: 2, 3, 7, 17, 43, 67, 739, 5023
regulator: 1928.37764178659258692362425865925129053680332034
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 20:04:12 UTC
last updated: 2026-10-22 20:04:12 UTC

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

(-1506570, 4195336194)
(4456758, 2540615490)
(-514349250/169, 9676294107102/2197)
(78582105/16, 341924746341/64)
(297075774/49, 3646439921286/343)

Commentary

(u,v) = (2881,2142) 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 20:04:12 UTC · history

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