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curve #5522

y² + xy = x³ − 147579016420436484x − 18615973296709092998610081

a-invariants: [1, 0, 0, -147579016420436484, -18615973296709092998610081]
c-invariants: [7083792788180951233, 16084200917730967168527683135]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 121253315032116033
discriminant (Δ): 55997716948835308489996889035773124392294879041258529
Faltings height: 8.8443
naive height: 130.2130
primes of bad reduction: 3, 13, 17, 71, 79, 107, 421, 503, 1439
regulator: 955759.02068611229387238270568201315005914106472522
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 21:25:26 UTC
last updated: 2026-10-22 21:25:26 UTC

Witness: 6 independent points log in to add more points →

(-166420155, 1155519118248)
(77926316037, 21753049816739859)
(-17087324490620032059/70760788081, 32277442755180394890878501208/18823006476638729)
(-7810298229/49, 317666427464121/343)
(-5531215625/36, 141942026433067/216)
(5246405712546/25, 12016876730347799679/125)

Commentary

(u,v) = (48348,53821) 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 21:25:26 UTC · history

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