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curve #5520

y² + xy = x³ − 597636985188624014x + 177344540222552625512023779

a-invariants: [1, 0, 0, -597636985188624014, 177344540222552625512023779]
c-invariants: [28686575289053952673, -153225682795315331375969474065]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 400014894778295223
discriminant (Δ): 74441693403418597142705733999196191988933896182667489
Faltings height: 9.0122
naive height: 134.4089
primes of bad reduction: 3, 7, 19, 23, 41, 43, 89, 227, 379, 3229
regulator: 252957.49216544900124799059992245778592838081040632
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 21:22:34 UTC
last updated: 2026-10-22 21:22:34 UTC

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

(4432470850, 290879537633323)
(280200174523, 148320281399693041)
(754026571/49, 4447790508628711/343)
(15514022809/256, 48697391127374299/4096)
(105538161697/64, 31042399868477027/512)
(56511543284893/94864, 167139842186988098513/29218112)

Commentary

(u,v) = (12341,73692) 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 21:22:35 UTC · history

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