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curve #5507

y² + xy + y = x³ + x² − 23099142350284x − 19736535367499654419

a-invariants: [1, 1, 1, -23099142350284, -19736535367499654419]
c-invariants: [1108758832813633, 17052358241828455315615]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 4324203609726
discriminant (Δ): 620524004664926027578658668402978055061504
Faltings height: 6.7143
naive height: 103.9261
primes of bad reduction: 2, 3, 7, 11, 13, 61, 101, 137, 853
regulator: 1069.97270664765900355925791577794282908037187941
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 20:04:22 UTC
last updated: 2026-10-22 20:04:22 UTC

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

(-4058113, 2680138347)
(-3487763, 4291377097)
(9771197, 26214858105)
(31753157, 176795680497)
(-43490907/49, 88504728535/343)

Commentary

(u,v) = (6161,4928) 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 20:04:22 UTC · history

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