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curve #3795

y² + xy + y = x³ + x² − 2302422481432239x + 42523104693927374768316

a-invariants: [1, 1, 1, -2302422481432239, 42523104693927374768316]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 716634354334569
discriminant (Δ): 2388123121079298731910956742190691881217889
Faltings height: 7.3904
naive height: 117.7318
primes of bad reduction: 3, 11, 31, 43, 47, 53, 97, 191, 353
regulator: 55455.3221645532119277705131817066126934621532059
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 05:28:41 UTC
last updated: 2026-10-02 05:28:41 UTC

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

(227912638/9, 576919894090/27)
(3339606488/121, 1187080045740/1331)
(28418537553/1024, 11626234677321/32768)
(10094044824621/354025, 1557001260758978859/210644875)
(172631772731634801/6176702464, 1074364749310654224322185/485439400050688)

Commentary

(u,v) = (18236,473) 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 2026-10-02 05:28:41 UTC · history

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