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curve #3794

y² + xy = x³ − 25276545025511674x + 1546766214855580207594259

a-invariants: [1, 0, 0, -25276545025511674, 1546766214855580207594259]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 276785038234887
discriminant (Δ): 11615057771198854388378199957024789945997809
Faltings height: 7.8666
naive height: 124.9196
primes of bad reduction: 3, 7, 13, 23, 37, 53, 127, 263, 673
regulator: 53407.2968675370887905650520924731287955229110746
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 05:27:55 UTC
last updated: 2026-10-02 05:27:55 UTC

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

(-149800939, 1404224178137)
(91178189, 10105293914)
(322526191931/3025, 42021961663661864/166375)
(863450318282/9409, 281050704917783/912673)
(168345850701406055/1834151929, 852072482129938502311/78551224663283)

Commentary

(u,v) = (33189,212) 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 05:27:56 UTC · history

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