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curve #3592

y² = x³ − x² − 111368911344x + 14304536635843584

a-invariants: [0, -1, 0, -111368911344, 14304536635843584]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 20634411504
discriminant (Δ): 8715036023132715570830785449984
Faltings height: 5.0008
naive height: 87.9219
primes of bad reduction: 2, 3, 7, 17, 47, 101, 761
regulator: 656.9602224749011432718776361889489331945015127
submitted by: Daniel Błażewicz
submitted at: 2026-09-29 06:05:14 UTC
last updated: 2026-09-29 06:05:14 UTC

Witness: 4 independent points log in to add more points →

(-179544, 168855960)
(207360, 11275488)
(50665704/121, 269791625544/1331)
(255629328/7921, 73072375867680/704969)

Commentary

(u,v) = (761,47) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 4.

last edited by Daniel Błażewicz at 2026-10-01 08:50:49 UTC · history

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