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curve #3779

y² = x³ + x² − 581035475893860x + 5297656759100492450400

a-invariants: [0, 1, 0, -581035475893860, 5297656759100492450400]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 608499109032360
discriminant (Δ): 430014528021737166378315289339520296121760000
Faltings height: 7.3562
naive height: 113.6011
primes of bad reduction: 2, 3, 5, 7, 13, 19, 43, 47, 73, 103, 193
regulator: 453.076682152449416149018103984157133668108584254
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 19:48:26 UTC
last updated: 2026-10-01 19:48:26 UTC

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

(11950860, 7787272080)
(17709830, 23708534850)
(36080910, 176931215370)
(364034970, 6930817127010)
(463235651430/7921, 291804453057512850/704969)

Commentary

(u,v) = (6570,1729) 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 2026-10-01 19:48:26 UTC · history

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