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curve #3783

y² + xy = x³ − 32742973718095x + 23590453460664334400

a-invariants: [1, 0, 0, -32742973718095, 23590453460664334400]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 65357874569085
discriminant (Δ): 2006232216892916831399589790985080550150625
Faltings height: 6.8091
naive height: 104.9727
primes of bad reduction: 3, 5, 7, 17, 19, 23, 41, 71, 107, 269
regulator: 610.343264038022997190505431331881850135098168847
submitted by: Daniel Błażewicz
submitted at: 2026-10-01 19:50:47 UTC
last updated: 2026-10-01 19:50:47 UTC

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

(-5794765, 4332347630)
(86297615/4, 773852917105/8)
(41643605, 266208350165)
(134500880, 1558395459980)
(32783033/64, 1349915153617/512)

Commentary

(u,v) = (6745,4284) 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 19:50:47 UTC · history

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