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curve #3793

y² + xy = x³ − 4067685412315444x + 99854713518280613120144

a-invariants: [1, 0, 0, -4067685412315444, 99854713518280613120144]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 101962964489622
discriminant (Δ): 11486278525950746184382695846669472625332224
Faltings height: 7.5293
naive height: 119.4392
primes of bad reduction: 2, 3, 17, 23, 31, 73, 103, 199, 937
regulator: 17574.9530267231244555475589767386551644384889204
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 05:27:44 UTC
last updated: 2026-10-02 05:27:44 UTC

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

(46221710, 102882418472)
(1837647806/49, 2451292132022/343)
(1845138584/49, 3006734045636/343)
(4805212443464/130321, 16688568501502124/47045881)
(531810729904832/14462809, 21021293298998847652/55002062627)

Commentary

(u,v) = (21024,527) 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 05:27:44 UTC · history

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