On the equation 𝑌²=𝑋(𝑋²+𝑝)

Bremner, A.; Cassels, J. W. S.

doi:10.1090/S0025-5718-1984-0726003-4

On the equation $Y^{2}=X(X^{2}+p)$
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by A. Bremner and J. W. S. Cassels PDF

Math. Comp. 42 (1984), 257-264 Request permission

Abstract:

Generators are found for the group of rational points on the title curve for all primes $p \equiv 5\;\pmod 8$ less than 1,000. The rank is always 1 in accordance with conjectures of Selmer and Mordell. Some of the generators are rather large.

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