On the equation 𝑌²=𝑋(𝑋²+𝑝)

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

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

On the equation $Y\sp{2}=X(X\sp{2}+p)$

Authors: A. Bremner and J. W. S. Cassels
Journal: Math. Comp. 42 (1984), 257-264
MSC: Primary 11D25; Secondary 11G05, 14G05
DOI: https://doi.org/10.1090/S0025-5718-1984-0726003-4
MathSciNet review: 726003
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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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