On the equation Y2=X(X2+p)

Andrew Bremner; J. W. Cassels

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

On the equation Y²=X(X²+p)

Andrew Bremner
, J. W. Cassels

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

Generators are found for the group of rational points on the title curve for all primes p = 5 (mod 8) less than 1, 000. The rank is always 1 in accordance with conjectures of Seltner and Mordell. Some of the generators are rather large.

Original language	English (US)
Pages (from-to)	257-264
Number of pages	8
Journal	Mathematics of Computation
Volume	42
Issue number	165
DOIs	https://doi.org/10.1090/S0025-5718-1984-0726003-4
State	Published - 1984
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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Cite this

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title = "On the equation Y2=X(X2+p)",

abstract = "Generators are found for the group of rational points on the title curve for all primes p = 5 (mod 8) less than 1, 000. The rank is always 1 in accordance with conjectures of Seltner and Mordell. Some of the generators are rather large.",

author = "Andrew Bremner and Cassels, \{J. W.\}",

year = "1984",

doi = "10.1090/S0025-5718-1984-0726003-4",

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AU - Cassels, J. W.

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AB - Generators are found for the group of rational points on the title curve for all primes p = 5 (mod 8) less than 1, 000. The rank is always 1 in accordance with conjectures of Seltner and Mordell. Some of the generators are rather large.

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DO - 10.1090/S0025-5718-1984-0726003-4

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IS - 165

ER -

On the equation Y²=X(X²+p)

Abstract

ASJC Scopus subject areas

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