### 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 | |

State | Published - 1984 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

^{2}=X(X

^{2}+p).

*Mathematics of Computation*,

*42*(165), 257-264. https://doi.org/10.1090/S0025-5718-1984-0726003-4

**On the equation Y ^{2}=X(X^{2}+p).** / Bremner, Andrew; Cassels, J. W.

Research output: Contribution to journal › Article

^{2}=X(X

^{2}+p)',

*Mathematics of Computation*, vol. 42, no. 165, pp. 257-264. https://doi.org/10.1090/S0025-5718-1984-0726003-4

^{2}=X(X

^{2}+p). Mathematics of Computation. 1984;42(165):257-264. https://doi.org/10.1090/S0025-5718-1984-0726003-4

}

TY - JOUR

T1 - On the equation Y2=X(X2+p)

AU - Bremner, Andrew

AU - Cassels, J. W.

PY - 1984

Y1 - 1984

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84968512782&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968512782&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1984-0726003-4

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

M3 - Article

VL - 42

SP - 257

EP - 264

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 165

ER -