## Abstract

We show that there are infinitely many nonisomorphic curves Y^{2} = X^{5} + k, k ∈ ℤ, possessing at least twelve finite points for k > 0, and at least six finite points for k < 0. We also determine all rational points on the curve Y^{2} = X^{5} − 7.

Original language | English (US) |
---|---|

Pages (from-to) | 371-374 |

Number of pages | 4 |

Journal | Experimental Mathematics |

Volume | 17 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2008 |

## Keywords

- Elliptic curve
- Fifth powers
- Genus two curve

## ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint

Dive into the research topics of 'On the equation Y^{2}= X

^{5}+ k'. Together they form a unique fingerprint.