## Title data

Cremona, John E. ; Fisher, Tom A. ; Stoll, Michael:

**Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves.**

*In:* Algebra & Number Theory.
Vol. 4
(25 September 2010)
Issue 6
.
- pp. 763-820.

ISSN 1937-0652

DOI: https://doi.org/10.2140/ant.2010.4.763

## Abstract in another language

We consider models for genus-one curves of degree n for n = 2, 3 and 4, which arise in explicit n-descent on elliptic curves. We prove theorems on the existence of minimal models with the same invariants as the minimal model of the Jacobian elliptic curve and provide simple algorithms for minimising a given model, valid over general number fields. Finally, for genus-one models defined over Q, we develop a theory of reduction and again give explicit algorithms for n = 2, 3 and 4.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | elliptic curves; genus-one curves; minimisation; reduction; descent |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - Univ.-Prof. Dr. Michael Stoll Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 21 Jan 2015 13:38 |

Last Modified: | 10 Feb 2015 12:01 |

URI: | https://eref.uni-bayreuth.de/id/eprint/5761 |