## Title data

Poonen, Bjorn ; Schaefer, Edward F. ; Stoll, Michael:

**Twists of X(7) and primitive solutions to x²+y³=z⁷.**

*In:* Duke Mathematical Journal.
Vol. 137
(2007)
Issue 1
.
- pp. 103-158.

ISSN 1547-7398

DOI: https://doi.org/10.1215/S0012-7094-07-13714-1

## Abstract in another language

We find the primitive integer solutions to x^2+y^3=z^7. A nonabelian descent argument involving the simple group of order 168 reduces the problem to the determination of the set of rational points on a finite set of twists of the Klein quartic curve X. To restrict the set of relevant twists, we exploit the isomorphism between X and the modular curve X(7) and use modularity of elliptic curves and level lowering. This leaves 10 genus 3 curves, whose rational points are found by a combination of methods

## Further data

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

Refereed: | Yes |

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: | No |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 30 Jan 2015 07:53 |

Last Modified: | 17 Nov 2020 09:05 |

URI: | https://eref.uni-bayreuth.de/id/eprint/6128 |