Arnth-Jensen, A. and Flynn, E. V. (2009) *Nontrivial Sha in the Jacobian of an Infinite Family of Curves of Genus 2.* Journal de Théorie des Nombres de Bordeaux, 21 . pp. 1-13. ISSN 1246-7405

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## Abstract

We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle.

Item Type: | Article |
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Subjects: | H - N > Number theory |

Research Groups: | Number Theory Group |

ID Code: | 802 |

Deposited By: | E. Victor Flynn |

Deposited On: | 01 Sep 2009 08:34 |

Last Modified: | 01 Sep 2009 08:34 |

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