On Ribet’s isogeny for $J_0(65)$ | Zendy

Krzysztof Klosin | Zendy; Mihran Papikian | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On Ribet’s isogeny for $J_0(65)$

Author(s) -

Krzysztof Klosin,

Mihran Papikian

Publication year - 2017

Publication title -

proceedings of the american mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.968

H-Index - 84

eISSN - 1088-6826

pISSN - 0002-9939

DOI - 10.1090/proc/14019

Subject(s) - isogeny , mathematics , kernel (algebra) , quaternion algebra , discriminant , order (exchange) , quaternion , pure mathematics , hecke algebra , divisor (algebraic geometry) , algebra over a field , conjecture , combinatorics , elliptic curve , division algebra , filtered algebra , geometry , computer science , finance , artificial intelligence , economics

Let $J^{65}$ be the Jacobian of the Shimura curve attached to the indefinite quaternion algebra over $\mathbb{Q}$ of discriminant $65$. We study the isogenies $J_0(65)\rightarrow J^{65}$ defined over $\mathbb{Q}$, whose existence was proved by Ribet. We prove that there is an isogeny whose kernel is supported on the Eisenstein maximal ideals of the Hecke algebra acting on $J_0(65)$, and moreover the odd part of the kernel is generated by a cuspidal divisor of order $7$, as is predicted by a conjecture of Ogg.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research