Relating Tate-Shafarevich group of an elliptic curve with class group
Dipendra Prasad, Sudhanshu Shekhar

TL;DR
This paper establishes a precise relationship between the Tate-Shafarevich group of an elliptic curve over Q and a quotient of the class group of a related number field, linking elliptic curve arithmetic with class field theory.
Contribution
It formulates and proves a relationship connecting the Tate-Shafarevich group of an elliptic curve with class groups of certain number fields, expanding understanding of their arithmetic connection.
Findings
Relationship established in most cases
Connection between Tate-Shafarevich group and class group quotient
Enhances understanding of elliptic curve arithmetic
Abstract
The paper formulates a precise relationship between the Tate-Shafarevich group of an elliptic curve over with a quotient of the classgroup of on which operates by its standard 2 dimensional representation over . We establish such a relationship in most cases.
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