Rank of elliptic curves and class groups of real quadratic fields

TL;DR

This paper explores the connection between the rank of elliptic curves and the non-triviality of class groups in infinitely many real quadratic fields, highlighting a deep link in number theory.

Contribution

It establishes a relation between elliptic curve ranks and class groups of real quadratic fields, a novel link in algebraic number theory.

Findings

Proves the relation between elliptic curve rank and class group non-triviality.

Shows this relation holds for infinitely many real quadratic fields.

Abstract

In this paper, we are going to prove the relation between rank of elliptic curves and the non-triviality of class groups of infinitely many real quadratic fields.