A graphical method to calculate Selmer groups of several families of non-CM elliptic curves

TL;DR

This paper introduces a graphical method to compute Selmer groups for various families of non-CM elliptic curves, extending previous approaches by Feng, Feng-Xiong, and Faulkner-James.

Contribution

It develops a new graphical technique to determine Selmer groups of specific non-CM elliptic curves, expanding on prior methods.

Findings

Successfully computes Selmer groups for the given elliptic curve families.

Extends existing methods to broader classes of elliptic curves.

Provides a practical approach for Selmer group calculation.

Abstract

In this paper, we extend the ideas of Feng [F1], Feng-Xiong [FX] and Faulkner-James [FJ] to calculate the Selmer groups of elliptic curves $ y^{2} = x (x + \varepsilon p D) (x + \epsilon q D). $