Bianchi's elliptic quintic curves and several modular function fields of level ten

TL;DR

This paper explicitly describes torsion points on Bianchi's elliptic quintic curve using Ramanujan's functions and derives generators and equations for modular function fields of level 10, advancing understanding of their algebraic structure.

Contribution

It provides explicit descriptions of torsion points and modular function fields of level 10, linking classical elliptic curves with modular functions in a novel way.

Findings

Explicit torsion points on Bianchi's elliptic quintic curve identified

Generators and defining equations for modular function fields of level 10 obtained

Connections between Ramanujan's functions and modular curves established

Abstract

We provide an explicit description of two torsion points on the classical Bianchi elliptic quintic curve in terms of Ramanujan's functions. As a byproduct, we describe generators and defining equations of several modular function fields of level 10 using those functions.