A construction of generalized elliptic curves from twisted curves

TL;DR

This paper presents a method to construct generalized elliptic curves from twisted curves and establishes an explicit modular isomorphism between two compactified moduli stacks of elliptic curves with level structure.

Contribution

It introduces a novel procedure for deriving generalized elliptic curves from genus-one twisted curves and defines an explicit isomorphism between different compactifications of elliptic curve moduli stacks.

Findings

Constructed generalized elliptic curves from twisted curves.

Established an explicit modular isomorphism between compactified moduli stacks.

Enhanced understanding of the relationship between twisted curves and elliptic curves.

Abstract

We introduce a procedure for constructing a generalized elliptic curve from a genus-one twisted curve, and we use this procedure to define an explicit, modular isomorphism between two compactifications of moduli stacks of elliptic curves with level structure.