$(p,d)$-elliptic curves of genus two

TL;DR

This paper investigates genus two stable curves that admit two finite morphisms onto elliptic curves, focusing on cases where the degrees are prime, to understand their structure and properties.

Contribution

It introduces a detailed study of $(p,d)$-elliptic curves of genus two, especially for prime $p$, expanding knowledge on their morphisms and classifications.

Findings

Characterization of $(p,d)$-elliptic curves of genus two

Conditions for the existence of morphisms onto elliptic curves

Structural properties of stable genus two curves with such morphisms

Abstract

We study stable curves of arithmetic genus 2 which admit two morphisms of finite degree $p$, resp. $d$, onto smooth elliptic curves, with particular attention to the case $p$ prime.