I‑AIMS Institute for Artificial Intelligence
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Genus two curves with many elliptic subcovers

Tanush Shaska

I-AIMS paper 2012-2 · Published in Comm. Algebra 44 (2016), 4450–4466 · 2016

We determine all genus 2 curves, defined over ℂ, which have simultaneously degree 2 and 3 elliptic subcovers. The locus of such curves has three irreducible 1-dimensional genus zero components in ℳ₂. For each component we find a rational parametrization and construct the equation of the corresponding genus 2 curve and its elliptic subcovers in terms of the parameterization. Such families of genus 2 curves are determined for the first time. Furthermore, we prove that there are only finitely many genus 2 curves (up to ℂ-isomorphism) defined over ℚ, which have degree 2 and 3 elliptic subcovers also defined over ℚ.

MSC classes: 14H10, 14H37, 14H45, 14K12, 14Q05, 14H70, 14D20, 14D22

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