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# Bo-Hae Im, A Hyperelliptic Curve Mapping to Specified Elliptic Curves

## February 22, 2022 @ 2:00 pm - 3:00 pm KST

B266,
IBS
Korea, Republic of

(This is a part of *Arithemetic Geometry Day in IBS-CCG*.)

We are interested in the existence and non-existence of rational curves on certain Kummer varieties which can be applied to the rank problem of quadratic twists of elliptic curves. In this talk, we prove that if the *j*-invariants of a 21-tuple of elliptic curves *E*_{1}, …, *E*_{21} over **C** are algebraically independent over **Q**, there is no hyperelliptic curve which admits a non-trivial morphism to each of the *E _{i}*, which shows the non-existence of rational curves of the Kummer variety of the products of more than 20 elliptic curves.

This is a joint work with Michael Larsen and Sailun Zhan.