# Integral Points in Families of Elliptic Curves

## Connections Workshop: Diophantine Geometry February 02, 2023 - February 03, 2023

**Speaker(s):**Stephanie Chan (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath))

**Location:**SLMath: Eisenbud Auditorium, Online/Virtual

**Tags/Keywords**

elliptic curve

integral point

quadratic twist

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**

#### Integral Points In Families Of Elliptic Curves

The number of integral points on any given elliptic curve is finite. Taking a family of elliptic curves and imposing some ordering, we expect that very few curves have non-trivial integral points. In certain quadratic and cubic twist families, we prove that almost all curves contain no nontrivial integral points. The proof uses a correspondence by Mordell between integral points on elliptic curves and integral binary quartic forms.

#### Integral Points In Families Of Elliptic Curves

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