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Integral Points in Families of Elliptic Curves

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

February 02, 2023 (03:20 PM PST - 04:20 PM PST)
Speaker(s): Stephanie Chan (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath))
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
  • elliptic curve

  • integral point

  • quadratic twist

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Abstract

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.

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