2018
Nov
15

# Colloquium: Ari Shnidman (Boston College) - Rational points on elliptic curves in twist families

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem

The rational solutions on an elliptic curve form a finitely generated abelian group, but the maximum number of generators needed is not known. Goldfeld conjectured that if one also fixes the j-invariant (i.e. the complex structure), then 50% of such curves should require 1 generator and 50% should have only the trivial solution. Smith has recently made substantial progress towards this conjecture in the special case of elliptic curves in Legendre form. I'll discuss recent work with Lemke Oliver, which bounds the average number of generators for general j-invariants.