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Answer by Joe Silverman for Elliptic Curves and Torsion Points
Probably the set of $E/\mathbb{Q}$ with $E(\mathbb{Q})=\{O\}$ has density 1/2 (in an suitable way of ordering curves). A recent (and very deep) result of Manjul Bhargava and Arul Shankar proves that...
View ArticleAnswer by Steven Landsburg for Elliptic Curves and Torsion Points
The curve $y^2+y=x^3-x$ has order 5 mod 2 and order 7 mod 3. Therefore the torsion injects into both $Z/5Z$ and $Z/7Z$ and hence is trivial. This is the first example in Husemoller's book on Elliptic...
View ArticleElliptic Curves and Torsion Points
So we know many useful theorems that help characterize torsion points on elliptic curves over $\mathbb{Q}$ such as the Nagell–Lutz theorem which provides a useful way to find torsion points on...
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