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Results tagged with elliptic-curves
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user 21171
An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.
7
votes
Division by 3 on elliptic curve
A similar criterion, although more complicated, can be obtained using division polynomials. Let $P'=(x',y') \in E(K)$ be the given point. Then $P'=3P$, for some $P=(x,y)$ if and only if $$(x',y')=\lef …
- 221
12
votes
Torsion subgroups in families of twists of elliptic curves
The maximum number of quadratic twists with $n$-torsion (n odd) that an elliptic curve over a number field $K$ can have is 2, and here is an easy proof.
You can see this by asking how many twists wi …
- 221