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Results tagged with elliptic-curves
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user 32332
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.
3
votes
Root number of a quadratic twist of an elliptic curve
The proof can (more or less) be found in section $4$ of Rubin's and Silverberg's article Twists of elliptic curves of rank at least four. They write $w_d(E)$ for the root number of the quadratic twist …
- 12.1k
4
votes
Accepted
Special type Diophantine equations with integer solutions
If one could prove the explicit $abc$-conjecture, i.e., with an explicit constant $C$, then one would have explicit bounds on the heights of the rational points in Falting's theorem. If this is not av …
- 12.1k
4
votes
Canonical form of cubic curves over general fields
Over the complex numbers, there are several normal forms.
A ternary cubic can be written as
$$
\lambda XYZ-(X+Y+Z)^3
$$
with a parameter $\lambda$.
This normal form is invariant under the symmetric gr …
- 12.1k